Natural convection in a vertical porous cavity: A numerical study for Brinkman-extended Darcy formulation
- Univ. de Nantes (France)
- Columbia Univ., New York, NY (United States)
A dimensional analysis of the Brinkman-extended Darcy formulation, which includes the transport and viscous terms, leads to four governing parameters for steady-state natural convection in a vertical porous cavity. They are: Rayleigh number, Darcy number, diffusion parameter {Omega}, and aspect ratio. Numerical results for 0 {le} Da {le} 10{sup {minus}1}, 10 {le} Ra* {le} 5 {times} 10{sup 3}, and A = 1 and 5, indicate that the temperature and velocity fields are significantly modified, the flow regimes are delayed, and the heat transfer rate is decreased when the Darcy number is increased beyond 10{sup {minus}5} for fixed Ra{sup {asterisk}} and A. The slope of the In (Nu) versus In (Ra*) curve in the boundary layer regime decreases from 0.53 at Da = 0 to 0.264 at Da = 10{sup {minus}1} when A = 5. The contribution of the transport term increases with {Omega}, Da, and Ra*, but the effect on the overall heat transfer is insignificant. However, the problem becomes ill formulated at high values of these parameters and may require the consideration of Forchheimer modifications. A scale analysis is also presented to show that the inertia term is of a low order of magnitude in comparison with the viscous term at high Prandtl numbers.
- OSTI ID:
- 6106161
- Journal Information:
- Journal of Heat Transfer (Transactions of the ASME (American Society of Mechanical Engineers), Series C); (United States), Vol. 109:3; ISSN 0022-1481
- Country of Publication:
- United States
- Language:
- English
Similar Records
Numerical study of forced convection of a power-law fluid in a porous channel
Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media