Transient 2D Heat Transfer with Convection in an Anisotropic Rectangular Slab

Mohammad Eshaghian^1, and Mohammadreza Najafpour²

¹Department of Computer, Payame Noor University, Tehran, Iran

²Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

Cite this paper:
Mohammad Eshaghian and Mohammadreza Najafpour. Transient 2D Heat Transfer with Convection in an Anisotropic Rectangular Slab. International Journal of Partial Differential Equations and Applications. 2014; 2(3):58-61. doi: 10.12691/ijpdea-2-3-3

Abstract

It is not unusual that the properties of a material vary with different crystallographic orientations and this property is said to be anisotropy. Paper presented here analytically studies the transient solution to the anisotropic heat conduction in an anisotropic rectangular thin film subjected to initial arbitrary temperature function throughout the medium. An integral transformation is applied to remove the partial derivatives with respect to two spatial variables and transform the partial differential boundary value problem to ordinary differential equations. The result is the multiple integral with respect to spatial variables where the mathematics and model ling software MAPLE 18 was used to numerically calculate the summation and to plot the temperature and heat flux vector profiles.

Keywords:
combined heat transfer anisotropic material analytical solution

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