Determination of a heat source in porous medium with convective mass diffusion by an inverse method

A formulation is given of the inverse natural convection problem by conjugate gradient with adjoint equations in a porous medium with mass diffusion for the determination, from temperature measurements by sensors located within the medium, of an unknown volumetric heat source which is a function of the solute concentration. The direct, sensitivity and adjoint set of equations are derived for a Boussinesq fluid, over an arbitrary domain in two dimensions. Solutions by control volumes are presented for a square enclosure subjected to known temperature and concentration boundary conditions, assuming a source term depending on average vertical solute concentration. Reasonably accurate solutions are obtained at least up to Ra=10^5 with the source models considered, for Lewis numbers ranging from 0.1 to 10. Noisy data solutions are regularized by stopping the iterations according to the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced.