Modelling boundary and nonlinear effects in porous media flow

We consider the problem of employing a Brinkman–Forchheimer system to model flow in a porous medium when Newton cooling conditions are appropriate at the boundary of the body. Specifically it is shown that the solution depends continuously on the Forchheimer coefficient and on the coefficient in the Newton cooling law at the boundary. Since we are dealing with non-slow flow rates and a porosity which is close to one we employ the Brinkman–Forchheimer equations and this leads to a second order differential inequality in the analysis as opposed to the first order one often found.