Presently, there is little information, concerning the heat shield systems, and this information is not completely reliable to use in so many cases. For example, the precise calculation can not be done for various materials. In addition, the real scale test has two disadvantages: high cost and low flexibility, and for each case, we must perform a new test. Hence, using a numerical modeling program that calculates the surface recession rate and interior temperature distribution is necessary. Also, the numerical solution of governing equation for non-charring material ablation is presented in order to anticipate the recession rate and the heat response of non-charring heat shields. The governing equation is nonlinear and the Newton-Rafson method along with TDMA algorithm(Thomas algorithm) is used to solve this nonlinear equation system. Using Newton- Rafson method for solving the governing equation is one of the advantages of the solving method because this method is 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.

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