Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-20T07:58:16.341Z Has data issue: false hasContentIssue false
  • English
  • Français

A study of thermal convection in non-Newtonian fluids

Published online by Cambridge University Press:  12 April 2006

E. M. Parmentier
E. M. Parmentier
Affiliation:
Department of Geological Sciences, Cornell University, Ithaca, New York 14850 Present address: Department of Geological Sciences, Brown University, Providence, Rhode Island 02912.
Get access Rights & Permissions [Opens in a new window]

Abstract

This study considers steady-state, finite amplitude thermal convection in a non-Newtonian fluid. Pseudoplastic (power-law) fluids are considered for a power-law exponent n in the range 1 ≤ n ≤ 9. Finite-difference solutions are obtained for two-dimensional periodic convective modes in a horizontally infinite fluid layer heated from below. The results show that the patterns of convective motions differ only slightly from those in a fluid of constant viscosity for n [lsim ] 3 while for n [gsim ] 3 significant differences are observed. An average viscosity is introduced which provides a good correlation of heat transfer across the layer with the Rayleigh number for the complete range of n considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 1 , 16 January 1978 , pp. 1 - 11
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below. J. Math. & Phys. 46, 140–150.Google Scholar
Krishnamurti, B. 1970 On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Le Pichon, X., Francheteau, J. & Bonin, J. 1973 Plate Tectonics. Elsevier.
Liang, S. F. & Acrivos, A. 1970 Experiments on buoyancy driven convection in non-Newtonian fluid. Rheol. Acta 9, 447–455.Google Scholar
Mckenzie, D. P., Roberts, J. M. & Weiss, N. O. 1974 Convection in the earth's mantle: towards a numerical simulation. J. Fluid Mech. 62, 465–538.Google Scholar
Mihaljan, J. M. 1962 A rigorous exposition of the Boussinesq approximations applicable to a thin fluid layer. Astrophys. J. 136, 1126–1133.Google Scholar
Nye, J. F. 1953 The flow of ice from experiments in glacier tunnels, laboratory experiments, and the Jungfraufirn borehole experiment. Proc. Roy. Soc. A 219, 477–489.Google Scholar
Ozoe, H. & Churchill, S. W. 1972 Hydrodynamic stability and natural convection in Ostwalde–de Waele and Ellis fluids: the development of a numerical solution. A.I.Ch.E. J. 18, 1196–1207.Google Scholar
Parmentier, E. M., Turcotte, D. L. & Torrance, K. E. 1976 Studies of finite amplitude non-Newtonian thermal convection with application to convection in the earth's mantle. J. Geophys. Res. 81, 1839–1846.Google Scholar
Serrin, J. 1959 Mathematical principles of classical fluid mechanics. In Encyclopedia of Physics, vol. VIII/1, pp. 125–263. Springer.
Silveston, P. L. 1958 Wärmedurchgang in waagerechten Flüssigkeiteschichten. Forsch. Geb. Ing. Wes. 24, 59–69.Google Scholar
Stocker, R. L. & Ashby, M. F. 1973 On the rheology of the upper mantle. Rev. Geophys. Space Phys. 11, 391–426.Google Scholar
Tien, C., Tsuei, H. S. & Sun, Z. S. 1969 Thermal instability of a horizontal layer of non-Newtonian fluid heated from below. Int. J. Heat Mass Transfer 12, 1173–1178.Google Scholar
Turcotte, D. L. & Oxburgh, E. R. 1967 Finite amplitude convection cells and continental drift. J. Fluid Mech. 28, 29–42.Google Scholar
Turcotte, D. L. & Oxburgh, E. R. 1972 Mantle convection and the new global tectonics. Ann. Rev. Fluid Mech. 4, 33–68.Google Scholar
Turcotte, D. L., Torrance, K. E. & Hsui, A. T. 1973 Convection in the earth's mantle. Methods in Comp. Phys. 13, 431–454.Google Scholar
Van Der Borght, R., Murphy, J. O. & Steiner, J. M. 1974 A theoretical investigation of finite amplitude thermal convection in non-Newtonian fluid. Z. angew. Math. Mech. 54, 1–8.Google Scholar
Weertman, J. & Weertman, J. R. 1975 High temperature creep of rock and mantle viscosity. Ann. Rev. Earth Planet. Sci. 3, 293–315.Google Scholar