Thermal Wave Propagation Phenomena in Thin Solid Films with Temperature-Dependent Thermal Conductivity
Shuichi Torii and Wen-Jei Yang
A numerical study is performed on the effect of temperature-dependent thermal conductivity on the wave nature of thermal propagation in a very thin film subjected to a symmetrical temperature change on both sides. The non-Fourier, hyperbolic heat conduction equation is solved by a numerical technique based on MacCormak’s predictor-corrector scheme. Consideration is given to the time history of heat transfer behavior before and after symmetrical collision of wave fronts from two sides of a film. It is disclosed that (i) in transient heat conduction, a heat pulse is transported as a wave in the film, and a sudden heating on both sides of the extremely thin film causes temperature overshoot within a very short period of time, and (ii) the thermal wave propagation speed of the solid medium with temperature-dependent thermal conductivity can be either lower or higher than that at constant thermal conductivity, depending upon whether the associated temperature coefficient is positive or negative. This effect of temperature-dependent thermal conductivity on the thermal wave propagation speed increases with decreasing film thickness.