Inverse heat conduction problem of determining time-dependent heat transfer coefficient

Abstract

The time-dependent Biot number in a one-dimensional linear heat conduction problem is obtained from the solutions of the inverse heat conduction problems of determining boundary heat flux and boundary temperature. The sequential function specification method with the linear basis function and the assumption of linearly varying future boundary heat flux or temperature components is used to solve the inverse problem. The expression for Biot number is found to be a nonlinear function of measured temperatures. The variance in input data is shown to cause variance and nonlinear bias in estimated Biot number. The method presented offers three tunable parameters that may be used to improve the quality of the solution.