Inverse estimation of front surface temperature of a plate with laser heating and convection-radiation cooling

The conjugate gradient method (CGM) is an efficient iterative regularization technique for solution of the inverse heat conduction problem (IHCP). However, most of the existing CGM schemes deal with linear boundary conditions and constant thermophysical properties. Little attention has been paid to formulate the CGM with radiation boundary condition and temperature-dependent thermophysical properties. In this study, a nonlinear CGM scheme is formulated to recover the front surface heating condition of a 3-D object, based on the temperature measurements at back surface. The 3-D object is subjected to a high-intensity Gaussian laser beam heating on the front surface and a combined radiation and convection boundary condition on the back surface. The derivations of the direct problem, adjoint problem and sensitivity problem are presented in detail. The results are presented for two materials and excellent agreement between the inverse and exact solutions are demonstrated.