Presently there is a little information that relates to heat shield systems. Also this information is not certain in so many cases. The main reason is that accurate calculations for measuring the sacrificing rate of various materials have not been obtained yet. In addition, the real scale test has two disadvantages which are: 1) high cost and 2) low flexibility, and for each case a new test must be performed. So having a reliable numerical program that calculates the surface recession rate and interior temperature history is necessary. In this study numerical solution of governing equations for charring material ablation are presented in order to anticipate the recession rate and the heat response of charring heat shields. Thermodynamic properties , ,k changes relative to the temperature accompany the nonlinear nature of the governing equations and 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 the solving method because it is relatively simple and it can be easily generalized to more difficult problems. In Newton-Raphson method the nonlinear equations complexity is not a dominating effect because by differentiation relative to every independent variable the structural coefficients of the governing equations system are obtained. Moreover the most important feature of the obtained equation system is that we can obtain the value of every independent variable in each iteration and by adding this amount of change in every variable to the previous one, the new variable value appears in governing equation structural coefficients and it continues up to complete convergence. The obtained results are compared with reliable sources in order to examine the accuracy of compiling code.

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