Component analysis of a steady inverse convection problem solution in a porous medium

A steady-state inverse free convection problem is solved by conjugate gradient and adjoint equations in a porous medium confined within a square enclosure subjected to an unknown heat flux on one side, and to isothermal and adiabatic conditions on the other sides. Numerical solutions for sinusoidal flux profiles are examined on the basis of a Fourier decomposition for Rayleigh numbers ranging from 0 to 104. Analytical perturbation results for the first iteration are provided, showing the initial effects of convection on the inverse solution. It is found that the problem involves scales of different magnitudes, slowing down convergence, mainly through the step size, as convection develops.