Temperatures in a thin metal plate traversed by an arc
Author:
R. L. Bish
Journal:
Quart. Appl. Math. 48 (1990), 491-497
MSC:
Primary 80A20; Secondary 78A55
DOI:
https://doi.org/10.1090/qam/1074963
MathSciNet review:
MR1074963
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Abstract: The temperature distribution within a thin metal plate of infinite extent traversed by an electric arc is obtained for the case when the plate remains electronegative. The potential application of this result to the experimental determination of the size of the cathode dark space is discussed.
J. M. Somerville, The Electric Arc, Methuen, London, (1959) p. 57
- R. L. Bish, Heat flux density distribution on the electrodes of an arc, Quart. Appl. Math. 47 (1989), no. 2, 379–383. MR 998111, DOI https://doi.org/10.1090/S0033-569X-1989-0998111-2
H. A. Wilson, On heat convection, Proc. Cambridge Phil. Soc. 12, 406–423 (1904)
D. Rosenthal, Mathematical theory of heat distribution during cutting and welding, Welding J. 20, 220–234 (1941)
- Barry Spain, Vector analysis, D. Van Nostrand Co. Ltd., London-Toronto-New York, 1965. MR 0183824
- M. G. Smith, Introduction to the theory of partial differential equations, D. Van Nostrand Co., Ltd., Princeton, N.J.-Toronto, Ont., 1967. MR 0219858
- G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
- H. S. Carslaw and J. C. Jaeger, Operational Methods in Applied Mathematics, Oxford University Press, New York, 1941. MR 0005988
G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, Longmans, 1936, pp. 54, 56, 84
J. M. Somerville, The Electric Arc, Methuen, London, (1959) p. 57
R. L. Bish. Heat flux density distribution on the electrodes of an arc, Quart. Appl. Math. 47, 379–383 (1989)
H. A. Wilson, On heat convection, Proc. Cambridge Phil. Soc. 12, 406–423 (1904)
D. Rosenthal, Mathematical theory of heat distribution during cutting and welding, Welding J. 20, 220–234 (1941)
B. Spain, Vector Analysis, Van Nostrand, 1965, pp. 66, 68
M. G. Smith, Introduction to the Theory of Partial Differential Equations, Van Nostrand. 1967, p. 113
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1945 pp. 202. 698–713
H. S. Carslaw and J. C. Jaeger, Operational Methods In Applied Mathematics, Oxford University Press, 1941, p. 350
G. W. C. Kaye and T. H. Laby, Tables of Physical and Chemical Constants, Longmans, 1936, pp. 54, 56, 84
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Article copyright:
© Copyright 1990
American Mathematical Society
