A general space marching algorithm for the solution of two-dimensional boundary inverse heat conduction problems

A numerical procedure for solving two-dimensional boundary inverse heat conduction problems is presented in this article. A boundary condition (surface temperatures and surface heat fluxes) of a body is estimated. The major advantage of this work is that the solution can be obtained using limited information about the problem. Another advantage is that the formulation of the problem is completely general. The proposed procedure does not need any stabilization method when exact data are used for solving the problem. A digital filter method is used to stabilize the inverse algorithm by smoothing the real (noisy) data. Then, we apply the control-volume formulation for the filtered data. Accuracy and stability of the solution method is verified by utilizing a solution of a direct problem. The influence on the numerical solution of the time step, digital filter coefficients, and measurement errors is also considered.