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Steady state free thermal convection of liquid in a saturated permeable medium

Published online by Cambridge University Press:  28 March 2006

R. A. Wooding
R. A. Wooding
Affiliation:
Applied Mathematics Laboratory, Department of Scientific and Industrial Research, Wellington, New Zealand
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Abstract

The partial differential equations which describe steady flow of fluid in saturated homogeneous permeable solid material under non-isothermal conditions are stated. From these are derived the equations for flow of liquid (in particular, water) using suitable approximations and making use of empirical laws when necessary.

It is then postulated that the only ‘ponderomotive’ (i.e. massmoving) forces present are those due to thermal expansion effects. Free convection results. An approximate solution of the equations is attempted for plane flow by means of classical perturbation methods, the temperature and stream-function variables being represented by power series in a convection parameter proportional to the Rayleigh number.

A numberical example of the method, with boundary conditions based on a geothermal area at Wairakei, New Zealand, is given. The results show features which are in fair agreement with temperature measurements made in the area, and it appears that the convection parameter η is of the order of 10.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 2 , Issue 3 , May 1957 , pp. 273 - 285
Copyright
© 1957 Cambridge University Press

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