U.S. patent number 3,777,117 [Application Number 05/107,351] was granted by the patent office on 1973-12-04 for electric heat generating system.
Invention is credited to Donald F. Othmer.
United States Patent |
3,777,117 |
Othmer |
December 4, 1973 |
ELECTRIC HEAT GENERATING SYSTEM
Abstract
When an insulated conductor wire inside a steel tube carries
alternating current as one leg of a circuit, and the tube itself
carries the A.C. for the return leg, induction and magnetic effects
develop which cause the A.C. flow to concentrate on the inner
surface or skin of the tube, thus greatly increasing the resistance
and the heat produced. No current is carried in the outer wall of
tube; thus, there is no loss to ground or other surroundings. The
heat-tube may be attached to or constructed so as to become an
integral part of the wall of a pipe carrying a fluid, thus heating
the pipe and the fluid. It may be the transport pipe itself, or it
may heat an unenclosed body of fluid using heat supplied by direct
contact of the fluid with both the conductor wire and the tube. The
heat-tube may supply A.C. to other circuits either related or
independent of the heating effect which may be quite unimportant in
some of these cases.
Inventors: |
Othmer; Donald F. (Brooklyn,
NY) |
Family
ID: |
26804692 |
Appl.
No.: |
05/107,351 |
Filed: |
January 18, 1971 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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805718 |
Mar 10, 1969 |
3617699 |
Nov 2, 1971 |
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Current U.S.
Class: |
392/469; 137/341;
219/530; 392/491; 219/629; 138/33; 392/478; 392/485 |
Current CPC
Class: |
H01B
7/16 (20130101); F24H 9/0047 (20130101); F24H
1/121 (20130101); H05B 6/108 (20130101); H05B
7/109 (20130101); Y10T 137/6606 (20150401) |
Current International
Class: |
F24H
1/12 (20060101); H01B 7/16 (20060101); H05B
7/00 (20060101); H05B 7/109 (20060101); H05B
6/10 (20060101); F24H 9/00 (20060101); H05b
003/00 () |
Field of
Search: |
;219/301,300,535,10.49,10.51,374,375,376,306,316 ;137/341
;138/33 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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919,184 |
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Oct 1954 |
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DT |
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756,945 |
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Sep 1956 |
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GB |
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Primary Examiner: Bartis; Anthony
Parent Case Text
This is a Continuation in Part of my application Ser. No. 805,718,
filed Mar. 10, 1969, now U.S. Pat. No. 3,617,699 of Nov. 2, 1971,
entitled System for Electrically Heating a Fluid being Transported
in a Pipe.
Claims
I claim:
1. A heat generating system comprising:
a. at least one elongated hollow tubular shape made of a metal
having magnetic properties and electrical conductivity;
b. a source of AC having a first terminal and a second
terminal;
c. an electrical connection between said first AC terminal and one
end of said tubular shape;
d. an electrical conductor means extending through the inside
length of said hollow tubular shape and insulated electrically
therefrom;
e. an electrical connection between said second AC terminal and the
end of said electrical conductor means which is near the electrical
connection of said tubular shape and said first AC terminal;
f. an electrical connection between said tubular shape and said
electrical conductor means remote from its electrical connection
with said second AC terminal;
g. an AC circuit established:
i. from said second terminal of said AC source through the
substantial length of said electrical conductor means inside the
said tubular shape, thus producing heat in said electrical
conductor means;
ii. then back through the said tubular shape so as to produce a
skin effect current concentrated in the inner skin of said tubular
shape, said tubular shape having at least twice the thickness of
said skin, said skin effect current thus producing heat in said
tubular shape; and
iii. finally back to said first AC terminal, to complete said AC
circuit;
h. means whereby a utilitarian fluid is caused to flow at a
substantial velocity in direct contact with a surface of said
tubular shape and in direct contact with said electrical conductor
means; whereby
i. substantially all of said heat produced in said electrical
conductor means is transferred to said fluid; and
j. at least some part of said heat produced in said tubular shape
is transferred directly to said fluid from said surface of said
tubular shape against which said fluid is directed.
2. In the system of claim 1, wherein said fluid is electrically
insulative and said electrical conductor comprises a bare metallic
member.
3. In the system of claim 1, wherein said inner surface of said
tubular shape is expanded, whereby the rate of said heat transfer
to said utilitarian fluid is increased.
4. In the system of claim 1, wherein the effective surface of said
tubular shape for skin effect conduction of AC lies on a surface of
an inscribing cylinder, but is less than the total area of said
inscribing cylinder.
5. In the system of claim 1, wherein the effective surface of the
metal of said electrical conductor means for skin effect conduction
of AC lies on a surface of a curcumscribing cylinder but is less
than the total area of said circumscribing cylinder.
6. In the system of claim 1, wherein said electrical conductor
means lies on the bottom of said tubular shape.
7. In the system of claim 1, wherein the metal of said electrical
conductor means has magnetic properties whereby a substantial skin
effect current is produced, flowing in the outer skin of the metal
of said electrical conductor means.
8. In the system of claim 1, wherein at least some part of said
elongated tubular shape is formed of an elongated strip wound as a
helical coil with space between each turn of said coil, whereby
said utilitarian fluid may be passed there through so as to
directly contact said electrical conductor.
9. In the system of claim 1, wherein an external electrical circuit
having a resistance representing an electrical load is connected in
parallel from a point of said tubular shape and a nearby point of
said electrical conductor means.
10. In the system of claim 1, wherein an external electrical
circuit with a resistance representing an electrical load is
connected in series with said electrical conductor means by a pair
of conductors penetrating said tubular shape and electrically
insulated therefrom.
11. In the system of claim 1, wherein an external electrical
circuit with a resistance representing an electrical load is
connected in series as a part of said AC circuit and forms the said
electrical connection between said tubular shape and said
electrical conductor means, remote from its electrical connection
with said source of the AC.
12. In the system of claim 1, wherein said electrical conductor
means comprises a metal tube.
13. In the system of claim 1, wherein said electrical conductor
means comprises a metal strip of rectangular cross section.
14. In the system of claim 1, wherein said AC has a frequency of
from 10 to 1000 cycles per second.
15. In the system of claim 1, wherein said electrical conductor
means is on the longitudinal axis of said tubular shape.
16. In the system of claim 1, wherein the length of at least one
of: - said tubular shape and said conductor, is expanded whereby
the effective length of said AC circuit established is
substantially greater than twice the axial length of said elongated
hollow tubular shape.
17. In the system of claim 1, wherein said tubular shape is
unenclosed.
18. In the system of claim 17, wherein the volume of said fluid is
very large compared to the volume of said tubular shape.
19. In the system of claim 17, wherein the fluid flow is due, at
least in part, to convection.
20. In the system of claim 1, wherein said fluid flow is
substantially in one direction.
21. In the system of claim 20, wherein said fluid flow is
substantially at right angles to the longitudinal axis of said
tubular shape.
22. In the system of claim 1, wherein said surface of said tubular
shape against which said utilitarian fluid is caused to flow is at
least in part an external surface of said tubular shape.
23. In the system of claim 22, wherein the said utilitarian fluid
is electrically non-conductive and is in direct contact with at
least some part of the inner surface of said tubular shape and at
least some part of the surface of the metal of said electrical
conductor means.
24. In the system of claim 23, wherein at least some part of the
surface of the metal of said electrical conductor means contacted
by said moving fluid is expanded, whereby the rate of said heat
transfer directly to said fluid is increased.
25. In the system of claim 22, wherein said outer surface of said
tubular shape is expanded, whereby the rate of said heat transfer
to said utilitarian fluid is increased.
26. In the system of claim 22, wherein the effective surface of the
metal of said electrical conductor means for skin effect conduction
of AC lies on a surface of a circumscribing cylinder, but is less
than the total area of said circumscribing cylinder.
27. In the system of claim 22, wherein said tubular shape has at
least some part of its wall removed and open, whereby said
utilitarian fluid passes through said wall at an angle of from
0.degree. to 90.degree. to the longitudinal axis of said tubular
shape and flows at substantially the same angle across the surface
of said electrical conductor means extending inside said tubular
shape.
28. In the system of claim 27, wherein said open part of said wall
of said tubular shape has the shape of a helix continuing some
distance along and around said tubular shape.
29. In the system of claim 27, wherein said open part of said wall
of said tubular shape is formed by a multiplicity of holes of a
diameter less than the internal radius of said tubular shape.
30. In the system of claim 1, wherein said tubular shape has at
least some part of its wall removed and open, whereby said
utilitarian fluid passes through said wall at an angle of from
0.degree. to 90.degree. to the longitudinal axis of said tubular
shape and flows at substantially the same angle across the surface
of said electrical conductor means extending inside said tubular
shape.
31. In the system of claim 30, wherein said open part of said wall
of said tubular shape has the shape of a helix continuing some
distance along and around said tubular shape.
32. In the system of claim 30, wherein said open part of said wall
of said tubular shape is formed by a multiplicity of holes, each of
a diameter less than the internal radius of said tubular shape.
33. In the system of claim 1, wherein said electrical conductor
means is displaced at some distance from the axis of said tubular
shape.
34. In the system of claim 33, wherein means is provided for
varying the amount of said displacement of said electrical
conductor means from the axis of said tubular shape during flow of
said AC in said circuit.
35. In the system of claim 1, wherein said electrical conductor
means is offset from the longitudinal axis of said tubular
shape.
36. In the system of claim 35, wherein said electrical conductor
means is closely adjacent to the inner periphery of said tubular
shape for substantially its entire length.
37. The system for heating a transport pipe carrying a fluid to be
transported in forced flow, comprising:
a. at least one elongated transport pipe made of a metal which has
magnetic properties and conducts electricity;
b. a source of AC having a first terminal and a second
terminal;
c. an electrical connection between the first AC terminal and one
end of said transport pipe;
d. an electrical conductor means extending through the inside
length of said transport pipe and insulated electrically
therefrom;
e. an electrical connection between said second AC terminal and the
end of said electrical conductor means which is near the electrical
connection of said transport pipe and said first AC terminal;
f. an electrical connection between said transport pipe and said
electrical conductor means remote from its electrical connection
with said second AC terminal;
g. an AC circuit established:
i. from said second terminal of said AC source through the
substantial length of said electrical conductor means inside the
transport pipe, thus producing heat in said electrical conductor
means;
ii. then back through said transport pipe so as to produce a skin
effect current on the inner skin of said transport pipe, said
transport pipe wall having at least twice the thickness of said
skin, said skin effect current thus producing heat in said
transport pipe; and
iii. finally back to said first AC terminal to complete said AC
circuit.
h. means whereby the transported fluid is forced through said
transport pipe at a substantial velocity in contact with the inner
surface thereof, and also in contact with said electrical conductor
means; whereby
i. substantially all of said heat produced in said electrical
conductor means is transferred to said fluid being transported in
forced flow through said transport pipe; and
j. at least some part of said heat produced in said wall of said
transport pipe is transferred directly to said transported fluid
from said inner surface of said transport pipe.
