We consider a low-aspect-ratio two-dimensional rectangular cavity, differentially heated with an arbitrarily large horizontal temperature difference. Steady-state results obtained from numerical solutions of the transient Navier-Stokes equations are given for air using the ideal gas law and Sutherland law transport properties. We clarify the different flow regimes possible by using numerical results for aspect ratios 0.025 ≤ A ≤ 1 and for Rayleigh numbers (based on height) 102 ≤ Ra ≤ 109. We present Nusselt numbers, and temperature and velocity distributions, and compare them with existing data. At high Ra in the Boussinesq limit we show the existence of weak secondary and tertiary flows in the core of the cavity. In addition we present novel solutions in the non-Boussinesq regime. We find that the classical parallel flow solution, accurate in the core of the cavity in the Boussinesq limit, does not exist when variable properties are introduced. For higher Rayleigh numbers, we generalize the well-known analytical boundary layer solution of Gill. The non-Boussinesq solutions show greatly reduced static pressure levels and lower critical Rayleigh numbers.
Skip Nav Destination
Article navigation
Research Papers
Natural Convection in Shallow Enclosures With Differentially Heated Endwalls
S. Paolucci,
S. Paolucci
Applied Mechanics Department, Sandia National Laboratories, Livermore, CA 94550
Search for other works by this author on:
D. R. Chenoweth
D. R. Chenoweth
Applied Mechanics Department, Sandia National Laboratories, Livermore, CA 94550
Search for other works by this author on:
S. Paolucci
Applied Mechanics Department, Sandia National Laboratories, Livermore, CA 94550
D. R. Chenoweth
Applied Mechanics Department, Sandia National Laboratories, Livermore, CA 94550
J. Heat Transfer. Aug 1988, 110(3): 625-634 (10 pages)
Published Online: August 1, 1988
Article history
Received:
February 6, 1987
Online:
October 20, 2009
Citation
Paolucci, S., and Chenoweth, D. R. (August 1, 1988). "Natural Convection in Shallow Enclosures With Differentially Heated Endwalls." ASME. J. Heat Transfer. August 1988; 110(3): 625–634. https://doi.org/10.1115/1.3250538
Download citation file:
Get Email Alerts
Cited By
Estimation of thermal emission from mixture of CO2 and H2O gases and fly-ash particles
J. Heat Mass Transfer
Non-Classical Heat Transfer and Recent Progress
J. Heat Mass Transfer
Related Articles
The Effect of Temperature Modulation on Natural Convection in a Horizontal Layer Heated From Below: High-Rayleigh-Number Experiments
J. Heat Transfer (August,1994)
Buoyancy-Driven Flow Transitions in Deep Cavities Heated From Below
J. Heat Transfer (August,2002)
Scaling of Natural Convection of an Inclined Flat Plate: Sudden Cooling Condition
J. Heat Transfer (April,2011)
Natural
Convection Measurements for a Concentric Spherical
Enclosure
J. Heat Transfer (June,2006)
Related Proceedings Papers
Related Chapters
VOCs Natural Convection in Partially Porous Cavity
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)
Finite Element Solution of Natural Convection Flow of a Nanofluid along a Vertical Flat Plate with Streamwise Sinusoidal Surface Temperature
International Conference on Computer and Electrical Engineering 4th (ICCEE 2011)
Dynamic Behavior of Pumping Systems
Pipeline Pumping and Compression Systems: A Practical Approach