Integral method of solving heat-conduction problems with the second-kind boundary condition. 3. Pulsed laser heating

Abstract

Exact and approximate solutions to the non-stationary problem on the heat conduction in a semi-bounded body exposed to a pulsed laser radiation flow have been obtained. The action of rectangular, triangular and parabolic laser radiation pulses on this body was investigated. Polynomial relations have been constructed on the basis of the boundary-characteristic method with introduction into consideration of the temperature-disturbance front, and they made it possible to obtain practically exact solutions for the temperature function and its time derivative at both the stages of heating and cooling of the body. It is shown by some examples that the success in solving problems on the pulsed plasma heating of bodies is associated in many respects with the necessity of definition of the time law of movement of the temperature-disturbance front with the use of the Pade diagonal approximation, which excludes, practically completely, the divergence of the power series defining the law of movement of this front, in particular, in small time intervals. The approach proposed for solving heat-conduction problems with the second-kind boundary condition allows one to simply and effectively find solutions for isotherms and lines of equal heating and cooling. Analysis of the results obtained allows the conclusion that the effectiveness of solving various technological problems, based on the use of pulsed laser radiation, is determined by the success in solving the problems on control of the time shape of a laser pulse and determination of the temperature fields in the body on the basis of polynomial representations.