38. In the system of claim 37, wherein said fluid is a gas.
39. In the system of claim 37, wherein said fluid is a liquid.
40. In the system of claim 37, wherein said electrical conductor
means lies in contact with the bottom of said transport pipe.
41. In the system of claim 37, wherein the metal of said electrical
conductor means has magnetic properties, whereby a substantial skin
effect current is produced, flowing in the outer skin of the metal
of said electrical conductor means.
42. In the system of claim 37, wherein said inner surface of said
transport pipe is expanded so as to increase the rate of said heat
transfer to said fluid being transported.
43. In the system of claim 37, wherein an external electrical
circuit having a resistance representing an electrical load is
connected in parallel from a point of said transport pipe and an
adjacent point of said electrical conductor means, whereby AC flows
in said external electrical circuit.
44. In the system of claim 37, wherein an external electrical
circuit having a resistance representing an electrical load is
connected in series with said electrical conductor means by a pair
of conductors penetrating said transport pipe and insulated
therefrom.
45. In the system of claim 37, wherein an external electrical
circuit having a resistance representing an electrical load is
connected in series as a part of said AC circuit and forms the said
electrical connection between said transport pipe and said
electrical conductor means, remote from its electrical connection
with said source of the AC.
46. In the system of claim 37, wherein said transported fluid
forced through said transport pipe is substantially electrically
non-conductive, whereby it serves to additionally insulate
electrically said transport pipe from said electrical conductor
means.
47. In the system of claim 46, wherein the surface of the metal of
said electrical conductor means is in direct contact with said
transported fluid, whereby heat produced in said electrical
conductor means passes directly to said transported fluid without
transfer through any other material.
48. In the system of claim 46, wherein at least some part of the
surface of the metal of said electrical conductor means contacted
by said transported fluid is expanded whereby the rate of said heat
transfer directly to said fluid is increased.
49. In the system of claim 37, wherein said means for forcing said
transported fluid at a substantial velocity produces a pressure at
the inlet of said fluid, thereby forcing it from one end to the
other of said transport pipe.
50. In the system of claim 49, wherein the total of said heat
produced in said electrical conductor means and transferred to said
fluid, and said heat produced in said transport pipe, is
substantially equivalent to that lost from the surface of said
transport pipe to its surroundings.
51. In the system of claim 37, wherein said electrical conductor
means is displaced at some distance from the axis of said transport
pipe.
52. In the system of claim 51 wherein means is provided for varying
the amount of said displacement of said electrical conductor means
from the axis of said transport pipe during flow of said AC in said
circuit.
Description
This invention relates to the use of the skin effect of alternating
current (A.C.) flowing with an adjacent or concentric steel
conductor supplying the return or "back" leg of the circuit, thus
causing induction and magnetic effects which greatly increase the
effective resistance of the steel conductor, and substantially make
its outer surface an insulator. The proximity relation of the two
conductors may be changed to increase further these two
effects.
Alternating current (A.C.) flows only along the skin of a steel
conductor under these conditions. In a tube having a minimum wall
thickness of about 1/16 inch -- less for many steels -- and with
A.C. carried out to the far end by an internal insulated wire, and
back by the tube, due to what is called "skin effect", all A.C.
flows back on the inside surface or skin of the tube and its
outside is completely insulated electrically. This considerable
reduction of what is normally regarded as the effective
cross-section of an electrical conductor greatly increases its
effective resistance, so that steel tubes of substantial
cross-section of metal, compared to the usual copper wire
conductor, offer greatly increased resistance, and hence can be
used for resistance heating with A.C., for which they would be
quite unsuitable with direct current (D.C.). It has been found that
these tubes can be designed to give off considerable heat; and they
may be used as heaters in many industrial and domestic operations.
Since A.C. flows only on the inside surface of such a heat-tube,
the outer wall of the steel pipe is perfectly insulated from the
A.C. It usually is grounded and may be touched without shock. The
tube may be used directly as a pipeline, even of considerable size,
for liquids to be kept heated in transit.
Such heat-tubes may be made to advantage with extended surfaces of
the same metal. Transverse or longitudinal fins or other
protuberances on the outside increase the external effective heat
transfer surface which is in contact with the gas or liquid to be
heated. The extended surface effectively dissipates a much larger
amount of heat generated by the skin effect than has hitherto been
used; and still other advancements have been found in the theory
which improves the practical use of heat-tubes.
HEATING OF PIPELINES BY SKIN-EFFECT AS IN PRIOR ART
Long distance pipelines which require heat to obtain the lower
viscosities of heavy oils at higher temperatures have used such
heat-tubes, but with very low heat fluxes to date, from 10 to 15
watts per foot. Skin-effect heating of pipelines, even with the low
performance of the prior art, has large advantages over other
systems which have been used, such as:
a. heating the pipe wall electrically and directly by normal
impedance or resistance to current flow, usually with low voltage
D.C.;
b. heating of the pipe wall by a conventional electric resistor by
attachment to its surface and suitably insulated therefrom;
c. heating of the pipe wall by a hot fluid, usually steam, in a
small tube called a "tracer tube" or "trace" running along and in
contact with an element of the pipeline.
For long pipelines, the considerable distances from a central
source of thermal energy (such as a boiler) makes the connecting
steam system for a tracer installation extensive and expensive.
Instead, tracer tubes can be heated economically throughout their
length by the skin effect, using A.C., which has frequencies as low
as the standard 50 and 60 cycles of practically all A.C.
generation.
The several economies of the installation and use of the skin
effect phenomenon has allowed its economical use in a tracer tube
so heated even though the BTU's of heat from electricity are
usually more expensive than from steam or heated liquids circulated
in a trace tube. Compared with steam: -- electricity may be
transported long distances, controlled much more readily, and
utilized much more efficiently. Thus, this method of heating of
pipelines is superseding other methods, which are relatively
expensive and clumsy in installation and maintenance.
The industrial practice of using the skin effect of 50 to 60 cycle
A.C. for resistance heating has so far been limited to the heating
of oil-pipes to reduce the viscosity of the oil being transported.
The teachings of U.S. Pat. No. 3,293,407 have been utilized; and a
relatively small steel heat-tube, 3/4 inch standard pipe size, has
been specified.
This heat-tube has always been substantially axially parallel to
the oil-pipe and on its axis, with an internal insulated copper
wire. This internal electric wire forms one leg - out - of the A.C.
circuit; and its other terminal was at the far end of the heat-tube
on the inside thereof. Electric current flows back on the return
leg of the circuit on the inside wall of the heat-tube because of
the skin-effect, with no current flowing on the outside wall, if
the steel tube is more than about 0.04 inches thick. The other
junction to the source of A.C. is a point at the near end of the
inner surface of the heat-tube adjacent the entrance of the
insulated copper wire into the heat-tube to carry the A.C. to its
far end. The heat-tube has thus always pierced the oil-pipe and
been in solid contact therewith.
The heat-tube has always been attached in substantially axially
parallel relation with the oil-pipe and along one of the elements
of this much larger pipe which carries the fluid. Temperatures of
the heat-tube more than a few degrees Fahrenheit higher than that
of the oil-pipe could not be tolerated because expansion strains
set up cracked off this type of attachment. The standard thermal
insulation around the main pipeline also covered the small
heat-tube to minimize heat losses; but this insulation had to be
supplied in specially cut pieces, around the one to a half dozen
heat-tubes built out as appendages on the surfaces of the
oil-pipe.
In the construction of the prior art, the outer walls of the
oil-pipe and of the heat-tube were two circles in contact and they
were tangent, i.e., formed an angle of 0.degree. at the point of
contact. Thus, heat transfer has not been good from heat-tube to
oil-pipe; heat fluxes have been low, particularly because of the
low temperature difference allowable between heat-tube and
oil-pipe. Also, thermal insulation has been difficult and expensive
to install.
In an alternate construction, less desirable because of the
inaccessibility, poorer heat distribution and greater pumping costs
of the oil, the heat-tube, again in substantially axially parallel
relation, has been installed inside of the oil-pipe supported along
the axis by sets of three braces at suitable distances. Besides
these solid contacts, there have been also the contact or contacts
of the heat-tube where it pierced the oil pipe.
However, only a small heat flux has been generated by skin-effect
heating in either of these systems used to date, not more than 10
to 15 watts per lineal foot of the heat-tubes. This has required a
large number of heat-tubes applied to the outside surface of even a
moderate size pipeline, even in very moderate winter temperatures
of 32.degree.F., three heat-tubes for a 12-inch line, and six for a
30-inch line.
THE PRESENT INVENTION
Methods have now been found to increase the heat flux supplied to
oil-pipes and other adjacent materials through the use of
heat-tubes by an order to magnitude, and to make possible the use
of heat fluxes as high as 100 to 500 watts, or even 200 to 500
watts per lineal foot of heat-tube. This reduces the cost of
application of the large number of heat-tubes, since only one
instead of six or more may be necessary; also it reduces pumping
costs of the oil. Furthermore, considerable savings in thermal
insulation costs are made possible. While the improved systems of
this invention singly or together do make possible these much
greater heat fluxes, some of them also may be used to great
advantage in those installations where low heat fluxes will
suffice.
Improved designs of the heating tube have been devised by making
the heat-tube conform closely to the external surface or to form an
integral part of the oil-pipe or its wall. These new designs allow
much greater heat fluxes than formerly thought possible, with
important advantages and economies. These new types of heat-tubes
also decrease greatly the costs of pipe insulation.
It has been found that, by correct design, the A.C. may be made to
travel several times the length of the pipe through spiral wound
heat-tubes, rather than going through the straight line path of
what would normally be quite the least resistance. These spiral
wound heat-tubes thus made possible have now been found to be
cheaper in both installation and operating costs, and to allow a
very much greater heat flux per unit length of heat-tube than the
longitudinal heat-tubes used to date, while substantially reducing
pumping costs in the oil-pipe line due to more uniform heating of
the pipe and the oil. While they may be used at any low heat flux,
they are particularly advantageous when using the high heat flux of
this invention.
