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Research Papers: Porous Media

# Natural Convection in an Anisotropic Porous Enclosure Due to Nonuniform Heating From the Bottom Wall

[+] Author and Article Information
Ashok Kumar

Department of Mathematics, Indian Institute of Technology, Roorkee 247667, India

P. Bera1

Department of Mathematics, Indian Institute of Technology, Roorkee 247667, Indiapberafma@iitr.ernet.in

1

Corresponding author.

J. Heat Transfer 131(7), 072601 (May 04, 2009) (13 pages) doi:10.1115/1.3089545 History: Received March 26, 2008; Revised December 03, 2008; Published May 04, 2009

## Abstract

A comprehensive numerical investigation on the natural convection in a hydrodynamically anisotropic porous enclosure is presented. The flow is due to nonuniformly heated bottom wall and maintenance of constant temperature at cold vertical walls along with adiabatic top wall. Brinkman-extended non-Darcy model, including material derivative, is considered. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been adopted to solve numerically the governing conservative equations of mass, momentum, and energy by using a stream-function vorticity formulation. Special attention is given to understand the effect of anisotropic parameters on the heat transfer rate as well as flow configurations. The numerical experiments show that in the case of isotropic porous enclosure, the maximum rates of bottom as well as side heat transfers ($Nub$ and $Nus$) take place at the aspect ratio, $A$, of the enclosure equal to 1, which is, in general, not true in the case of anisotropic porous enclosures. The flow in the enclosure is governed by two different types of convective cells: rotating (i) clockwise and (ii) anticlockwise. Based on the value of media permeability as well as orientation angle, in the anisotropic case, one of the cells will dominate the other. In contrast to isotropic porous media, enhancement of flow convection in the anisotropic porous enclosure does not mean increasing the side heat transfer rate always. Furthermore, the results show that anisotropy causes significant changes in the bottom as well as side average Nusselt numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow dynamics and temperature profile and consequently on the heat transfer rates.

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## Figures

Figure 2

Variation in average Nusselt numbers (Nub as well as Nus) as a function of aspect ratio for different values of Ra: (a) K∗=1, (b) K∗=0.5, and (c) K∗=5 when Da=10−4 and ϕ=45 deg

Figure 3

Effect of aspect ratio on streamlines: (a) K∗=0.5 and (b) K∗=5 for Ra=106, Da=10−4, and ϕ=45 deg

Figure 4

Effect of aspect ratio on temperature: (a) K∗=0.5 and (b) K∗=5 for Ra=106, Da=10−4, and ϕ=45 deg

Figure 5

Variation in average Nusselt numbers (Nub as well as Nus) as a function of orientation angle (ϕ) for different values of Ra: (a) K∗=0.2 and (b) K∗=5 when Da=10−4 and A=1.5

Figure 6

Effect of orientation angle on streamlines: (a) K∗=5 and (b) K∗=0.2 for Ra=106, Da=10−4, and A=1.5

Figure 7

Dependence of the (a) average bottom Nusselt number and (b) side Nusselt number on the permeability ratio for different values of Ra when Da=10−4, ϕ=45 deg, and A=1.5

Figure 8

Effect of permeability ratio (K∗) on streamlines at Da=10−4, A=1.5, and ϕ=45 deg

Figure 9

Dependence of the (a) average bottom Nusselt number and (b) side Nusselt number on the Darcy number for different values of K∗ when Ra=106, ϕ=45 deg, and A=1.5

Figure 10

Variation in average Nusselt numbers (Nub as well as Nus) as a function of Rayleigh number for different values of Da: (a) K∗=0.2 and (b) K∗=5 when ϕ=45 deg and A=1.5

Figure 11

Contour plots of streamlines and temperature: (a) Ra=105 and (b) Ra=3×105 when K∗=0.2, ϕ=45 deg, and A=1.5

Figure 1

Schematic of the dimensional physical problem considered

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