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Analytical Study of Heat Conduction in a Finite Region Due to a Laser Source
Tien-Chien Jen and Gustavo Gutierrez

This paper presents a theoretical study for the temperature distribution in a finite region subjected to a spatially and temporally exponential decaying laser source. The governing heat conduction equation, the boundary conditions and the initial condition are presented in dimensionless form as functions of a group of dimensionless parameters, namely, c, t, B, Bi, w. The importance of the different parameters is discussed in detail. Three different sets of thermal boundary conditions imposed at the “far” boundary, including convection, adiabatic and constant surface temperature conditions are investigated in the present study. The influence of the different boundary conditions on the location and the magnitude of the maximum temperatures as well as the local temperature distribution is investigated too. The calculated results are compared with previous analytical studies, assuming semi-infinite body. Parametric studies are done to show the range of dimensionless parameters where this simplified assumption is not valid. Finally, the present analytical solutions are compared to existing experimental results.

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