It has also been found that an internal steel electric wire or tube
for the "out" conductor leg can be used to give an additional
skin-effect, the increased resistance of which generates still more
heat. The use of steel instead of copper as the material for this
conductor reduces greatly the cost of the installation, even if the
skin-effect is not utilized on this internal conductor, and only
the normal conductivity or resistance is effective and
considered.
These new developments, and others, all a part of this invention,
by creating heat fluxes, allow larger pipelines for transporting
oil, particularly viscous oils such as crudes or residues, to
operate in colder ambient conditions and to be heated more
economically by the use of:
a. new designs of the heat-tube as an integral part of the wall of
the pipe. The angle of the wall of the heat-tube section with that
of the oil-pipe has been found best when it is at least 90.degree.,
and preferably more. By entirely burying the heat-tube in the wall
of the oil-pipe, and sometimes partly in the internal fluid, this
angle reaches the optimum, i.e., 180.degree.;
b. higher temperatures of the heated oil-pipes;
c. larger heat-tubes than heretofore thought possible, i.e., as
large as 31/2 inches standard iron pipe instead of 3/4 inch
standard pipe;
d. higher operating temperatures of the heat-tubes, and
particularly much higher differences of temperature between the
heat-tube and the oil-pipe;
e. spirally-wound heat-tubes, even though the length of the A.C.
path through the wall of the steel pipe is thus increased several
times;
f. steel wire or tubes for the conductor of the A.C., which also
reduces cost of installation;
g. improved forms of heat-proof insulation of the internal
conductor;
h. use of the heat-tube itself as the transport pipeline.
Because of the high heat fluxes now possible by the methods of this
invention, the heat-tube may be used in many applications by itself
and independent of its use as an appendate to an oil-pipe of the
previous art, as in the invention of U.S. Pat. No. 3,293,407.
Such uses include heating of fluids in open space and in shells
(heat exchangers) either with simple cylindrical heat-tubes,
heat-tubes of other shapes, and particularly those with extended
surfaces. Whereas the prior art allowed the heating of solids by
imbedding heat-tubes, this takes no advantage of the mobility of
fluids, their natural movement due to convection currents. By
modifications of the structure of the heat-tube system, the direct
transfer of the heat dissipated from the electrical conductor to
the material being heated has been accomplished without first
passing through the wall of the heat-tube.
Particularly, even very large steel pipes transporting oil may be
heat-tubes themselves. Only an internal conductor is necessary,
with greatly reduced costs of installation and maintenance. It has
been found that, by moving the location of the internal conductor
away from the axis of the tube, the effective resistance of the
"skin" of the oil-pipe may be increased greatly. This may be
important in large oil-pipes.
FUNDAMENTALS OF THE INVENTION
Skin Effect Caused by Inducted Magnetic Flux
Skin effect is a phenomenon of A.C., which restricts the flow of
A.C. to the surfaces of some metal conductors exposed to
electromagnetic fields. Iron and steel conductors-resistors are
affected at commercial A.C. frequencies of 50 to 60 cycles per
second, when another adjacent conductor carries A.C. so as to
generate surface magnetic and induction effects with corresponding
diffusional functions of the A.C. in these ferromagnetic materials.
In some cases, all three phases of standard A.C. current generation
may be used to advantage, as may frequencies from 10 to 1000 or
more.
The electro magnetic flux surrounding a wire carrying an A.C. has
been found to extend without practical dimunition of its influence
on the skin effect for some distance, if not shielded by another
metal. Thus, it has been found possible to use a larger individual
heat-tube than before -- up to 3 inches or 4 inches iron pipe size
-- and even to use a much larger tube, the transport pipe itself,
as its own heat-tube.
The use of the larger individual heat-tubes allows a much greater
effective conductor-resistor, i.e., the inner skin of the larger
heat-tube. Particularly it allows a heavier internal insulated
electric wire, which larger size wire is necessary for carrying the
high voltage and intensity A.C. required for heating long distance
pipelines. Also, the larger heat-tube allows the use of a poorer
conductor for the A.C., hence of larger diameter for the same
intensity of A.C. than the usual copper wire. Steel wire or
stranded steel cable may thus be used instead; and, if desired,
only the skin effect of steel conductors may be utilized if wires
larger than about 1/8 inch diameter are used. The increased
resistance of the steel wire, whether or not the skin effect is
utilized, gives more line loss and heat -- all of which adds to
that supplied by the heat-tube itself. The use of steel gives the
advantage of its high tensile strength in pulling the conductor
through a pipeline of considerable length.
Where the terms "skin" and "skin effect" are used, these are not
absolute terms. There is a great tendency for A.C. flow to be near
the inner surface of the wall of a tube having a nearby conductor
of A.C., herein called a "heat-tube"; and the current density falls
off in the tube wall according to an exponential function of the
distance from the inner surface.
Under such conditions, it has been found that the effective
thickness or depth of the skin through which A.C. is flowing, is
directly proportional to the square root of the resistivity of the
metal under the particular conditions and inversely proportional to
the square root of the magnetic permeability, also inversely
proportional to the square root of the frequency. However, a
commerical A.C. with a frequency of 50 or 60 cycles per second
gives very usable skin depths, as do those from 10 to 1000 or
more.
Variations in this skin effect are influenced by changes in the
resistivity and the magnetic permeability which are caused by the
temperature of the conductor. The gradation of current density
against wall thickness from the inner surface of a small heat-tube
is so large that, with the voltage drop experienced with steel
tubes in heat-tube service (i.e., usually between 0.05 and 1.0
volts per lineal foot) and at temperatures up to about 400.degree.
to 500.degree.F, the effective zero of current flow or availability
is reached within a depth somewhat less than approximately 1/16
inch from the inside tube surface when using 50- 60 cycle A.C. For
most mild steels worked with, this depth has been found to be
between 0.025 inch and 0.075 inch. For any particular steel, the
effective conductor area is thus the inner perimeter of the
heat-tube times a value of the depth between 0.025 inch and 0.075
inch.
In the outer part of the wall beyond this "skin" on the inner
surface of the tube, there is practically no current flow; and that
part of the tube near the outer wall may be regarded as practically
insulated from this A.C. flow a small fraction of an inch away. To
be sure that there is no current leakage or danger from the high
voltage A.C. flowing on the inside skin, the thickness of the tube
from the inner to the outer wall should be about two to three times
the skin thickness, or 1/8 inch under the usual intensities of A.C.
flow used. There will then be no measurable voltage or power loss,
even when the outside of the heat-tube is grounded or submerged in
salt water. Unburied pipelines are grounded at reasonable
distances, and pipelines in corrosive conditions may have the
conventional sacrificial cathodic protection system with no
interference with the skin effect heating.
It has been found that extended surfaces, e.g., fins, outside of
the normal outer diameter and surface of the steel tube, help
further to dissipate the high flux of the heat flow, due to the
greater contact area of the metal in the extended surface with the
adjacent materials.
Proximity Effect
The proximity effect is a very important phenomenon of the
electromagnetic field produced by an A.C. passing in one conductor
in penetrating an adjacent conductor of a ferromagnetic material in
this case, the inner skin of the heat-tube of whatever diameter it
may be. As a relatively simple geometric example may be taken a
steel heat-tube having a diameter which is large compared to that
of the electrical conductor wire acting as one leg of the A.C.
circuit. The inner skin of the heat-tube acts as the other leg of
the A.C. circuit.
If the conductor wire is on the axis of the heat-tube, from the
characteristics of such a magnetic field it follows that the
concentration of the field, its degree of penetration of the wall
of the heat-tube, and of the current flow in the heat-tube are
uniform. There is a fixed resistance in the heat-tube leg of the
circuit to the flow of the A.C., which has a definite number of
cycles; and the resistance may be calculated from the permeability
and resistiveity of the metal. The effective cross-section of this
skin-effect-conductor is calculated -- and confirmed in practice --
by the assumption that the effective skin thickness is
approximately 0.04 inch for usual mild steel, varying slightly with
the properties of the particular steel used. This depth, multiplied
by the inner perimeter of the tube, gives the effective area of the
conductor, i.e., the "skin" which carries the A.C. The resistance
may now be calculated using the tabular values of the properties
for mild steel. This resistance may be called R.sub.o, i.e., the
resistance of the heat-tube leg of the circuit with the wire
conductor along the axis or at the center, point o. This position,
with the uniform field and uniform penetration resulting, shows the
lowest resistance of the skin of the heat-tube.
If now the center of the conductor be displaced some distance, e,
from the center of the tube to an eccentric point, e, its proximity
to one part of the skin of the inner perimeter of the tube and its
distance from the opposite parts gives an entirely different degree
of penetration of the magnetic field, and this non-uniform
penetration gives a different resistance, and current flow for each
different point of the "skin" on the inner perimeter of the tube.
This non-uniformity and its effects depend on the distance of the
eccentricity of the conductor. An integration of these effects for
the different points of the perimeter will result in a value for
the effective equivalent, R.sub.e, the resistance of the heat-tube
leg of the circuit, when the wire conductor is parallel to the axis
but at the distance, e, from the center.
This effective resistance of the skin of the heat-tube leg has been
found to increase greatly as the eccentricity, e, increases; and it
may be expressed as a ratio to the value R.sub.o. Here, the radius,
r, is taken an unity, and e is the distance from the axis of the
heat-tube to the axis of the wire, which is assumed to be small in
diameter compared to the diameter of the heat-tube.
R.sub.e = R.sub.o [(r/e + e/r)/(r/e - e/r)]
Or, if R.sub.e is the ratio of the value of R.sub.o taken as
unity:
e/r R.sub.e 0 1.0 0.1 1.02 0.2 1.08 0.3 1.2 0.4 1.38 0.5 1.67 0.5
2.12 0.7 2.91 0.8 4.56 0.9 9.57 0.95 19.6 0.96 25.0 1.00
Infinity
Thus, it is seen that the displacement of the wire to a point near
the inner surface of the pipe increases very greatly the effective
resistance of the return leg of the A.C. circuit. This eccentricity
is limited by the size of the wire and thus the outer radius of the
insulation enclosing the wire when it is touching the inner surface
of the pipe. The center of the wire cannot have greater
eccentricity than the radius of the pipe minus the radius of the
outside of the insulated wire. The resistance of the conductor
wire, if of copper, is substantially unaffected; and the total
resistance which produces the heat in the heat-tube is the sum of
that of the two legs. Changing the size of the copper conductor
changes its resistance, but not that of the skin effect heat-tube
surface. Proper design locates the wire to give the desired
resistance; or eccentricity may often be varied in use to control
the resistance and heat input.
