Abstract
A boundary-value problem for steady-state heat conduction in a three-dimensional, two-layered composite is studied. The method of Green's function is used in the study. Green's functions are constructed as double sums in terms of eigenfunctions in two of the three directions. The eigenfunctions in the direction orthogonal to the layers are unconventional and must be defined appropriately. The use of different forms of the Green's functions leads to different representations of the solutions as double sums with different convergence characteristics and it is shown that the method of Green's functions is superior to the classical method of separation of variables.
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References
J.V. Beck, K.D. Cole, A. Haji-Sheikh and B. Litkouhi, Heat Conduction Using Green's Functions. Washington, D.C.: Hemisphere Press (1992) 523 pp.
D.P. Kennedy, Spreading resistance in cylindrical semiconductor devices. J. Appl. Phys. (1960) 1490–1497.
A. Haji-Sheikh, J.V. Beck and D. Agonafer, Steady-state heat conduction in multilayer bodies. Int. J. Heat Mass Transfer 46 (2003) 2363–2379.
A. Haji-Sheikh, J.V. Beck, Temperature solutions in multi-dimensional multi-layered bodies. Int. J. Heat Mass Transfer 45 (2002) 1865–1877.
A. Haji-Sheikh, J.V. Beck, An efficient method of computing eigenvalues in heat conduction. Num. Heat Transfer, Part B. Fundamentals 38, No. 2 (2000) 133–156.
B. Friedman, Principles and Techniques of Applied Mathematics. New York: John Wiley and Sons (1956) 315 pp.
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Yen, D.H., Beck, J.V. Green's functions and three-dimensional steady-state heat-conduction problems in a two-layered composite. Journal of Engineering Mathematics 49, 305–319 (2004). https://doi.org/10.1023/B:ENGI.0000031192.01996.71
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DOI: https://doi.org/10.1023/B:ENGI.0000031192.01996.71