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.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 4

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

Grahic Jump Location
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.

Grahic Jump Location
Figure 2

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

Grahic Jump Location
Figure 1

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



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In