Materials for Heat Tubes
Other magnetic metals than carbon steel, usually other alloys of
iron, also exhibit this skin effect and may be used in the systems
of this invention. Usual conductors such as copper, brass, and
aluminum also exhibit a slight skin effect but require frequencies
of many more cycles per second to reduce the effective permeability
or skin depth. Such high frequency A.C. is considerably more
expensive to generate than the standard 50 to 60 cycles.
A metal which has properties which give effectively only a thin
skin for A.C. conductance gives the least effective conducting
cross-sectional area, and hence the greatest resistance. Metals, of
desired characteristics, may be selected from the above indicated
relation of skin thickness as dependent on resistivity and magnetic
permeability under the given conditions of temperature, A.C. flow,
and the geometry of the system.
Such ferromagnetic metals, besides usual mild steel, which do have
a relatively pronounced skin effect, i.e., a thin skin of
conductance for A.C. under conditions of the present invention are:
-- very pure iron; iron-nickel alloys, as Hipernik; those with a
small amount of manganese, called Permalloys; and those with
molybdenum, such as Superalloy. These have from four to six times
the resistivity, and a thinner skin for conductances of A.C. in
comparison with ordinary mild steel. Compared with ordinary steel,
all of these are more expensive -- some are many times as costly.
Thus, they are not to be considered except for very special
applications.
While the term "steel" is used herein to describe the material of
construction of the heat-tube, it may be understood that this term
for mild or ordinary carbon steel is used only as an example; and
other metals, both ferrous and non-ferrous, may also be used.
Usually they have a less desirable skin-effect, or are more
expensive. In some particular instances, other physical or chemical
properties of other metallic conductors make them worthy of
consideration; but carbon steel is preferred for its cheapness,
workability, and availability in many forms. Thus, the word "steel"
is used as an example without being a limitation of the material of
construction of the heat-tubes of this invention.
Most pipelines for commercial liquids are of steel or other metals,
and the principal use of heat-tubes with the high heat flux and as
described by this invention is in heating such pipes, which may
thus be of substantially the same steel as that of the heat-tube.
If the pipe is of other material, with a substantially lower
resistivity, care should be taken that the steel heat-tubes have a
wall thickness at least twice the depth of penetration of the skin
effect, otherwise a current flow of some magnitude may result in
the pipeline. In general, it has been found desirable to use a
pipeline material with a resistivity not substantially lower than
that of the heat-tube; if both are of ordinary mild steel, there is
no question.
Pipelines are now also being made of plastics and of composites;
and especially glass-reinforced polyesters or other resins are
being used for some systems of larger size pipes. The heat-tube may
be used with these pipes, and it may be exactly controlled against
overheating which would burn the resin. The heat-tube would usually
be made of steel; and it is preferred to be spirally wound around
the plastic pipeline in one of the systems, suitable for such
materials, as hereinafter described.
Fluids
Many fluids have low viscosities at ambient tempertures. Besides
petroleum oils (crudes, distillates, or residues), commercial
fluids transported by pipe, include molasses, other food syrups or
melts -- such as butter, other oils and fats, chocolate, etc. --
strong sulfuric acid, tar, bitumin, and many others.
Some materials are frozen solid at some ambient temperatures; in
particular, there may be noted water and aqueous solutions, sulfur,
also benzene, acetic acid, etc. These must be kept heated to
prevent congealing or freezing if the ambient temperature is below
the respective solidification temperature and sufficient heat above
the freezing point cannot be added before the fluid enters the cold
length of pipe. With acetic acid, the pipe may be of aluminum,
stainless, steel, or copper -- because of corrosion of carbon
steel. The heat-tube would be of steel and particular care would be
taken that its thickness be at least twice that of the skin or
penetration depth of the A.C. Most desirable would be a stainless
steel. In other cases, it may be that ice and snow, with or without
liquid being present, fall within the classification of fluids to
be heated or melted, because of their being adjacent to the
heat-tube.
Also, in handling some vapors or gases, it is desired to keep them
in the vapor state by heating to a temperature above the ambient
and above their dew point, so that their condensation is prevented.
For example, it has been found that hydrochloric acid in gaseous
form with water vapor and air, if present, may be piped in a steel
pipe if the pipe is always at a temperature above the condensing
point of water, i.e., 212.degree.F, at atmospheric pressure.
Gaseous HCl does not attack steel, only is it corrosive if it
dissolved in the water which condenses on the inside of the pipe at
temperatures below 212.degree.F. In handling other vapors, it may
be desired also to superheat them above their boiling point at the
particular pressure of the pipeline.
All of these, and many other fluids, may be heated to a temperature
above the ambient, by the methods of this invention, particularly
through the high heat flux made possible. Temperatures as high or
higher than 400.degree. to 500.degree. may be reached in an
"oil-pipe".
In those cases where the heat-tube is also the oil-pipe, and the
fluid is an oil, which may be an excellent di-electric, no linear
insulation is required for the internal conductor if there are
insulated supports from the tube.
Heat-Tubes as Electrical Heaters
Many uses of heaters, such as, for example, direct heaters open to
the bulk of gas or liquids, allow the heat-tube to be used alone,
without transfer of heat to another metallic section more or less
permanently contacted, but with desirably an extended outer surface
better to dissipate the large heat fluxes now possible with the
improved heat-tubes of this invention.
The tube, through which the A.C. encounters greatly increased
electrical resistance due to the skin-effect, generates heat
thereby the develop and maintain a temperature higher than the
ambient, up to 400.degree. to 500.degree.F, or even more when
desired, with the higher heat fluxes of the improved systems of
this invention.
The heat-tube is particularly useful in heating fluids in which it
may be directly immersed, particularly when advantage is taken of
the convection currents of such fluids, and especially when
extended surfaces, as fins, increase the rate of heat transfer. In
many cases, as with gases and most non-aqueous liquids, where the
fluid is a non-conductor of electricity, both the inside and the
outside of the heat-tube and the surface of the electrical
conductor may be partly or fully exposed to contact the liquid,
thereby increasing greatly the rate of heat transfer and preventing
the necessity of the heat given off due to the resistance of the
conductor having to pass through the walls of the heat-tube to
reach the fluid itself. This eliminates much thermal resistance
inside the heat-tube and lowers the operating temperature of the
electrical conductor as it transfers the heat more efficiently.
This is particularly important in those cases where considerable
heat may be developed in the electrical conductor; and it may be
desirable to use an expanded surface to transfer it most
efficiently to the fluid being heated.
Elements of the Heat-tube
The heat-tube may be of a shape other than cylindrical and have
varied configurations in respect to the oil-pipe or other structure
to be heated; or it may be an integral part thereof. However, it is
referred to here simply as the "heat-tube" regardless of its
cross-sectional shape or convolutions, whether it is made of
several sections formed together longitudinally, or even laterally,
or is a unitary tube, a strip, or other steel shape.
Also, the electric conductor for the one side of the A.C. circuit,
if carried inside of the heat-tube in whatever configuration that
may take, may be a copper wire in most cases -- or of other
commercial metals or alloys. It may be of single or multiple
strands of any desired arrangement or cross-section. It is referred
to usually simply as the "electric wire."
The electric wire may be made of other than usual metals. Metallic
sodium may be used as the conductor. A lining tube of polyethylene,
or more heat-resistant resin for the insulation, is drawn through
the heat-tube and this may be filled with molten metallic sodium
which solidifies and acts as the electric wire.
Whatever line loss of A.C. there may develop in the electric wire
gives all of its heat to the heat-tube which surrounds it, and
hence is utilized in heating the adjacent materials, e.g., if
attached to an oil-pipe, to the oil therein. If the electric wire
is of copper, steel, or other metal of greater resistivity, the
additional heat which it gives up due to the larger line loss will
all be utilized in the fundamental heating operation. Thus, a
relatively inexpensive steel conductor or wire may be used in place
of the more expensive but standard copper. However, the heat so
generated within the wire will have to pass through the electrical
insulation, thence through any air space between the insulation and
the heat-tube before it adds to the heat from the heat-tube to be
passed to the surrounding materials. The electric wire will usually
have a somewhat higher temperature, i.e., 1.degree.-5.degree.F,
than that of the heat-tube; and this must be considered in
specifying insulation materials. As previously noted, if the fluid
does not conduct electricity, it may be in contact with the
surfaces of both the electrical conductor and the heat-tube, thus
reducing the temperature rise in the electrical conductor.
If the internal conductor for the A.C. is of steel or one of those
materials which develop the skin-effect -- possibly even more than
does steel -- the resistance, and hence heat output, will be even
greater. A large steel wire or even steel tube may be used inside
the heat-tube; and the heat generated by its electrical resistance
accentuated by its own skin effect passes through the electrical
insulation and adds to that generated by the surrounding heat-tube.
The skin effect of the inner steel wire or tube will be now on the
outer surface, which is that part closest to the A.C. flow in the
opposite conductor.
Insulation for the electric wire may be of any suitable material
which will maintain its physical, electrical, and chemical
characteristics as the temperature of the heat-tube. It is
specified depending on its operating temperature. Polyvinyl
chloride is satisfactory up to about 180.degree.F, polyethylene up
to about 215.degree.F, and specially cross-linked polyethylene up
to about 260.degree.F. Silicon resin materials are available to be
used from 350.degree.- 400.degree.F. Higher temperatures up to
500.degree.F or above may use the insulation made of chloro-fluoro
hydrocarbon resins commercially available at much higher
prices.
The electric wire has not been more than a fraction of a degree
warmer than the heat-tube in the prior art. Thus, the cheapest
resins for insulation, PVC and Polyethylene give adequate heat
transfer without increasing the cost by expensive insulation
materials. Particularly is this true in most cases of the present
invention because of the much better heat conduction of the novel
heat-tube designs of this invention.
Essentially, the heat-tube is a steel shape which, because of its
position in an A.C. electromagnetic field, changes its effective
resistance to the conduction of the A.C. Particularly important is
the steel tube around a conductor, but other steel shapes, strips,
bars, will exert this same effect to a lesser degree, but may be
more adaptable to taking advantage of the proximity effect, as will
be exemplified later.
Furthermore, while the temperature of the heat-tube itself was
limited by the former art to a relatively few degrees above that of
the oil-pipe and not much more than that above the ambient, it has
been found that the new designs of the heat-tube allow it to be
used up to at least 400.degree. F or 500.degree.F -- with special
materials even higher. Thus, very large heat flux and heat input to
the adjacent materials being heated are possible. By using
different of the novel systems of this invention for the heat-tube,
any desired difference up to 100.degree.F or even more, between the
heat-tube and the oil-pipe, may be used satisfactorily. Higher
heat-tube temperatures are not usually necessary to secure the
large advantages of the high heat fluxes of this invention, but an
upper limit may be about 500.degree.F where the magnetic properties
of the steel may change.
