The numerical analysis of heat transfer by finite element method (FEM) has been used widely. It is usually assumed that the parameters relevant to the heat transfer process are accurately known. However, many of these parameters may vary in a random way in reality. The reliability of the heat transfer performance is needed to be evaluated. The paper introduces an accurate, efficient sensitivity analysis method to compute the FEM response with respect to input parameters. Combining this sensitivity analysis, first order reliability method (FORM) algorithm based stochastic finite element method (SFEM) method is used to evaluate the reliability of the limit state for heat conduction of a benchmark plate with input uncertainties.

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