Solution of the inverse steady state convection problem in a porous medium by adjoint equations

The inverse free convection problem in a porous medium is solved by adjoint equaitons and conjugate gradient. A derivation of the set of adjoint equations in the steady case is provided. Numerical solutions are obtained for the case of a rectangular enclosure subjected to an unknown heat flux on one side, and to known conditions on the remaining sides. Results are presented for different flux profiles with a Rayleigh number ranging from 0 to 104 and the effect of noise in the input data is also examined.