Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry

A numerical algorithm is proposed for solving a three-dimensional unsteady nonlinear inverse heat conduction problem of estimating the boundary conditions at the heated surface of a solid. In this study, the geometrical form of the solid is a finite hollow half-cylinder. As additional information, needed to solve the inverse problem under study, we use both temperature measurements at the internal surface (case of the use of thermo-couples or an infrared camera) inside the half-cylinder (case of the use of thermo-couples) and those at the heated surface (case of the use of an infrared camera). The iterative regularization method is used to build the numerical algorithm. The method is based on the residual functional minimization by using the unconstrained conjugate gradient method with the regularizing discrepancy principle as a stopping criterion of the iterative processes. The unknown function of three variables is sought for as a grid function.