Analytical solution to non-Fourier heat conduction as a laser beam irradiating on local surface of a semi-infinite medium

Abstract

The two dimensional non-Fourier heat conduction in a semi-infinite medium on which local surface is irradiated by a laser beam is analyzed. The mathematical model is based on hyperbolic heat conduction equation with thermal relaxation time and is deals with boundary condition with time step heating and uniform temperature distribution in local area of the surface. A new analytic solution to the problem is derived by using Laplace and Hankel transforms and is owing to finding analytic result of inverse Laplace transform to time domain exactly. The solution of the temperature field in semi-infinite medium is expressed as an infinite integral of known function. The proposed numerical technique to the integral is implemented. Non-Fourier effect of temperature field is shown in numerical examples. The evolution of contour plots of temperature field over time is presented by evaluating the analytic solution demonstrated significant difference between hyperbolic and classical heat conduction.