Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil
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.