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Li, M., & Lai, A. C. (2012). Heat-source solutions to heat conduction in anisotropic media with application to pile and borehole ground heat exchangers. Applied Energy, 96, 451-458.

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Article

Heat Diffusion in an Anisotropic Medium with Central Heat Source

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


International Journal of Partial Differential Equations and Applications. 2014, Vol. 2 No. 2, 23-26
DOI: 10.12691/ijpdea-2-2-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Mohammad Sameti, Alibakhsh Kasaeian. Heat Diffusion in an Anisotropic Medium with Central Heat Source. International Journal of Partial Differential Equations and Applications. 2014; 2(2):23-26. doi: 10.12691/ijpdea-2-2-1.

Correspondence to: Alibakhsh  Kasaeian, Department of Renewable Energies, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran. Email: akasa@ut.ac.ir

Abstract

Anisotropy is a property of some materials in which the physical properties vary with different crystallographic orientations. In this study, the analytical steady state solution to the anisotropic heat conduction in an orthotropic sphere is presented. There is a point heat source in the center of the sphere which supply the constant thermal energy. Using a transformation can change the anisotropic problem to an isotropic one which can be solved by the change of variables. The results showed that the isothermal surfaces are concentric ellipsoids which approach spheres while the conductivities in different directions are close to each other. The analytical results were validated with the 2D experimental tests performed for quartz as an orthotropic material. Despite the isotropic materials, it can be seen that the vectors of temperature gradients and the heat flux q are not parallel.

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