含对流与蒸发表面的有限厚度材料的双曲型热传导分析

HYPERBOLIC HEAT CONDUCTION IN A FINITE MEDIUM WITH CONVECTIVE AND EVAPORATION BOUNDARIES

本文对于含有对流与蒸发表面的有限厚度材料，在遭受一脉冲表面热流作用时的双曲型热传导进行了分析，采用热势函数描述的双曲型热传导方程来描述该问题，并用有限差分法进行数值求解．同时，本文还就表面对流与蒸发对材料表面与内部瞬态温度变化的影响以及材料双曲型热传导对表面蒸发的影响进行了分析．

This paper investigated the hyperbolic heat conduction in a finite medium with convective and evaporative surface and a pulsed heat flux prescribed on its surface. Because the derivation of the step change in surface heat flux is a delta function, it is difficult to deal with when a numerical solution is needed. So a new formulation of hyperbolic heat conduction based on a scalar field called thermal potential is employed to describe this problem and the numerical solution is obtained using FDM method. It can be seen that the present method is practical from the comparison between the analytical solution and numerical results for the hyperbolic heat conduction in the finite medium with no convection and evaporation on it surface. The effect of surface convection and evaporation on the transient propagation of temperature in the materials and the effect of hyperbolic heat conduction on the surface evaporation are also analyzed.