Two-dimensional inverse heat conduction problem of source strength estimation in cylindrical rods

The radial and circumferential (azimuthal) transient dependence of the strength of a volumetric heat source in a cylindrical rod is estimated with Alifanov's iterative regularization method. This inverse problem is solved as an optimization problem in which a squared residue functional is minimized with the conjugate gradient method. A sensitivity problem is used in the determination of the step size in the direction of descent, while an adjoint problem is solved to determine the gradient. In order to examine the accuracy of estimations, two test cases are considered, one with a radial and timewise dependence and the second with radial, azimuthal as well as timewise dependence. The effects of number of sensors and measurement errors are investigated.