AN APPROACH TO CONVERGENCE OF KINETIC-THEORY TO FOURIER THEORY IN RELATION TO LASER-HEATING PROCESS

Fourier theory may be derived from analytical considerations of the he at transfer process in a substance and neglecting of higher order term s in Fourier analysis becomes important at high input power fluxes. It is apparent from the previous work that the kinetic theory equations governing the heat conduction process are more general than the Fourie r equation. The special case may exist where the kinetic theory soluti ons converge to solutions extracted from the Fourier analysis. Consequ ently, research into the convergence of kinetic theory approach to Fou rier analysis becomes necessary. To achieve this, the special case in which local thermal equilibrium is assumed to exist between the electr ons and atoms at any section on the surface region of the solid substa nce is studied in the present work, providing that the study does not allow the existence of phase changes. For this purpose, an analytical approach is introduced and a computer solution of the reduced integral equations is obtained. It is found that the solutions of electron kin etic theory equations based on the assumption of existence of thermal equilibrium between electrons and atoms are identical with those obtai ned from Fourier theory.