Steady state free thermal convection of liquid in a saturated permeable medium
- 1 January 1957
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 2 (3), 273-285
- https://doi.org/10.1017/s0022112057000129
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.Keywords
This publication has 1 reference indexed in Scilit:
- LVIII.A theory of the viscosity of liquids.—Part IIThe London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1934