Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefficient


1 Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

2 Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil

3 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Avenida Reina Mercedes S/N, 41012 Sevilla, Spain


In this paper we investigate the fluid flow through a thin (or long) channel filled with a fluid saturated porous medium. We are motivated by some important applications of the porous medium flow in which the viscosity of fluids can change significantly with pressure. In view of that, we consider the generalized Brinkman’s equation which takes into account the exponential dependence of the viscosity and the drag coefficient on the pressure. We propose an approach using the concept of the transformed pressure combined with the asymptotic analysis with respect to the thickness of the channel. As a result, we derive the asymptotic solution in the explicit form and compare it with the solution of the standard Brinkman’s model with constant viscosity. To our knowledge, such analysis cannot be found in the existing literature and, thus, we believe that the provided result could improve the known engineering practice.