Numerical simulation of non-linear heat conduction subjected to a laser source: the effects of variable thermal properties

This paper presents a numerical study of the temperature distribution in a body subjected to a spatially exponential decaying laser source. The governing heat conduction equation, the boundary conditions and the initial condition are presented in a dimensionless form as a function of a group of dimensionless parameters, namely, χ, τ, Bi, w, c1, c2 and c3. Three different sets of thermal boundary conditions imposed at the “far” boundary, including convection, insulated and constant surface temperature conditions are investigated in the present study. The governing equation is discretized using a control volume approach, with a variable grid to increase the resolution of the domain near the boundary where the laser heat source is applied. The effects of the different parameters and the temperature dependent thermal properties are studied in detail. The calculated results are compared with previous analytical studies for constant thermal properties obtained for both semi-infinite and finite domains. Finally, the present numerical solutions are compared to existing experimental data.