ESTABLISHING APPLICATION LIMITS FOR CLASSICAL FOURIER AND WAVE HEAT CONDUCTION EQUATIONS FOR METALS ON THE BASIS OF ANALYTICAL SOLUTION AND CALCULATED TEMPERATURE DISTRIBUTION IN CASE OF GIANT HEAT PULSE

Abstract

The paper presents the solution of the wave-type heat conduction equation considered in the case of uniform heat flux absorption by the solid surface. The solution of the hyperbolic equation for the model of heat flux relaxation as well as non-relaxation heat flux have been compared with the Fourier equation. On the basis of analytical solutions some temperature profiles have been calculated for the given metal and the assumed value of relaxation time t_r= 10⁻¹¹ s and the heat flux value typical for great power lasers. It has been found out that for time values t > 100 t_r no measurable differences in temperature profiles calculated from wave and Fourier equations occured. It has been assartained that temperature profiles near the surface calculated from Fourier equation range between temperature profiles determinated from the wave equation with regard and with no regard to the relaxation of heat flux.