A second order approximation to natural convection in a square cavity
Abstract
A second order numerical model is developed for fluid flow driven by convective forces within a heated, closed cavity. The model is defined in terms of convection within a square, with account taken of the stream, vorticity, and normalized temperature functions and the boundary conditions. Finite difference equations are formulated for boundary vorticities and the stream values on the inner boundary. A rectangular array of nodes is established and initial values of the stream, vorticity, and temperature functions are assigned to each node. The method has yielded converged solutions for Rayleigh numbers up to 100,000 and Prandtl numbers as low as 0.0001. The technique is considered useful for problems in reactor insulation, cooling radioactive waste containers, and in solar collectors.
- Publication:
-
Numerical Methods in Laminar and Turbulent Flow
- Pub Date:
- 1983
- Bibcode:
- 1983nmlt.proc..764S
- Keywords:
-
- Approximation;
- Cavities;
- Computational Fluid Dynamics;
- Flow Geometry;
- Free Convection;
- Difference Equations;
- Heat Transfer;
- Solar Collectors;
- Vortices;
- Fluid Mechanics and Heat Transfer