Analytical and FDM Solutions for Anisotropic Heat Conduction in an Orthotropic Rectangular

Mohammad Sameti¹, Fatemeh Razi Astaraie¹, Fathollah Pourfayaz^1, and Alibakhsh Kasaeian¹

¹Department of Renewable Energies, Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran

Cite this paper:
Mohammad Sameti, Fatemeh Razi Astaraie, Fathollah Pourfayaz and Alibakhsh Kasaeian. Analytical and FDM Solutions for Anisotropic Heat Conduction in an Orthotropic Rectangular. American Journal of Numerical Analysis. 2014; 2(2):65-68. doi: 10.12691/ajna-2-2-6

Abstract

Anisotropic materials have physical properties such as thermal conductivity which vary with orientation throughout the structure. These properties make the analysis of heat transfer much more complex than standard isotropic materials. Therefore, the heat flux equation and Fourier’s Law should be expanded in order to properly govern the thermal conduction. The analytical exact solutions and numerical finite difference solutions of a fundamental heat conduction problem in an anisotropic medium are presented in this study. The problem is solved for steady state condition in a rectangular thin film of quartz. The key for analytical solution is to use two variables to convert the anisotropic equations into isotropic ones. The temperatures of 35 points on the rectangular are obtained and compared by the two methods. The results show an excellent accuracy for the numerical method. The temperature and the heat flux profile are also illustrated to show how the anisotropicity influences the thermal behavior of the media. MAPLE and EES were used to numerically integrate or solve the system of the eqautions.

Keywords:
anisotropic materialsheat conduction Finite Difference Method (FDM)

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