### A comprehensive study on the efficiency of three different types of the variable metric method in determining the unknown Rocket inner heat flux

#### Abstract

**In this paper, the unknown heat flux is estimated with Davidon-Fletcher-Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS) and Symmetric Rank-one (SR1) version of variable metric method (VMM). The numerical techniques used in this study solved the inverse problems with various boundary and environmental conditions very efficiently. The results shows the sensitivity of measurement errors and different parameter including changes of slope and angle which can be functions of an unknown parameter. Further, the speed of convergence is assessed and the convergence behavior is found. The accuracy of results show that this study is a powerful reference for comparing results obtained based on the three proposed techniques. The solution procedure introduced a general cheap and fast method which can be used for the inverse heat conduction problem in rocket nuzzle and same heat conduction, radiation and convection problems.**

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