Numerical study of heat conduction with a chemical reaction at the moving frontal surface for a graphite plate

A physical and mathematical model for a diffusion-controlled Stefan problem with chemical reaction at moving boundary was established for a graphite heat shield plate withstanding aerodynamic heating. With introduction of two dimensionless variables of moving interface location and spatial coordinates, the problem was numerically studied at a fixed grid computational domain with finite volume method. The temperature, net heat flux, and the location of moving frontal surface and the internal temperature distribution inside the plate were predicted and discussed at different input aerodynamic heating heat fluxes. The complete evolution included initial and developed stages with a turning point F_O number.