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TECHNICAL BRIEFS

On the Use of the Fully Compressible Navier-Stokes Equations for the Steady-State Solution of Natural Convection Problems in Closed Cavities

[+] Author and Article Information
Sandip Mazumder

Department of Mechanical Engineering, The Ohio State University, E410 Scott Laboratory, 201 W. 19th Avenue, Columbus, OH 43210mazumder.2@osu.edu

J. Heat Transfer 129(3), 387-390 (Jun 15, 2006) (4 pages) doi:10.1115/1.2430726 History: Received December 21, 2005; Revised June 15, 2006

The steady-state compressible form of the Navier-Stokes equations, along with no-slip boundary conditions on walls, represents a boundary value problem. In closed heated cavities, these equations are incapable of preserving the initial mass of the cavity and predicting the pressure rise. A simple strategy to adjust the reference pressure in the system is presented and demonstrated. The strategy is similar to solving the transient form of the governing equations, but completely eliminates truncation errors associated with temporal discretization of the transient terms. Results exhibit good agreement with previous reports. Additional results are shown to highlight differences between the fully compressible formulation and the Boussinesq approximation.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flowchart of the SIMPLE algorithm with the proposed modification to update the reference pressure highlighted in gray

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Figure 2

Error in local Nusselt numbers at the hot wall, defined as (Nucompressible−NuBoussinesq)×100∕Nucompressible

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Figure 3

Predicted temperature and flow distributions with and without the Boussinesq approximation for RaL=3×105(Th−Tc=1565.9K). The velocity vectors have been set to uniform size and plotted at intervals of four grid points to better depict the flow pattern.

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Figure 4

Density distributions without the Boussinesq approximation for RaL=3×105(Th−Tc=1565.9K)

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