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Three-dimensional natural convection in a box: a numerical study

Published online by Cambridge University Press:  12 April 2006

G. D. Mallinson  and
G. De Vahl Davis
G. D. Mallinson
Affiliation:
Department of Defence, Aeronautical Research Laboratories, Melbourne, Australia
G. De Vahl Davis
Affiliation:
Department of Defence, Aeronautical Research Laboratories, Melbourne, Australia
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Abstract

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 83 , Issue 1 , 1 November 1977 , pp. 1 - 31
Copyright
© 1977 Cambridge University Press

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References

Aziz, K. 1965 Ph.D. thesis, Rice University.
Batchelor, G. K. 1954 Quart. Appl. Math. 12, 209.
Bödewadt, U. T. 1940 Z. angew. Math. Mech. 20, 241.
Boussinesq, J. 1903 Théorie Analytique de la Chaleur, vol. 2, p. 172. Gauthier-Villars.
Brooks, R. G. & Probert, S. D. 1972 J. Mech. Engng Sci. 14, 107.
Chorin, A. J. 1968 Math. Comp. 22, 745.
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 J. Fluid Mech. 65, 209.
Cormack, D. E., Leal, L. G. & Seinfeld, J. H. 1974 J. Fluid Mech. 65, 231.
Davis, S. H. 1967 J. Fluid Mech. 30, 465.
Deardorff, J. W. 1970 J. Fluid Mech. 41, 435.
De Vahl Davis, G. 1968 Int. J. Heat Mass Transfer 11, 1675.
De Vahl Davis, G. & Mallinson, G. D. 1975 J. Fluid Mech. 72, 87.
Elder, J. W. 1965a J. Fluid Mech. 23, 77.
Elder, J. W. 1965b J. Fluid Mech. 23, 99.
Elder, J. W. 1966 J. Fluid Mech. 24, 823.
Fromm, J. E. 1971 I.B.M. J. Res. Dev. 15, 186.
Gershuni, G. Z. 1953 Zh. Tekh. Fiz. 23, 1838.
Gill, A. E. 1966 J. Fluid Mech. 26, 515.
Gill, A. E. & Davey, A. 1969 J. Fluid Mech. 35, 775.
Gill, S. 1951 Proc. Camb. Phil. Soc. 47, 96.
Hart, J. E. 1971 J. Fluid Mech. 47, 547.
Hirasaki, G. J. & Hellums, J. D. 1968 Quart. Appl. Math. 16, 331.
Hirt, C. W. & Cook, J. L. 1972 J. Comp. Phys. 10, 324.
Holst, P. H. & Aziz, K. 1972 Int. J. Heat Mass Transfer 15, 73.
Mallinson, G. D. & de Vahl Davis, G. 1973 J. Comp. Phys. 12, 435.
Pao, H. S. 1970 J. Appl. Mech. 37, 480.
Patanker, S. V., Pratap, V. S. & Spalding, D. B. 1974 J. Fluid Mech. 62, 53.
Patanker, S. V., Pratap, V. S. & Spalding, D. B. 1975 J. Fluid Mech. 67, 58.
Patanker, S. V. & Spalding, D. B. 1972 Int. J. Heat Mass Transfer 15, 1787.
Poots, G. 1958 Quart. J. Appl. Math. 11, 157.
Quon, C. 1972 Phys. Fluids 15, 12.
Romanelli, M. J. 1960 In Mathematical Methods for Digital Computers (ed. A. Ralston & H. S. Wilf), vol. 2, p. 110. Wiley.
Rubel, A. & Landis, F. 1969 Phys. Fluids Suppl. 12, II 208.
Schumann, U. 1973 Ph.D. dissertation, University of Karlsruhe. (Trans. N.A.S.A. Tech. Trans. F15391.)
Thomas, R. W. & de Vahl Davis, G. 1970 In Heat Transfer 1970, vol. 4, paper NC 2.4. Elsevier.
Thompson, J. F., Shanks, S. P. & Wu, J. C. 1974 A.I.A.A. J. 12, 787.
Truesdell, C. 1954 The Kinematics of Vorticity. Bloomington: Indiana University Press.
Vest, C. M. & Arpaci, V. S. 1969 J. Fluid Mech. 36, 1.
Wilkes, J. O. & Churchill, S. W. 1966 A.I.Ch.E. J. 12, 161.
Williams, G. P. 1969 J. Fluid Mech. 37, 727.