An integral approximate solution to ablation of a two-layer composite with a temporal gaussian heat flux

Ablation is the most common approach for thermal management for reentry of the spacecraft to the atmosphere. An analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented in this paper. The problem is divided into five stages and the temperature distributions in both layers in the five stages are obtained using an integral approximate method. The locations of ablation interface, thermal penetration depth, and ablation rate are obtained and the effects of Stefan number, subcooling parameter, thickness of the ablative material, and ratio of thermal diffusivities between two materials are investigated.