However, with the higher heat fluxes made possible by the present
invention, the electric wire may operate at higher temperatures;
and ceramic and other special inorganic insulations may be used in
powder, cement, or bead form for these higher temperatures.
Special inorganic powders have been found to be useful for this
purpose, particularly the oxides of the alkaline earth metals, such
as Beryllium, Magnesium, and Calcium. These oxides, such as
magnesia, may be incorporated as an insulator inside the heat-tube
and around the electric wire if of copper or particularly if of
iron or other material of greater resistivity then copper. This
powder must be firmly packed with the wire correctly aligned in the
center of the tube in a factory operation. To compact adequately
the insulation powder so that its heat conductivity will be
improved, the assembled heat-tube, insulation, and wire may be
passed hot or cold through rolls to reduce the size of the
heat-tube slightly. A notable one of these oxides in powder form is
beryllium oxide, which has excellent electrical insulation
properties, while being a good heat conductor. It, like magnesium
oxide, or calcium oxide, may be used in the upper limit of
effectiveness of heat-tubes of the high heat fluxes of the present
invention, but is too expensive for most uses. The heat-tube
preformed with the electric wire and its heat-proof insulation may
then be brazed or welded into the oil-pipe in the shop or in the
field by one of the several designs of this invention.
When the heat-tube is also the oil-pipe, no insulation of the wire
may be required if the oil, by itself, is a good dielectric, and
the same is true with other liquids and gases which are also good
dielectrics by themselves.
If the so-called heat-tube does not completely surround the
so-called wire, each of which carries one leg of the A.C., either
or both, in cross-section, may be strips of steel, half tubular
shapes or channels, or may take still other forms which develop
concentrations of the magnetic field generated or influenced by the
A.C. passing in the order. Thus, the skin effect may be less
pronounced in one or the other, but may, nevertheless, in
conjunction with the proximity effect, influence very markedly the
resistance of either or both conductors, the "heat-tube" and the
"wire."
FIGURES
In the equipment of this invention and in the figures as drawn,
only A.C. is used; the conventional signs plus (+) and minus (-)
indicate simply the two terminals for connection to the supply of
A.C. by alternator or transformer. These symbols represent the
direction of flow at only one instant of one cycle of the A.C.,
which is reversed many times per second.
Thermal losses are minimized by application of conventional
insulation materials in the usual manner to pipelines heated by
this or other methods. Such insulation is not shown in the Figures
as it is not a part of this invention, by itself. However, one of
the major objects of this invention as applied to the heating of
pipelines is the improvement of the ease and economy of application
of insulation, because the rough contours of a small heat-tube (or
several or more such) on the periphery of the large oil-pipe have
been largely eliminated. Insulation is a very substantial part of
the cost of a large pipeline. By making the periphery of the
heat-tube when combined with the oil-pipe deviate as little as
possible from the general circular cross-section, or preferably not
at all, as is done by the new systems of heat-tubes now possible,
the costs of labor and material for application of insulation are
reduced very considerably. Besides this reduction of costs, the
firmness, strength and life of the insulation covering is greatly
increased; and maintenance or replacement costs are reduced or
eliminated.
All figures are to be regarded as diagramatic -- no scale is
followed. In particular, for ease of representation, the ratio of
the size of a heat-tube to its oil-pipe is usually somewhat larger
as drawn than it would be in commercial pipelines, particularly if
the oil-pipes are large. Also, the electrical wiring connections
are merely basic circuit indications.
Especially it should be noted that those representations of
sections of long heat-tubes might continue for tens of thousands of
times the diameter, although conventional breaks are not
indicated.
FIG. 1 represents the cross-sectional view of an oil-pipe which is,
by itself, the heat-tube. The single electrical conductor is shown
in three possible positions - at the center, along the axis at some
indefinite distance from the axis; and lying on the bottom or at
other outer points.
FIG. 2A represents a longitudinal view of an oil-pipe as heat-tube,
also with the conductor along axis.
FIG. 2B is a cross section showing insulating supporters for the
conductor wire. In (a), (b) and (c) of FIG. 2A are diagrams of
added wiring to the heat tube circuit; (a) and (b) show additional
resistance electrical loads connected in parallel between the
conductor wire and the inside of the oil pipe, and (c) shows an
additional resistance electrical load connected in series with the
conductor wire.
FIG. 2C diagrams an additional electrical load as a resistance
added in series between the end of the conductor wire and a nearby
point of the inside of the pipe wall.
FIG. 3 diagrams an outer heat-tube and an inner coaxial tubular
conductor, also operating as a source of heat.
FIG. 4A represents an air heater formed of an unenclosed heat-tube
with extended surface and an internal conductor. In (a), (b), and
(c) of FIG. 4 a longitudinal view is shown, in FIG. 4B an end view
is shown. In (a) the heat-tube has fins; in (b) only the fins act
as the heat-tube as the tube is removed, and in (c) the fins are on
the tube which has perforations.
FIG. 5A is a longitudinal cross-sectional view at the cross-section
A--A in 5B which is the horizontal cross-section taken at B--B in
5A. The fluid heater has both heat-tube and conductor with fins,
all enclosed in a shell.
FIG. 6 is a horizontal cross-section of the electrical conductor
with expanded surface as longitudinal fins inside a smooth bore
heat-tube.
FIG. 7 is a longitudinal elevation of another electrical conductor
with expanded external surface in the form of a screw thread inside
a smooth bore heat-tube.
FIG. 8 is a cross-section of a heat-tube with an electrical
conductor so arranged that it may be moved from the axis to very
near the inner surface of the heat-tube.
HEAT-TUBES AS OIL-PIPES
The heat-tube may actually be the oil-pipe itself, as diagrammed in
FIGS. 1 and 2 of a pipeline carrying the oil or other liquid which
must, in this case, be a non-conductor of the A.C., unless the
internal electrical conductor is insulated. The electric-conductor
is in direct contact with the fluid and thus supplies some heat
directly to the oil or other liquid without the necessity of
passing this heat through the wall of the heat-tube. The wall of
the heat-tube, now the oil-pipe also, supplies more. The relative
amounts are controlled by their relative resistances since they are
in series and have the same intensity of A.C. flow. This design is
preferred for long oil-pipes and may be used in any size of pipe
used in present practice. There is thus no solid contact of a
heat-tube in being attached to or piercing the wall of another
transport pipe.
In one type of installation, as shown, lower 33, FIG. 1, the
electric wire may be well insulated with material resistant to the
oil or other fluid and simply dropped on the bottom, well anchored
along its length, to prevent movement due to friction of the liquid
movement. There is a difference of the proximity relation of the
A.C. conductor and of the penetration of the magnetic field which
causes the current flow due to the skin effect to vary somewhat
around the periphery of the heat-tube when the electric wire is
thus so much closer to some part of the wall (here the bottom) than
to the rest of the wall. However, this may be computed in designing
the system and makes no substantial difference in operation of an
oil-pipe which is also a heat-tube. For example, in a 48" pipe, the
resistance to A.C. flow of the heat-tube might be expected to be as
much as 25 times as great for the inner skin effect of the pipe
when the conductor is lying on the bottom at 33, as when it is in
the center at 3. In some cases, two or three wires, as 33, may be
in parallel near the inner perimeter in order to divide the current
flow and reduce the proximity effect.
The alternative position 133 of the wire represents any other
position between the axis and the wall of the oil pipe; and the
effective resistances at such different positions will be discussed
below.
Usually, however, the internal conductor is carried axially, and
this will be considered first. Thus, in FIG. 2, the electric wire
connected to one terminal (+) of the A.C. is shown uninsulated
except for the connection through the branch, 9, which has the
tubular insulator, 14, and flange insulator, 44. Polyethylene or
other suspenders, 4, support the wire, 3, along its length from
eyes, 10, welded on the inside wall of the pipeline. The other
connection to the A.C. is made at a point, 7, near the end where
the electric wire enters. Here again, a branch, 9, allows a tubular
insulator, 14, and a flange insulator, 44, to carry the wire
outside the tube to the (-) terminal.
In a 48 inch oil-pipe 10 miles long and in ambient temperatures of
-50.degree.F, 175 watts of electric heat would have to be supplied
per foot of length. In the use of an axial conductor, a copper
cable, concentrically braided of 0.772 inch diameter, would be
satisfactory. A 3/4 inch copper bar would also suffice. It may be
uninsulated if handling crude oil without water; or it may have a
suitable insulation, not considered in the present examples. It
would be supported at intervals of about 10 feet by three
suspenders of suitable material, as polyethylene, carried from
small eyes welded on the inner surface of the pipe. An aluminum bar
may be used for the axial conductor. It would be slightly larger in
cross-section in inverse proportion to resistivities, but would be
lighter and less costly. Normally, this would be of circular
cross-section, but it could be a flat strap or of other shape to
give greater surface for heat transfer, for mechanical rigidity, or
otherwise.
Approximately one-half of the heat input would be from the axial
cable or bar and one-half would come from the resistance in the
inner skin of the 48 inches conbined heat-tube and oil-pipe. A.C.
is supplied for the 10 miles at 5,300 volts, or 0.1 volt per foot,
and its intensity is 1750 amperes.
Both smaller and larger internal conductors may be used. If it is
of copper wire, 0000 gauge, the weight of copper and its cost will
be less. However, its resistance is higher, and therefore it will
supply a larger percentage of the total heat supply. The A.C. for
the 10 mile pipeline will be 1445 amperes at 6,400 volts.
If an aluminum bar is used, it may be designed to have the same
A.C. specification as for the 0000 copper wire. If circular, it
will be 0.531 inch in diameter. Its 0.221 square inches of
cross-section could be of other shape. If the aluminum bar is 3/4
inch diameter, the current for 10 miles will be 1,800 amperes at
5,100 volts; if the bar is 1 inch diameter, the current for 10
miles is 2,070 amperes at 4,450 volts. Increasing the size of the
conductor makes its resistance less when compared to that of the
skin of the 48 inch steel pipe; thus, its resistance will develop
less of the total heat required.
The central conductor may also be of steel, but if it is a bar more
than about 1/8 inch in diameter, the skin effect greatly reduces
its effective cross-section area for A.C. flow. Also, any steel
tube with wall thicker than the depth of penetration, or about
1/25th inch, will have steel which is not conducting. A strip about
twice as thick as the penetration depth is one preferred shape. A
steel shape, tube, or cable may have advantages of tensile strength
in pulling, or rigidly in support; or if of large surface per unit
length, of increased rate of heat dissipation.
