Conduction of heat in a semi-infinite solid with an exponential-type initial temperature profile: temperature and heat flux solutions due to an instantaneous laser source

A closed-form model for the computation of temperature and heat-flux distribution in a semi-infinite solid with an exponentially-decaying, initial-temperature profile is investigated. The solutions are presented for the case of an instantaneous laser source which is absorbed partially in the surface layers followed by an exponential decay with position in the material itself. The appropriate dimensionless parameters are identified and the reduced temperature and heat flux solutions are presented in the graphic form as a function of these parameters. Some limiting cases of practical interest are also discussed. It is demonstrated that the present analysis covers the classical case of no heat generation in the solid as well as some new solutions.