a.b rahimi - Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. ۹۱۷۷۵- ۱۱۱۱, Mashhad, Iran
h mohammadiun - Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. ۹۱۷۷۵- ۱۱۱۱, Mashhad, Iran

Accurate calculations for measuring the sacrificing rate of various materials in heat shield systems have not been obtained yet. So having a reliable numerical program that calculates thesurface recession rate and interior temperature history is necessary. In this study numerical solutionof governing equations for charring material ablation are presented. Thermodynamic properties  , p C , k changes relative to the temperature accompany the nonlinear nature of the governing equations. The Newton-Raphson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Raphson method is one of the advantages of solving method because it is relatively simple and it can be easily generalized to more difficult problems. The obtained results are compared with reliable sources in order to examine the accuracy of compiling code

Ablation and surface recession rates; Interior temperature history; Charring material ablation; Newton Raphson; Numerical method