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Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

Published online by Cambridge University Press:  17 June 2016

M. R. Talaee  and
V. Sarafrazi
M. R. Talaee*
Affiliation:
Rolling StockSchool of Railway EngineeringIran University of Science and TechnologyTehran, Iran
V. Sarafrazi
Affiliation:
Rolling StockSchool of Railway EngineeringIran University of Science and TechnologyTehran, Iran
*
*Corresponding author ([email protected])
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Abstract

This paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

Keywords

Hyperbolic heat conductionSource termLaser interaction of biological tissueEigen function expansion method
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 1 , February 2017 , pp. 65 - 75
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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