An inverse analysis for determination of space-dependent heat flux in heat conduction problems in the presence of variable thermal conductivity

Abstract

This article presents an inverse problem of determination of a space-dependent heat flux in steady-state heat conduction problems. The thermal conductivity of a heat conducting body depends on the temperature distribution over the body. In this study, the simulated measured temperature distribution on part of the boundary is related to the variable heat flux imposed on a different part of the boundary through incorporating the variable thermal conductivity components into the sensitivity coefficients. To do so, a body-fitted grid generation technique is used to mesh the two-dimensional irregular body and solve the direct heat conduction problem. An efficient, accurate, robust, and easy to implement method is presented to compute the sensitivity coefficients through derived expressions. Novelty of the study is twofold: (1) Boundary-fitted grid-based sensitivity analysis in which all sensitivities can be obtained in only one direct solution (at each iteration), irrespective of the number of unknown parameters, and (2) the way the measured temperatures on part of boundary are related to a variable heat flux applied on another part of boundary through components of a variable thermal conductivity. The conjugate gradient method along with the discrepancy principle is used in the inverse analysis to minimize the objective function and achieve the desired solution.