A 4 inch outside diameter tube of 1/25 th inch wall steel with a
resistivity of 30 .times. 10.sup.-.sup.6 micro-ohms centimeters may
be used. The A.C. supply for the 10 mile pipe of the example would
be 12,300 volts at 750 amperes and the division of heat between the
central conductor and the pipe wall (both of the same material and
both having an effective thickness for current conductivity of 0.04
inch) would be inversely proportional to the 4 inch O.D. of the
conductor and the 48 inch I.D. of the pipe. Relatively this is 12
for the axial conductor and 1 for the pipe. This divides 1/13
.times. 175 watts = 13.5 watts input per foot from the steel pipe
itself, and 12/13 .times. 175 watts = 161.5 watts input per foot
from the axial steel conductor 4 inch O.D. .times. 1/25 inch.
If the central steel conductor is 2 inch O.D. and 0.04 inch wall
(or any thicker wall), 7 watts would be given up by the steel wall
of the pipe and 168 watts by the axial steel conductor. The A.C.
required would be 0.322 volts per foot or 17,000 volts for the 10
miles, with 540 amperes flowing.
In large pipelines, say of 48 inch diameter, the eccentricity may
be made as much as 0.96 of the radius, with the center of the
conductor wire about 1 inch from the inner wall of the pipe. The
ratio of the resistance of the return leg of the A.C. -- the inner
skin of the pipe -- is therefore about 25 times that when the
conductor is on the axis. In large pipelines, this is important
because the cross-sectional area of the "skin" becomes very large.
This, for a 48 inch pipe, the "skin" with a thickness of 0.04 inch
represents an effective electrical conductor of steel having a
cross-section of about six square inches. This has a very low
resistance indeed when the conductor wire is on the axis. However,
this low resistance may be multiplied by a value of 25 or the
effective cross-section of the heat-tube as a conductor may be
divided by 25 to equal an effective cross-section of only about
0.25 square inches of steel conductor, as is possible when the
conductor wire is laid on the bottom of the pipe, inside.
It is thus apparent that the resistance increases very greatly from
what would otherwise be obtained from the nominal skin as
calculated above on the basis of the conductor on the axis. The use
of the transport pipe as the heat-tube thus becomes quite practical
despite the large apparent cross-section of the effective "skin".
Moreover, depending on the voltage drop per foot which is desired,
the effective resistance of the wall of the pipeline may be varied
within a range of about 25 times by moving the conductor wire from
the center to the inner wall, e.g., the bottom of the pipe. This
relation has been indicated above as a means of regulating or
controlling the electrical input; and because of the increased
resistance of the pipe wall itself, either the voltage supplied or
the size of the conductor wire may have to be increased.
In placing the insulated internal conductor on the bottom of the
oil-pipe, as compared to an axial position, while the resistance is
greatly increased in the pipe, the percent of the current flow, and
thus of the heat given off near the bottom, is very greatly
increased, not only by the presence of the conductor and the heat
which it produces, but also because of the much greater
concentration of A.C. flow in the lower section of the skin of the
pipe itself. Usually this will be of advantage, particularly at
times of heat-up after a cooling-down. However, there will always
be some concentration of current and hence of heat throughout the
entire perimeter of the "skin."
These examples show some relations of the several variables for
large, long-distance pipelines, with an axial electrical conductor
when the oil-pipe is also a heat-tube. In every case, the effective
field penetration would average much less, and resistance of the
skin of the pipe to A.C. flow would increase very much if the
conductor was lying on the bottom of the pipe, rather than being
along the axis.
One advantage of this system is that, by supplying heat directly to
the oil-pipe wall, as well as to a conductor directly contacted by
the oil, a more uniform distribution of the heat is possible. It is
noted that particular advantages in design and operation are
possible with the large heat fluxes made possible by the present
invention; but this novel heat arrangement is also useful with the
lower heat fluxes of the prior art.
Another advantage is that the conductor contacts directly the oil
in the pipe to increase greatly heat transfer efficiency, since
heat does not have to be transferred through a heat-tube to add to
that which must be dissipated from its surface.
Here, as in other uses of the heat-tube principle, the oil pipes
would be grounded frequently throughout their length; and they may
also have the usual cathodic system for cathodic protection without
reference in either case to the major A.C. current on the inner
skin.
In many cases of long distance pipe transport, it may be necessary
to install alternators, whose principal duty is the heating of the
pipeline. If several or more are required so that a special design
is warranted, these may be made to develop some other number of
cycles than the usual 60. Since the thickness of the effective skin
is inversely proportional to the square root of the number of
cycles of the A.C., it follows that increasing this by nine times
to 540 would reduce the thickness to 1/3; while reducing it to 20
would increase the thickness by the square root of 60/20 or 3,
which is by 1.73 times. 10 to over 1000 cycles may be used.
The change in the eccentricity of the conductor and the number of
the cycles of the current thus allows wide latitude in establishing
the optimum resistance for the design of a major installation.
TWO COAXIAL HEAT-TUBES
In FIG. 3, the outer thin cylindrical section, 2, is a heat-tube;
the inner thin cylindrical section, 3, takes the place of the usual
electric wire; and it conducts the A.C. on the out leg of the
circuit. The outside surface of tube, 3, connects with the inside
surface of the outer heat-tube, 2, near the far end. At the near
end, the inside surface of 2 and the outside surface of 3 are
connected to the respective terminals of the source of A.C. The
inner tube, 3, is in the field of the electrical current passing
through the outer heat-tube, 2. If 3 is also of steel or other
material with a pronounced skin effect, this skin effect will be on
the outer surface (closest to the flowing current in 2). The inner
heat-tube, 3, will also generate heat which usually must pass
through 2 to the surroundings. In the usual case, heat losses are
all that are important; thus, this heat would merely be
compensatory for these losses. However, 2 and 3 must be insulated
from each other by a suitable tubular insulation, 4, which must
retain its properties at the temperatures involved. In some cases,
the space between 2 and 3 may be an air gap and there may be
suitable spacers for maintaining this spacing.
This use of the skin effect resistance in 3 would have advantage if
it was necessary to insulate the inside of 3 from the flow of A.C.
on its outside. Otherwise, a lighter weight conductor would give
the desired resistance and heating. This conductor of one leg of
the A.C. would usually be a tube with a wall at least about 1/8
inch thick if, for some purpose in design, the inside of 3 was to
be insulated from the A.C. flowing on its outer surface.
Because of the relatively large currents which will flow at the
surfaces of even moderate size tubes, the coaxial tube system will
have very low voltage requirements per unit of length because of
its low resistance. There are some means of increasing the
resistance. However, this low voltage drop is a very large
advantage in long-distance pipelines using the heat-tube as the
oil-pipe.
HEAT-TUBES AS ELECTRIC HEATERS
A heat-tube may also be used for heating a fluid not only in a
pipeline, but if a liquid in an open vessel or other container, or
if a gas in an open space. A very much higher heat flux may be
generated by the internal skin effect resistance of the heat-tube
of the present invention than is used in heating an oil pipeline.
This heat may be dissipated to the atmosphere, or into other
surrounding liquids or gases. Especially if heat transfer is to air
or gases, the heat transfer away from the heat-tube may be
increased by means of expanded surfaces to dissipate the large heat
input developed.
In these, as in every other application of heat-tubes, and with
every other electrical heater, a careful design is necessary based
on conductor size, and hence resistance, current carrying capacity
at given voltage drops, and mechanical design as to configuration
and particularly as to dissipation of the heat input.
Of major importance in such designs of electrical heaters is the
relation now demonstrated that, whereas in ordinary heating
resistors or conductors the resistance is proportional to the
resistivity of the material, in the use of heat-tubes the effective
resistance due to the skin effect is proportional only to the
square root of the resistivity. The apparent resistance is greatly
increased by the fact that the conductor only conducts through its
skin, and the balance of the normal cross-section may not be used.
Precise designs are not given for these heaters but may be made by
the usual calculations of electrical heat input balancing the
calculations of heat transfer of the surfaces involved to determine
temperatures which will be developed in the heater. The
permeability of the metal on surfaces of irregular shapes and
distances from the conductor adds some complexity to design
calculation which can only be made rigorously for some idealized
shapes. The operation is, however, quite definite but may require a
slightly different voltage than that calculated to give the desired
heat input and slight adjustments in the design to obtain the
optimum.
Because of the large cross-section of the resistors, i.e., the
surface or skin, even though it usually is not quite 1/16 inch
thick, large intensities of A.C. are usually drawn at low voltages.
This factor is particularly helpful in designs for many types of
heaters; including those where long lengths use commercial voltages
to give a drop per unit length which is reasonable with a heat-tube
of a size which is satisfactory from other considerations. Other
methods to be discussed allow higher resistances and hence voltage
drops, thus reducing the length of the heater required even with
the high heat fluxes possible with this invention.
The amount of heat transferred from a heat-tube is a function of
the area of metal contact with the cold fluid receiving the heat.
Extended surfaces as an integral part of the steel heat-tube may
add greatly to these surfaces and they may be of steel or, in many
cases, of other metals.
FIG. 4A and FIG. 4B diagram a heat-tube, 2, with one standard type
of extended surface, a spirally wound, helical fin, 20, which coils
transversely to the flow of gases and may be attached to the
heat-tube in any one of the several standard ways. A longitudinal
view of the unit of fins and tube is in FIG. 4A, an end view in
FIG. 4B. Simple disk type fins or any one of the other type of
extended surfaces: -- pegs, studs, stars, spines, etc. -- may be
applied or made integral with the tube itself, as is conventional
practice with tubes having extended surfaces, for increasing heat
transfer to the surrounding fluid. The extended surface system is
particularly useful in transmitting the large heat flux which may
be generated in the internal skin of the heat-tube by the skin
effect to air or other gas or liquid in flow across the extended
surfaces on the outside. This cross flow of fluid at an angle to
the axis quite often at 90.degree. is to be distinguished from the
flow of the fluid being heated in parallel, or generally parallel
flow to the heat-tube as used with an oil-pipe.
Such extended surface as that on the tube of FIG. 4 are commonly
used in many heating services using a heating fluid passing through
the center tube; e.g., steam, which, by condensing, gives up its
heat to the tube, thence to the fins, and thence to the surrounding
fluid, often air in cross flow.
Practically the same designs of radiators, air heaters, etc. as the
conventional ones heated by steam may be used with heat-tubes and
with either natural convective or with forced movement of air
across the tubes. The heat-tube, 2, in FIG. 4A is supplied with
A.C., for which it acts as a conductor-resistor through the tube on
one leg of the circuit due to the magnetic, inductive factors of
the A.C. passing through an axial electric wire forming the other
leg of the circuit.
