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An experiment on free thermal convection of water in saturated permeable material

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

A small-scale experimental model has been constructed for the study of steady-state slow free convection of water in saturated sand. The convection field is confined between coaxial cylinders maintained at constant temperature difference, and the upper and lower boundaries consist of planes with thermal and fluid insulation. Measurements of the temperature distribution within the convection space have been obtained for average boundary temperature differences (T1 − T0) of (I) 18·40° A, (II) 32·70° A, and (III) 46·68° A. Theoretical temperature values predicted from perturbation theory have been fitted by least squares. The first-order estimates of η/(T1 − T0), where η is the convection parameter or modified Rayleigh number, do not differ significantly from a constant value (± 3% S. D.) for the three given values of T1 − T0, indicating good agreement between theoretical and experimental results. First-order estimates are made also of the temperature coefficient of thermal conductivity b of the sand-water mixture, and of the coefficient of radiation loss c at the upper insulated boundary, but these estimates are less reliable. Separate determinations of η/(T1 − T0), b, c by direct physical measurement are in good agreement with the least-squares estimates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 3 , Issue 6 , March 1958 , pp. 582 - 600
Copyright
© 1958 Cambridge University Press

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References

Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Chandrasekhar, S. 1943 Rev. Mod. Phys. 15, 1.
Muskat, M. 1937 The flow of Homogeneous Fluids Through Porous Media. Ann Arbor: Edwards.
National Research Council, U.S.A. 1929 International Critical Tables, Vol. 4. New York: McGraw-Hill.
Pearson, H. S. & Hartley, H. O. 1954 Biometrika Tables for Statisticians, Vol. 1. Cambridge University Press.
Rayleigh, Lord 1899 Phil. Mag. 47, 246.
Slichter, C. S. 1899 United States Geological Survey, 19th annual report, part 2, p. 295.
Wooding, R. A. 1957 J. Fluid Mech. 2, 273.