Inverse determination of a heat source from a solute concentration generation model in porous medium

The conjugate gradient method with adjoint equations is applied to the natural convection problem in a porous medium for the determination of an unknown heat source which is dependent on a solute concentration generation rate. The direct, sensitivity and adjoint equations are given for a Boussinesq fluid, over an arbitrary domain in two dimensions. Solutions by control volumes are presented for a square enclosure under known temperature and concentration boundary conditions, assuming a source term proportional to the vertical average generation rate of a solute concentration governed by a Monod model. Reasonably accurate solutions are obtained at least up to Ra=10⁵.