Two differences from conventional construction with an internal
heating fluid are: -- (i) the requirement of connections for A.C.
supplied as above described to one or more heat-tubes, straight and
parallel usually, or in any bent or other configuration, (ii) the
heat-tube, using A.C. by the skin effect with the higher heat flux
input of this invention may require the fins to be designed
somewhat larger and more effective to dissipate the heat input than
when using a hot fluid as the heat source.
The heat flux which may be usefully developed by the skin effect on
the inside of the heat-tubes of this invention are from 200 or even
300 to 500 watts per lineal foot; and the fin surface must be
designed by standard methods, to dissipate this amount of heat to
the fluid flowing usually at an angle to the axis. A very high
performance heater is thus available where electric heat is to be
used for heating a fluid.
It has been found that the normal design methods for extended
surface heat exchangers for heating of air or other gas which are
based upon the so-called "fin effectiveness" may be used
immediately along with the same heat transfer coefficients for
fins, as have been developed for these when using a heating fluid
inside the tube. The rate of heat loss from the fins is immediately
calculable with the heating done by the skin effect on the
heat-tube, using the same methods and equations as are used if the
cylindrical core-tube is brought to the same temperature by a
heating fluid.
FIG. 4A indicates simply the heat-tube, 2, with an extended
surface, 20, which may be used, for example, as an air heater. It
may be heated by connecting one terminal (+) for A.C. supply to the
electric wire, 3, covered with insulation, 4, entering the left
side, and as a dotted line passing from left to right through the
center of the tube. Near the right end at the point, 6, the inside
surface is connected to this wire, 3, thence A.C. flows back on the
inside skin of the inner tube wall. Near the left end, it is
connected to the wire, 13, at point 16, and to the other terminal
right (-) for A.C.
No housing or duct work is indicated around this heat-tube for
supply of adequate movement of air across the surface by normal
convection or by forced motion by a fan or blower. Such ducts,
housings, fans, and blowers are familiar in the art and need not be
described since they are not a part of this invention. The simple
heat-tube with such expanded surface may furthermore be used
without housing or ducts as a space or room heater, e.g., along the
baseboard of a wall near the floor, or with a reverse or "hairpin"
bend for direct immersion in liquids. Again, normal convection may
suffice, but greatly increased heat transfer rates will come, as
always, with positive induced velocity of the fluid over the
surface.
The extended surface of 2, which is heated by the A.C. and skin
effect resistance, heats the surrounding air which rises around the
fins, as it is displaced by cooler air from below. A convective
motion is set up. This increases as the surface becomes warmer
until a balance or steady state is reached of heat input to inner
skin of 2 by the A.C. resistance, metallic conduction to fins, and
dissipation by convection to the surrounding air.
In the use described above of the heat-tube with an oil-pipe, only
a relatively minor amount of heat is required to maintain the fluid
at a temperature sufficiently above the ambient for whatever
purpose is involved, e.g., to lower viscosity so that the viscous
fluid may be pumped to keep the temperature above a solidification
point, etc. Now it has also been found that with the large heat
fluxes made possible by the present invention, the heat-tube may be
used for relatively larger duties of heat transfer, and indeed in
place of a conventional double pipe heat exchanger using the larger
heat flux of this invention.
As an example, the extended surface on the heat-tube of FIG. 4 may
be of the type adapted for longitudinal flow of fluid; one or many
tubes as FIG. 4A may be encased in a shell with the two ends
extended; and an inlet nozzle to the shell side may be added at one
end for the cold fluid entering, and at the other end a nozzle for
heated fluid leaving the shell side. This is a simple heater for
fluids. Instead of a simple electric wire from the axial conductor
of one leg of the circuit, the two coaxial heat-tubes of FIG. 3 may
be used. Normal problems of electrical insulation will have to be
taken care of, as indicated elsewhere, if the fluid is a
conductor.
The electrical conductor, 4, running the length of the heat-tube in
FIG. 4 has resistance to A.C. and also gives off heat, particularly
in the heavy duties possible with this electrical heating system.
With the solid tube structure of (a) in FIG. 4, air could still
circulate through the heat-tube to help cool 4. In (b) of FIG. 4,
which would represent a construction used through most or all of
the length, the tube is eliminated and only the helical fins remain
with the helical opening between -- as the space between the coils
of a helical spring. The gas can go through this opening to cool
the insulated conductor wire, now completely exposed to its
movement and heating. The electrical current passing in the inner
cylindrical skin of the heat-tube now does not go end-to-end, but
must go through the much greater length of the coils of the helix,
and the effective depth of penetration will be only about 0.04
inches of the inner cylindrical boundary or wall of the helical.
Thus, the effective resistance of the heat-tube may be increased
many times.
The removal of the heat generated by the inner conductor wire, 4,
may also be accomplished by having many holes, 35, drilled in the
tubular part of the heat-tube, 2, to allow air to pass through and
contact 3 or its insulation 4. This is shown in (c) of FIG. 4.
An even simpler heater is that of FIG. 2 for oil or other liquid or
gas which does not conduct the A.C. This heater was discussed above
under Heat-Tubes as Oil-Pipes. The heat-tube, 2, is now the heated
shell or oil-pipe; and it may be covered with thermal insulation if
desired. Also, the ends of the tube, 2, are closed, although this
is not shown in FIG. 2, which represents one advantageous use in
oil transport operations wherein heat may be supplied both to
increase the temperature of the oil and to balance that lost to the
colder surroundings.
If the heater of FIG. 2 is used as a space heater for ambient air,
the heater may have extended surfaces attached to or an integral
part of 2. A.C. is supplied as (+) to the electric wire, 3, which
is immune to the surrounding material inside the heat-tube and at
its operating temperature. The electric wire is brought into the
heat-tube, 2, through a branch connection, 9, with special
insulation, 44, passes the length of 2, and is firmly connected
electrically at 6 to a point near the end, and on the inside
surface of 2. The A.C. on its return leg heats the inside surface
of 2, flows from a connection at point 7 to another wire, 13, with
insulation, 14, passing through the special insulation, 44, inside
the branch connection to the (-) terminal of A.C.
This heat-tube of any desired length, and bent to any desired
shape, may be closed at the ends and filled with oil. Convective
motions will be set up in the tubular vessel to give a uniform
temperature throughout with considerable heat storage capacity for
use as a space heater. The masses and respective specific heats of
the oil and of the metal stores heat which gives a tempering effect
between the on-and-off of the high heat flux supplied. Other
materials than oil: -- gas, liquids, or soild, which are
non-conductors of A.C. -- may be used. This electric wire may have
usual insulation and simply be lying on the bottom of the outer
pipe. Alternately, it may be carried axially by suspenders, 4, of
polyethylene or other insulating materials, attached, as shown, to
rings, 10, on the inside of the pipe.
A version of FIG. 2, relatively shorter than the heat-tube as
oil-pipe already discussed, may be used primarily as a liquid
heater rather than as a liquid transporter. It would have a much
larger heat flux and would have open ends, as in FIG. 2, for liquid
flow while being heated.
A further development of this use of heat-tubes with high thermal
flux is shown in FIG. 5B, a longitudinal sectional view on the
plane represented by the line A-A of FIG. 5A, which is a
cross-sectional view on the plane represented by the line B--B of
FIG. 5B. The steel heat-tube, 2, has a series of longitudinal fins,
20, applied by grooving the tube and peening the fins into the
grooves, by welding, by extrusion, or other standard method. The
fins thus are formed as a substantially integral part of the tube.
The heat-tube is inserted into a shell, 1, with a narrow clearance
-- or none -- between the outside of the longitudinal fins and the
inside of the shell which carries the fluid to be heated to a
substantially higher temperature than its inlet temperature. The
use of the heater of FIG. 5 is as a heater for air, oil, or other
fluid which does not conduct electricity; but other variations
permit the heating of fluids which do conduct electricity. For this
example, air is being heated.
FIG. 5 indicates a heat-tube, 2, with a large number of
longitudinal fins, 20, extending substantially its entire length,
in order to transfer the relatively much higher flux of heat used
here from the supply of A.C., and the electric resistance, and the
skin effect, to a fluid moving in the shell space outside the tube.
In this use, the ratio of the internal diameter of the heat-tube to
the internal diameter of the shell would be of the order of 1 to 5,
to 3 to 5; or if more than one heat-tube is used in a shell, the
ratio of the sum of their internal diameters to that of the shell
might be 5 to 5, or even more. (A heat-tube has a relatively small
internal diameter -- or sum of internal diameters if more than one
- when attached to an oil-pipe. The ratio may be 1 to 10, to 1 to
30; thus the heat flux is low, i.e., small in amount per unit
length.)
The two coaxial heat-tubes of FIG. 5 use the principle of those of
FIG. 3. The inner one, 3, carries the A.C. from left to right, here
also fitted with extended surface fins, 30, in this case extending
inwardly toward the axis. The skin effect of the inner tube is on
its outer surface, close to the flow of A.C. in the outer tube.
There could be an insulation surrounding 3 to protect it from
shorting with the outer tube. Instead, this may be merely an air
space through which additional air passes to be heated. Ceramic or
other insulating spacers, such as the solid beads, 7, keep the two
heat-tubes apart. The A.C. reaching the heat-tube, as usual, by
connections shown here as the short conductors, the open beads, 6,
which may also act as spacers at this far end.
In FIG. 5, the fluid being heated, e.g., air, moves along the axis
of the heat-tube. The air supply indicated from the left inlet
nozzle, 8, may pass in contact with the outer fins, 20, of 2, with
the inner fins, 30, of 3, and also with both cylindrical surfaces
where conduction of A.C. gives the respective skin effects, the
inner surface of 2, and the outer surface of 3. A very compact
utilization of surface is thus attained. By having separate inlets
for the shell side and for the inner heat-tube, the space between
the coaxial tubes does not need to be in contact with the flowing
fluid (or two fluids may be used) if there is danger of shorting
these two conductors of A.C.
While FIG. 5 shows a fluid heater with only a single pair of
coaxial tubes, several or more such pairs may be incorporated as a
bundle inside a shell. The outer fins of adjacent heat-tubes may
come within the respective circles of the outer tips of the fins of
other heat-tubes in order to give the maximum surface for
dissipating the relatively large heat flux per unit length which is
thus available.
In either case, the fluid would pass either left or right between
the two flanged openings, 8 and 9. The arrows show a left-to-right
movement of all gas.
