A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

An analysis of inverse non-linear heat conduction with point or line distributed heat sources is presented. The contribution due to the loading vector coming from heat sources integrals are evaluated analytically. The inverse solution may be categorized into finding either the solution of the problem in the form of the intensity of the loading at a specific location, or the location and orientation of the generators assuming the intensity is known. The first category is an ill-posed problem and the solution to the second category may be found by an iterative search procedure. To regularize the solution to the first category, least-squares method is employed in conjunction with an addition of a regularization term. To find the solution to the second category a new and simple algorithm, called ‘A Good Neighbour’ is devised. For non-linear problems where the thermal conductivities are functions of the temperature, the Kirchhoff transformation is employed. The efficiency and accuracy of the proposed methods employed are explored through several examples.