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Asymptotic approach to the generalized Brinkman’s equation with pressure dependent viscosity and drag coefficient

 

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Opened Access Asymptotic approach to the generalized Brinkman’s equation with pressure dependent viscosity and drag coefficient
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Author: Pažanin, Igor
Corrêa Pereira, Marcone
Suárez Grau, Francisco Javier
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2016
Published in: Journal of Applied Fluid Mechanics, 9 (6), 3101-3107.
Document type: Article
Abstract: 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.
Cite: Pažanin, I., Corrêa Pereira, M. y Suárez Grau, F.J. (2016). Asymptotic approach to the generalized Brinkman’s equation with pressure dependent viscosity and drag coefficient. Journal of Applied Fluid Mechanics, 9 (6), 3101-3107.
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URI: http://hdl.handle.net/11441/53704

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