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Research Papers: Porous Media

Mixed Convection in a Vertical Channel Containing Porous and Viscous Fluid Regions With Viscous Dissipation and Inertial Effects: A Perturbation Solution

[+] Author and Article Information
Mastaneh Hajipour

Department of Chemical and Petroleum Engineering,  Sharif University of Technology, P. O. Box 11155-9465, Tehran, Iranamolaeid@sharif.edu

Asghar Molaei Dehkordi1

Department of Chemical and Petroleum Engineering,  Sharif University of Technology, P. O. Box 11155-9465, Tehran, Iranamolaeid@sharif.edu

1

Corresponding author.

J. Heat Transfer 133(9), 092602 (Jul 27, 2011) (11 pages) doi:10.1115/1.4003969 History: Received September 12, 2010; Revised April 06, 2011; Published July 27, 2011; Online July 27, 2011

In this paper, combined forced and natural convection in a vertical channel containing both porous and viscous regions taking into account the influences of inertial force and viscous dissipation has been studied. In this regard, fully developed fluid flow in the porous region was modeled using the Brinkman–Forchheimer extended Darcy model. To solve governing equations of both the porous and viscous regions including thermal energy and momentum equations, a two-parameter perturbation method was applied. The velocity and temperature distributions of both the regions were obtained in terms of various parameters such as inertial force, Grashof, Reynolds, and Brinkman numbers, as well as various types of viscous dissipation models. In addition, numerical solution was conducted using finite difference method to compare the results. The predicted results clearly indicate that the type of viscous dissipation model has significant effect on the temperature and velocity distributions. The acquired knowledge in this study can be used by designers to control channel flow as suitable for a certain application.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configuration of the problem and its boundary conditions

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Figure 2

Dimensionless velocity profiles for different values of ɛ

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Figure 3

Dimensionless temperature profiles for different values of ɛ

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Figure 4

Dimensionless velocity profiles for different values of γ

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Figure 5

Dimensionless temperature profiles for different values of γ

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Figure 6

Dimensionless temperature profiles for different values of κ

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Figure 7

Dimensionless temperature profiles for different values of m

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Figure 8

Comparison of dimensionless velocity profiles for different values of GR

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Figure 9

Effect of Forchheimer number on the skin friction: (a) left wall and (b) right wall

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