The heater of FIG. 5 has a resemblance to a standard heat exchanger
except there is the same fluid flowing shell-side and tube-side,
also in the space between the two heat-tubes. The electric current
passing in the skins of the two tubes does supply heat uniformly
throughout the length. The additional surfaces of the fins, 20 and
30, and their relative effectiveness in heat transfer may be
calculated by the standard methods and equations, which have been
derived for similar use wherein the heat is supplied by a hot fluid
flowing inside the tube. Again, the square feet of effective
extended surface per square foot of heated surface (i.e., the skin
effect surface) may be higher than with steam heated tubes; for
example, because of the greater heat flux which may safely be
developed by the skin effect and the greater extended surface
needed to dissipate it.
Heat exchangers using a heat-tube with an internal electric wire or
with two coaxial heat-tubes, as in FIG. 5, may be used for heating
gases or liquids; but, as always, in design of heat exchangers, the
amount of extended surface should be increased for use with a gas
as air because of the low volumetric heat capacity and low heat
transfer coefficients of gases.
FOr either liquids or gases, the standard design practices may be
used, within these modifications.
The connection (+) by the electric wire, 3, through the special
insulation, 4, carries the A.C. as in the usual case via the
internal conductor, 3, but on its outer surface; thence through the
inner surface of the heat-tube, 2, and back out through the wire,
13, with special insulation, 14, to the other (-) terminal of the
A.C.
INCREASING SKIN EFFECT RESISTANCE
The proximity effect in determining the pentration of the magnetic
field is important in those cases where the heat-tube may have a
special configuration, i.e., internal fins in a tube, so that only
the edges of some fins or teeth may come near the conductor itself.
In this case, the calculation of the field penetration, the
proximity effects, and hence the resistance, becomes difficult; and
the resistance may most easily be actually determined
experimentally for a given combination of heat-tube and
conductor.
In the converse case, the internal conductor "wire" may actually be
a steel axial conductor with an expanded or irregular surface. A
skin effect on the conductor itself, will be experienced, as well
as in the inner surface of the steel tube which is assumed to be
close thereto.
The design of the geometry and arrangement of the two components of
the heat-tube and the internal conductor, if of steel, may thus be
made to take advantage of the skin effect and of the uneven
pentration of the magnetic field due to the proximity effect. The
eccentricity factor noted above is one means; and considerable
change of the effective resistance of either the heat-tube or of
the electrical conductor, or of both, and thus of power input to
the combined system, may be made.
Thus FIGS. 6 and 7 illustrate a somehwat converse relation of the
use of skin effect in heater design to the use of extended surfaces
in FIGS. 4 and 5, although advantage may also be taken
simultaneously of those extended surfaces for heat transfer to
fluids contacting them and in motion.
FIG. 6 represents a design of a central conductor, 3, which might
take the place of the one, 3, in FIG. 5; but which has a very much
higher electrical resistance because the effective cross-section of
the skin effect has been greatly reduced. The skin effect of the
electrical conductor, 3, is due to a proximity effect of the
surrounding tube, not shown in FIG. 6, but as 2 in FIG. 5A. In FIG.
6, the dashed outside circle, 2, represents the inside surface of
such a heat-tube. If the width of the outer fins, 30, of 3 are
greater than about twice the depth of penetration of the skin
effect, and if the depth of the teeth is also greater than about
this much, the magnetic field cannot penetrate more deeply;
therefore, substantially the only electrical conduction can be
along the outer edges of the fins, 30. (For many steels the depth
of penetration has been found to be about 0.04 inch.) This outer
surface of the teeth alone may be only a small part of the total
cross-section of the central conductor, and the resulting
resistance is increased accordingly.
The same effect may also be obtained in reverse. The heat-tube may
be assumed to have the cross-section of a shape something like that
of 3, the internal conductor of FIG. 5A with the many fins, 30,
projecting inwardly from a tube wall. At their center is an
insulated electrical wire, 33, shown here as a dotted circle,
because it does not refer to the other design of FIG. 5. What now
becomes the heat-tube, 3, of FIG. 5A has its effective perimeter of
its inner surface reduced to the depth of penetration of the
magnetic and induction effect back from the inner edges, thence
into the teeth. The balance of the cross-section of the extended
surface and of the tube itself is merely to conduct away and
dissipate the heat flux to the fluid stream moving in the confines
of what is now both the heat-tube and transport-pipe.
Similarly, FIG. 7 diagrams another internal conductor, this time
with an expanded outer surface in a form like that of a screw
thread of a bolt. Here again the heat-tube outside of the conductor
is not shown, but is indicated by the dashed lines, 2.
If the width of the above groove does not exceed its depth, which
is in turn not less than twice the depth of penetration, the only
effective conductor is the periphery of the threads. The A.C. must
then go around the outside of the threads and follow a path very
much longer and very much higher resistance than that
conventionally, i.e., the axial length of the screw. This is a
practical and very inexact experimental solution, but almost
correct, of what is a rather complicated theoretical analysis.
While other types of screw threads may be used instead of the
square ones of FIG. 7, e.g., those shaped as the fins of the
heat-tube of FIG. 4, the estimation in advance of the proximity
effect and field penetration and inter-shielding factors is much
more difficult in evaluation of the effective penetration depth for
A.C. in the skin. Other geometric modifications to take advantage
of minimizing the effective conductor cross-section of either the
heat-tube or of the internal conductor, may be made to advantage in
the various embodiments of this invention.
The proximity effect on a conductor in a non-uniform field may
change very considerably the extent of penetration of the magnetic
forces, hence of the resistance of the heat-tube and/or of the
conductor when one or both are of steel. As noted above, the system
may be designed to best advantage to use this effect. Also, in
those cases where practical, the proximity of the conductor to the
heat-tube may be varied during service.
Thus, FIG. 8 diagrams the steel heat-tube, 1, which is a transport
pipe. The conductor, 3, may or may not be insulated depending on
the electrical conductivity of the fluid and it may or may not be
of steel, depening on whether a skin effect in it is to be
utilized, particularly in regard to whether a change in its
resistance is desired due to the proximity effect.
The conductor, 3, is supported by one or more pivot arms, 32, made
of an insulating material, which are in turn supported by a
rotatable shaft mechanism, 31. This mechanism, 31, may be attached
to the inner wall of the pipe; and it functions by allowing the
rotation of 32, and hence of 3, so that 3 may occupy any position
on the arc, 31, as shown by the several possible positions of the
conductor varying from axial through a general position shown
dotted as 33; and if insulated, the conductor, 3, may be rotated
until its insulation touches the inner wall of 2.
As noted above, the increase of the resistance is limited by the
closeness with which the conductor can approach the wall to
increase this eccentricity. The thickness of the insulation and the
radius of the conductor control this. To minimize the effective
radius (i.e., the distance from the center to the wall side of the
conductor) a strip of metal, 33, may be used, the thickness of
which is less than twice the radius of an equivalent conductor;
thus, its effective distance, with the same insulation, will be
less than that of a round conductor. This may also be rotated so 33
falls on the axis. If the conductor, 3 or 33, is of copper, there
will be no measurable change in its own resistance in moving it
from the axis to a position near the pipe wall. If 33 is of steel,
and particularly if its effective diameter (or thickness) is
greater than twice the depth of penetration or "skin", its
resistance will also increase markedly as the eccentricity
increases. Other shapes and sizes of 3 or 33 may be used to change
the effective resistance, as has been already described.
This device with a movable conductor allows the wide variation of
its effective resistance and the amount of heat developed, as well
as of the overall line loss.
HEAT-TUBES AS TRANSMISSION LINES FOR A.C.
While the heat-tube as heretofore described has been primarily
concerned with the heating of a steel surface by the skin effect,
it is also essentially a 2-conductor circuit for A.C.; and in some
cases it may be designed so that its production of heat is not much
different than that of a standard 2-wire conductor.
Thus, in FIGS. 1, 2, or 3 as described above, the internal
conductor, 3, usually insulated, is surrounded by a heat-tube, 2.
In a pipeline of some length, it may be desirable to utilize
electric current from this circuit by tapping off from 3 and from
the heat-tube, 2, connector wires to supply A.C. power for some
other purpose. A common use is the withdrawal of current for a
branch connection of oil from the transport line; and a new
heat-tube circuit would be set up using the taps or connections
from 3 and 2 to connect to the corresponding conductor and
heat-tube of the transport pipeline circuit. This connection could
be in either series, or in parallel relation.
Such circuits including a resistor as an electrical load are
diagrammed in FIG. 2A. A parallel connection between the skin of
the heat tube and the conductor wire is diagrammed in (a) by taps
to corresponding points. Diagram (b) also shows a parallel
connection near the end; but if the conductor wire is connected to
this auxiliary circuit at the end rather than to the inside of the
heat-tube, circuit (b) is in series with the basic circuit of the
heat-tube at its far extremity. Similarly, if the conductor wire is
broken at any point along its length, and circuit (c) is connected
to the two ends so formed, an auxiliary circuit in series is
established.
FIG. 2C shows an added electrical resistance or load in series with
the basic heat tube electrical circuit, and inserted between the
extremity of the condcutor 3 and its connection with the far end of
the transport pipe 2. Here the other side of the new resistance
load in series is connected back to the transport pipe 2,
preferably at an inside point on the wall as shown, and hence
electrically insulated from the wall in piercing it. The connection
to the wall of the pipe (indicating now the length of the heated
part of the transport pipe) may actually be made to the outside of
the pipe, the current flows through the pipe wall at this point,
then through the skin to the other end as previously described.
There is no noticeable electrical disturbance at the connection on
the outside for more than a millimeter or two distance.
Many other reasons for utilizing the current so available have been
found, particularly if there is no other source of electric current
throughout the route of the pipeline. The tapping off of A.C. is
usually in parallel. Contrary to a normal A.C. transmission line,
in which it is attempted to maintain as nearly constant a voltage
between the two conductors as is possible throughout their length,
the available voltage of the A.C. between wire and heat-tube varies
from a high point at the one end of the heat-tube circuit, to zero
at the far end. There is a substantial voltage difference between 3
and 2 at the inlet of the heat-tube, wherein the corresponding
connections are made to the alternator or to the transformer; while
at the far end of the conductor and the heat-tube, the voltage drop
has been reduced to zero. However, any new resistance or load
inserted at the far end as in FIG. 2C as an electrical load in
series is supplied with A.C. through the entire length - heat-tube
plus conductor.
Thus, it is always necessary to determine the voltage available on
a point of tapping off A.C., depending on the voltage drop up to
that particular point in the heat-tube circuit.
Nevertheless, in some cases it has also been found that the
heat-tube may thus be used along the length of the pipeline to
provide an A.C. source, when proper attention is paid to the
voltage available.
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