Separation of variables on a triangular geometry
Author:
D. C. Look Jr.
Journal:
Quart. Appl. Math. 50 (1992), 141-148
MSC:
Primary 65N15; Secondary 35C10
DOI:
https://doi.org/10.1090/qam/1146629
MathSciNet review:
MR1146629
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Abstract: The usual separation of variables technique is used to obtain solutions on a triangular region of interest. The resulting error is noted and a forced orthogonality procedure is used to investigate the error. The forced method allows a means to indicate the onset of error based on the magnitude of two parameters.
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- Clive R. Chester, Techniques in partial differential equations, McGraw-Hill Book Co., New York-Düsseldorf-London, 1971. MR 0269961
E. R. G. Eckert and R. M. Drake, Jr., Analysis of Heat and Mass Transfer, McGraw-Hill, New York, 1972, p. 80
R. K. Irey, Errors in the one-dimensional fin solution, ASME J. Heat Transfer 81, 151–156 (1968)
W. Lau and C. W. Tan, Errors in one-dimensional heat transfer analysis in straight and annular fins, ASME J. Heat Transfer 95, 549–551 (1973)
M. N. Özisik, Heat Transfer, a Basic Approach, McGraw-Hill, New York, 1985, p. 80
A. D. Snider and A. D. Kraus, Recent developments in the analysis and design of extended surfaces, ASME J. Heat Transfer 105, 302–306 (1983)
H. C. Unal, The effect of the boundary condition at a fin tip on the performance of the fin with and without generation, Internat. J. Heat Mass Transfer 31 (7), 1483–1496 (1988)
L. C. Burmeister, Triangular fin performance by the heat balance integral method, ASME J. Heat Transfer 101, 564–565 (1979)
C. R. Chester, Techniques in Partial Differential Equations, McGraw-Hill, New York, 1971, p. 107
E. R. G. Eckert and R. M. Drake, Jr., Analysis of Heat and Mass Transfer, McGraw-Hill, New York, 1972, p. 80
R. K. Irey, Errors in the one-dimensional fin solution, ASME J. Heat Transfer 81, 151–156 (1968)
W. Lau and C. W. Tan, Errors in one-dimensional heat transfer analysis in straight and annular fins, ASME J. Heat Transfer 95, 549–551 (1973)
M. N. Özisik, Heat Transfer, a Basic Approach, McGraw-Hill, New York, 1985, p. 80
A. D. Snider and A. D. Kraus, Recent developments in the analysis and design of extended surfaces, ASME J. Heat Transfer 105, 302–306 (1983)
H. C. Unal, The effect of the boundary condition at a fin tip on the performance of the fin with and without generation, Internat. J. Heat Mass Transfer 31 (7), 1483–1496 (1988)
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Article copyright:
© Copyright 1992
American Mathematical Society
