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RESEARCH PAPERS: Applications

# A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity

[+] Author and Article Information
P. Kumar

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, Indiadpradeep@iitk.ac.in

V. Eswaran1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, Indiaeswar@iitk.ac.in

1

Corresponding author.

J. Heat Transfer 132(2), 023501 (Nov 30, 2009) (13 pages) doi:10.1115/1.4000180 History: Received September 30, 2008; Revised August 15, 2009; Published November 30, 2009; Online November 30, 2009

## Abstract

This article presents a numerical simulation of combined radiation and natural convection in a three-dimensional differentially heated rectangular cavity with two opposite side walls kept at a temperature ratio $Th/Tc=2.0$ and $Tc=500 K$, with others walls insulated. A non-Boussinesq variable density approach is used to incorporate density changes due to temperature variation. The Navier–Stokes (NSE), temperature, as well as the radiative transfer (RTE) equations are solved numerically by a finite volume method, with constant thermophysical fluid properties (except density) for Rayleigh number $Ra=105$ and Prandtl number $Pr=0.71$. The convective, radiative, and total heat transfer on the isothermal and adiabatic walls is studied along with the flow phenomena. The results reveal an extraordinarily complex flow field, wherein, along with the main flow, many secondary flow regions and singular points exist at the different planes and are affected by the optical properties of the fluid. The heat transfer decreases with increase in optical thickness and the pure convection Nusselt number is approached as the optical thickness $τ>100$, but with substantially different velocity field. The wall emissivity has a strong influence on the heat transfer but the scattering albedo does not.

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## Figures

Figure 1

The geometry of the three-dimensional natural cavity problem

Figure 2

Hexahedral cell

Figure 3

Angular discretization

Figure 4

Temperature distribution at y=1 m

Figure 5

Distribution of isosurfaces of temperature for (a) pure convection, (b) τ=0.0 (transparent medium), (c) τ=1.0, and (d) τ=10.0

Figure 6

Distribution of isosurfaces of density for (a) pure convection, (b) τ=0.0 (transparent medium), (c) τ=1.0, and (d) τ=10.0

Figure 7

Effect of optical thickness on the local convective and radiative Nusselt numbers on the cold wall

Figure 8

The vertical line-averaged convective and radiative Nusselt numbers at the cold wall for various values of optical thickness

Figure 9

Effect of optical thickness on the total Nusselt number at the cold wall

Figure 10

The vertically line-averaged total Nusselt number at the cold wall for various values of optical thickness

Figure 11

Effect of optical thickness on the local convective and radiative Nusselt numbers on the bottom wall

Figure 12

Effect of optical thickness on the local convective and radiative Nusselt numbers on the top wall

Figure 13

Effect of optical thickness on the line-averaged convective and radiative Nusselt numbers on the bottom wall

Figure 14

Effect of optical thickness on the line-averaged convective and radiative Nusselt numbers on the top wall

Figure 15

Projection of streamlines and contours of nondimensionalized normal velocity on the X-plane for the pure convection for Ra=105 and Pr=0.71: (a) X∗=0.01, (b) X∗=0.25, (c) X∗=0.35, (d) X∗=0.50, (e) X∗=0.65, and (f) X∗=0.75

Figure 16

Projection of streamlines and contours of nondimensionalized normal velocity on the Z-plane for the pure convection for Ra=105 and Pr=0.71

Figure 17

Projection of streamlines and contours of nondimensionalized normal velocity on the Y-plane for the transparent medium for Ra=105 and Pr=0.71

Figure 18

Projection of streamlines and contours of nondimensionalized normal velocity on the Z-plane for the transparent medium for Ra=105 and Pr=0.71

Figure 19

Projection of streamlines and contours of nondimensionalized normal velocity on the Z-plane for the radiative medium of optical thickness τ=10.0 for Ra=105 and Pr=0.71

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