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An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions. (English) Zbl 1234.74021

Summary: An analytical method is proposed to solve the equation of heat conduction in a layered sphere subject to a time-dependent boundary temperature. It is well known that for such problems in general, eigenvalue and residue computation poses a challenge, which can become too complicated to handle with many layers. In this Letter, the proposed analytical method is free of eigenvalue and residue calculations. A closed-form approximate solution is derived with high accuracy.

MSC:

74F05 Thermal effects in solid mechanics
74E30 Composite and mixture properties
80A20 Heat and mass transfer, heat flow (MSC2010)
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[1] Carslaw, H.S.; Jaeger, J.C., Conduction of heat in solids, (1959), Oxford Univ. Press Oxford, UK · Zbl 0029.37801
[2] Snabre, P.; Perez, A.; Arhaliass, A., Eur. phys. J: appl. phys., 1, 315, (1998)
[3] M.C.B. Gough, Modelling heat flow in buildings: an eigenfunction approach, Ph.D. Thesis, University of Cambridge Press, 1982
[4] Sun, Y.; Wichman, I.S., Int. J. heat mass transfer, 47, 1555, (2004)
[5] Fredman, T.P., Heat mass transfer, 39, 285, (2003)
[6] Tsai, C.; Hung, C., Int. J. heat mass transfer, 46, 5137, (2003)
[7] Haji-Sheikh, A.; Beck, J.V., Int. J. heat mass transfer, 45, 1865, (2002)
[8] Haji-Sheikh, A.; Beck, J.V.; Agonafer, D., Int. J. heat mass transfer, 46, 2363, (2003) · Zbl 1033.80002
[9] Lu, X.; Tervola, P., J. phys. A: math. gen., 38, 81, (2005)
[10] Patankar, S.V., Numerical heat transfer and fluid flow, (1980), Hemisphere New York · Zbl 0595.76001
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