Journal of Applied Mathematics
Volume 2009 (2009), Article ID 604695, 18 pages
Research Article

Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

Department of Mathematics, King Faisal University, P.O. Box 1982, Dammam 31413, Saudi Arabia

Received 28 June 2008; Revised 2 March 2009; Accepted 12 May 2009

Academic Editor: George Jaiani

Copyright © 2009 R. T. Al-Khairy and Z. M. AL-Ofey. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g(x,t)=I(t)(1R)μeμx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discussion of solutions for different time characteristics of heat sources capacity (constant, instantaneous, and exponential) is presented. The effect of absorption coefficients on the temperature profiles is examined in detail. It is found that the closed form solution derived from the present study reduces to the previously obtained analytical solution when the medium velocity is set to zero in the closed form solution.