TY - JOUR
ID - 1872
TI - Asymptotic Approach to the Generalized Brinkman’s Equation with Pressure-Dependent Viscosity and Drag Coefﬁcient
JO - Journal of Applied Fluid Mechanics
JA - JAFM
LA - en
SN - 1735-3572
AU - Pažanin, I.
AU - Pereira, M. C.
AU - Suárez-Grau, F. J.
AD - Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
AD - Departamento de Matemática Aplicada, Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil
AD - Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Avenida Reina Mercedes S/N, 41012 Sevilla, Spain
Y1 - 2016
PY - 2016
VL - 9
IS - 6
SP - 3101
EP - 3107
KW - Brinkman’s equation
KW - dependent viscosity
KW - Pressure
KW - dependent drag coefﬁcient
KW - Transformed pressure
KW - Asymptotic analysis
DO - 10.29252/jafm.09.06.25756
N2 - 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.
UR - https://www.jafmonline.net/article_1872.html
L1 - https://www.jafmonline.net/article_1872_3545fb4abeaba226cc181c808ca29878.pdf
ER -