The natural convection of water through permeable formations is an important phenomenon governing the behavior of geothermal aquifers. In such situations the temperature of the fluid can vary by amounts of the order of 250 K, over which range the viscosity of the water may decrease by as much as a factor of 10, and the coefficient of thermal expansion may increase by an even greater factor. Although previous studies have examined the effect of this behavior on the onset conditions at which natural convective flow in the medium first occurs, the actual flow patterns that will result from the convection of a fluid with such widely varying properties has not been reported. To this end, numerical methods of solution are applied to this problem and a visualization of the flows obtained. By solving in terms of both pressure and stream function instead of stream function alone, it was possible to maintain semiconservative properties of the numerical scheme. The convective motion is unstable (in two dimensions) at even moderate values of the Rayleigh number and exhibits a fluctuating convective state analogous to the case of a fluid with constant viscosity and coefficient of thermal expansion. In some cases the acceleration of the flow in certain areas due to the decrease in viscosity causes localized thermal instabilities.
Skip Nav Destination
Article navigation
Research Papers
Convection in a Porous Medium Heated from Below: The Effect of Temperature Dependent Viscosity and Thermal Expansion Coefficient
R. N. Horne,
R. N. Horne
Department of Petroleum Engineering, Stanford University, Stanford, Calif. 94305
Search for other works by this author on:
M. J. O’Sullivan
M. J. O’Sullivan
Department of Theoretical and Applied Mechanics, University of Auckland, New Zealand
Search for other works by this author on:
R. N. Horne
Department of Petroleum Engineering, Stanford University, Stanford, Calif. 94305
M. J. O’Sullivan
Department of Theoretical and Applied Mechanics, University of Auckland, New Zealand
J. Heat Transfer. Aug 1978, 100(3): 448-452 (5 pages)
Published Online: August 1, 1978
Article history
Received:
March 22, 1978
Online:
August 11, 2010
Citation
Horne, R. N., and O’Sullivan, M. J. (August 1, 1978). "Convection in a Porous Medium Heated from Below: The Effect of Temperature Dependent Viscosity and Thermal Expansion Coefficient." ASME. J. Heat Transfer. August 1978; 100(3): 448–452. https://doi.org/10.1115/1.3450829
Download citation file:
Get Email Alerts
Cited By
Surrogate Modeling-Based Analysis of Concentration Decay in Diffusion-Reaction Mass Transfer Problems
J. Heat Mass Transfer (June 2025)
External Conjugate Boiling On Channels. A Graetz Problem With Multiple Solutions
J. Heat Mass Transfer
Related Articles
Heatline Visualization of Natural Convection in a Porous Cavity Occupied by a Fluid With Temperature-Dependent Viscosity
J. Heat Transfer (January,2008)
On Natural Convective Heat Transfer in Vertical Channels With a Single Surface Mounted Heat-Flux Module
J. Heat Transfer (August,2003)
Visualization and Prediction of Natural Convection of Water Near Its Density Maximum in a Tall Rectangular Enclosure at High Rayleigh Numbers
J. Heat Transfer (February,2001)
Natural Convection of Viscoplastic Fluids in a Square Enclosure
J. Heat Transfer (December,2013)
Related Proceedings Papers
Related Chapters
Completing the Picture
Air Engines: The History, Science, and Reality of the Perfect Engine
Experimental Investigation of Ventilated Supercavitation Under Unsteady Conditions
Proceedings of the 10th International Symposium on Cavitation (CAV2018)
Compressive Deformation of Hot-Applied Rubberized Asphalt Waterproofing
Roofing Research and Standards Development: 10th Volume