Research On Nonlinear Inverse Heat Conduction Problems

This article mainly researches on the nonlinear inverse heat conduction problems. In applied problems, unknown properties of a material are often to be determined. Especially the material is not homogeneous or piecewise-homogeneous, and the properties of material depend on space and temperature, which are to be researched in this paper. Firstly, because temperature depends on space and time, we can transfer nonlinear problems into linear problems. We use the central.difference derivative to discrete the equation and the boundary conditions in uniform, and use marching method to obtain iterative equations which is a direct problem when a guessed value of the thermal conductivity given. Accordingly, we can get the temperature of the grid nodes. Secondly, we use least square method to determine the thermal conductivity, which depends on space and time. First-order Taylor approximate expansion of the first-order partial derivatives of the error function ,then get a Newton iterative format. Two standards to judge the convergence of Newton iterative format:solution estimated criterion and the max number of iterative criteria.Inverse problems are often ill-posed, which need to be regularized. In this paper, we choose generalized cross check (GCV) criteria to determine the regular parameters and the Tikhonov regularization method to solve the ill-posed problem. Finally, we obtain the thermal conductivity dependent on space and temperature according to that dependent on space and time. Numerical simulations show that the results have a good approximation effect.