Analytical Solution of Hyperbolic Heat Conduction Equation in a Finite Medium Under Pulsatile Heat Source

This paper presents a pure analytical solution of one-dimensional hyperbolic heat conduction equation in a homogeneous finite medium under series of time pulsed heat source which is exponentially distributed and acts symmetrically on both sides. The solution is obtained without any numerical procedures, using the Eigenvalue function. The problem is solved under two types of step and exponential time pulse series functions, which are used in simulation of laser interaction of tissues, and the closed-form solutions are introduced. The ability of the solution to estimate the effect of pulse duration and intensity is investigated. The results can be applied as a verification branch for other numerical solutions such as pulse laser interaction phenomenon.