Exponential basis functions in solution of time –dependent heat equation in axially layered materials

Document Type : Research Article

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Abstract

In this paper we present a novel method based on using Exponential Basis Functions (EBFs) to solve heat conduction problem in axially layered materials. In the first step, we have considered each layer of material as a separate element. Then the solution in each element was approximated by a summation of EBFs satisfying the differential equation of transient heat conduction problem. The unknown coefficients of the series solution were related to initial condition and Dirichlet side conditions of each layer employing a discrete transformation technique. Finally, the general solution of material was completed by satisfying the continuity conditions between adjacent layers in a manner similar to conventional finite element method. In this hybrid method, a collocation scheme was used for satisfying the time dependent boundary conditions as well as the initial conditions. The capability of the presented technique was investigated in the solution of some benchmark problems.

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[1] Barbaro, S., Giaconia, C., Orioli, A., “A computer oriented method for the analysis of non steady-state behavior of buildings”, Building and Environment , Vol. 23(1), pp. 19- 24, 1988.
[2] Boroomand, B., Mossaiby, F., “Dynamic solution of unbounded domains using finite element method: discrete Green’s functions in frequency domain”, International Journal of Numerical Methods in Engineering, Vol. 67, pp. 1491- 1530, 2006.
[3] Boroomand, B., Soghrati, S., Movahedian, B., “Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style”, International Journal of Numerical Methods in Engineering, Vol. 81, pp. 971- 1018, 2010.
[4] Chantasiriwan, S., “Methods of fundamental solutions for time-dependent heat conduction problems”, International Journal of Numerical Methods in Engineering, Vol. 66, pp. 147- 165, 2006.
[5] de Monte, F., “An analytical approach to the unsteady heat conduction processes in one-dimensional composite media”, International Journal of Heat and Mass Transfer, Vol. 45, pp. 1333- 1343, 2002.
[6] de Monte, F., “Transient heat conduction in one-dimensional composite slab. A natural approach”, International Journal of Heat and Mass Transfer, Vol. 43, pp. 3607- 3619, 2000.
[7] Dong, CF., “An extended method of time-dependent fundamental solutions for inhomogeneous heat conduction”, Engineering Analysis with Boundary Element method, Vol. 33, pp. 717- 725, 2009.
[8] Friedman, A., “Partial differential equations of parabolic type”, Englewood Cliffs, NJ: Prentice-Hall Inc., 1964.
[9] Huang, SC., Chang YP., “Heat conduction in unsteady, periodic and steady states in laminated composites”, Journal of Heat Transfer, Vol. 102, pp. 742- 748, 1980.
[10] Johansson, BT., Lesnic, D., “A method of fundamental solutions for transient heat conduction in layered materials”, Engineering Analysis with Boundary Element method, Vol. 33, pp. 1362- 1367, 2009.
[11] Johansson, BT., Lesnic, D., “A method of fundamental solutions for transient heat conduction”, Engineering Analysis with Boundary Element method, Vol. 18, pp. 1463- 1473, 2004.
[12] Mikhailov, M.D., Ozisik, M.N., Vulchanov, N.L., “Diffusion in composite layers with automatic solution of the eigenvalue problem”, International Journal of Heat and Mass Transfer, Vol. 26, pp. 1131- 1141, 1983.
[13] Shamsaei, B., Boroomand, B., “Exponential Basis Functions in Solution of Laminated Structures”, Journal of Composite Structures. Vol. 93, pp. 2010-2019, 2011.
[14] Sun Y, Wichman IS, “On transient heat conduction in a one-dimensional composite slab”, International Journal of Heat and Mass Transfer, Vol. 47, pp. 1555- 1559, 2004.
[15] Zandi, SM., Boroomand, B., Soghrati, S., “Exponential basis functions in solution of incompressible fluid problems with moving free surfaces”, Journal of Computational Physics, Vol. 231, pp. 505– 527, 2012.

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