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Convection in an internally heated layer

Published online by Cambridge University Press:  29 March 2006

R. Thirlby
R. Thirlby
Affiliation:
School of Mathematics, University of Newcastle upon Tyne
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Abstract

A numerical study has been made of steady laminar convection in an infinite horizontal layer of fluid, bounded above by a rigid plate held at constant temperature, and below by a thermal insulator. The fluid is heated by a uniform distribution of heat sources. Recent methods for the solution of the Navier-Stokes equations by finite differences are discussed, and the results of integrations in two and three space dimensions and time are presented in an attempt to determine the planform and other flow properties as functions of the Rayleigh and Prandtl numbers.

These results are compared with a preliminary study by Roberts (1967) using a mean-field equation approach and with experimental observations by Tritton & Zarraga (1967) and Hooper (private communication).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 44 , Issue 4 , 16 December 1970 , pp. 673 - 693
Copyright
© 1970 Cambridge University Press

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References

Busse, F. 1967a J. Fluid Mech. 30, 62.
Busse, F. 1967b J. Maths. Phys. 46, 14.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Chorin, A. 1967a J. Comp. Phys. 2, 1.
Chorin, A. 1967b Bull. Am. Math. Soc. 73, 92.
Debler, W. R. 1966 J. Fluid Mech. 24, 16.
Douglas, J. 1962 Numerische Math. 4, 4.
Ehrenzweig, P. 1969 Quart. J. Mech. App. Math. 22, 35.
Fromm, J. E. 1965 Phys. Fluids, 8, 1757.
Harlow, F. H. & Welch, J. E. 1965 Phys. Fluids, 8, 2182.
Jakeman, E., Hurle, D. T. J. & Pike, R. E. 1967 Proc. Roy. Soc. A 296, 469.
Krishnamurti, R. 1969 Geophys. Fluid Dynamics Inst. Florida State Univ. Tech. Report no. 14.
Palm, E. 1960 J. Fluid Mech. 8, 18.
Peaceman, D. W. & Rachford, H. H. 1955 J. Soc. Industr. Math. 3, 2.
Pearson, J. R. A. 1958 J. Fluid Mech. 4, 48.
Pearson, J. R. A. 1964 Sperry Rand Research Centre, Sudbury, Mass. Report no. SRRC-RR-64–17.
Plows, W. H. 1968 Phys. Fluids, 11 1593.
Roberts, P. H. 1967 J. Fluid Mech. 30, 3.
Rossby, H. T. 1969 J. Fluid Mech. 36, 30.
Samarskií, A. A. 1963 U.S.S.R. Comp. Math. and Math. Phys. 5, 89.
Schlüter, A., Lortz, D. & Busse, F. 1965 J. Fluid Mech. 23, 12.
Segel, L. A. & Stuart, J. T. 1962 J. Fluid Mech. 13, 28.
Somerville, R. C. J. 1969 To appear.
Stuart, J. T. 1958 J. Fluid Mech. 4, 1.
Tritton, D. J. & Zarraga, M. N. 1967 J. Fluid Mech. 30, 2.