Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

Abstract

AbstractIn this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.