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 $Tc=500\u2002K$, 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 $\tau >100$, 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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# A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity

P. Kumar,

P. Kumar

Department of Mechanical Engineering,

e-mail: dpradeep@iitk.ac.in
Indian Institute of Technology Kanpur

, Kanpur 208 016, India
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V. Eswaran

V. Eswaran

Department of Mechanical Engineering,

e-mail: eswar@iitk.ac.in
Indian Institute of Technology Kanpur

, Kanpur 208 016, India
Search for other works by this author on:

P. Kumar

Department of Mechanical Engineering,

Indian Institute of Technology Kanpur

, Kanpur 208 016, Indiae-mail: dpradeep@iitk.ac.in

V. Eswaran

Department of Mechanical Engineering,

Indian Institute of Technology Kanpur

, Kanpur 208 016, Indiae-mail: eswar@iitk.ac.in

*J. Heat Transfer*. Feb 2010, 132(2): 023501 (13 pages)

**Published Online:**November 30, 2009

Article history

Received:

September 30, 2008

Revised:

August 15, 2009

Online:

November 30, 2009

Published:

November 30, 2009

Citation

Kumar, P., and Eswaran, V. (November 30, 2009). "A Numerical Simulation of Combined Radiation and Natural Convection in a Differential Heated Cubic Cavity." ASME. *J. Heat Transfer*. February 2010; 132(2): 023501. https://doi.org/10.1115/1.4000180

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