Heat source estimation with the conjugate gradient method in inverse linear diffusive problems

摘要

In this work, we present the solution of a class of linear inverse heat conduction problems for the estimation of unknown heat source terms with no prior information for the functional forms of timewise and spatial dependence of the source stength by the conjugate gradient method with the gradient given by an adjoint problem. After describing the mathematical formulation of a general direct problem and the procedure for the solution of the inverse problem, we show applications to three transient heat transfer problems in nuclear engineering: a one-dimensional problem with fuel elements without cladding; a two-diemnsional problem also with fuel elements without cladding; and a one-dimensional problem considering the cladding.