On the solvability of the Brinkman-Forchheimer-extended Darcy equation

The nonlinear Brinkman-Forchheimer-extended Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with nonconstant porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy's range.