Thermal convection in a horizontal porous layer with internal heat sources
Abstract
A numerical method is used to derive steady solutions to the finite-amplitude thermal convection in a horizontally infinite layer of porous material saturated with fluid and heated from within by a uniform distribution of heat sources. Three steady flows are analyzed: down-hexagons, up-hexagons, and two dimensional rolls. The stability of the solutions with respect to small disturbances is examined. It is found that the down-hexagons are stable for Rayleigh numbers R up to eight times the critical Rayleigh number (Rc), and that up-hexagons are unstable for all R values. The two-dimensional rolls are stable for Rayleigh number between 3Rc and 7Rc.
- Publication:
-
International Journal of Heat and Mass Transfer
- Pub Date:
- October 1977
- DOI:
- 10.1016/0017-9310(77)90189-2
- Bibcode:
- 1977IJHMT..20.1045T
- Keywords:
-
- Convective Heat Transfer;
- Flow Stability;
- Heat Sources;
- Numerical Analysis;
- Porous Boundary Layer Control;
- Temperature Gradients;
- Boussinesq Approximation;
- Cartesian Coordinates;
- Newton-Raphson Method;
- Nusselt Number;
- Rayleigh Number;
- Thermal Conductivity;
- Vertical Distribution;
- Fluid Mechanics and Heat Transfer