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The effective thermal conductivity of sheared suspensions

Published online by Cambridge University Press:  11 April 2006

Avinoam Nir  and
Andreas Acrivos
Avinoam Nir
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305 Department of Chemical Engineering, Technion—Israel Institute of Technology, Technion City, Haifa, Israel 32000.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, California 94305
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Abstract

Formal expressions are derived for the effective thermal conductivity Kij of randomly dispersed suspensions undergoing shear. These are then evaluated for the cases of dilute suspensions of cylinders and of spheres when the bulk motion is a simple shear, the Péclet number Pe is large, and the particle Reynolds number is small enough for inertia effects to be negligible. It is shown that as Pe → ∞ the presence of shear can significantly affect the O(ϕ) contribution to Kij (ϕ being the volume fraction of the solids), which becomes independent of k, the thermal conductivity of the suspended material. This results from the presence of regions of closed streamlines surrounding each particle which, for sufficiently large Pe, attain an isothermal state and therefore act as regions of infinite conductivity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 1 , 5 November 1976 , pp. 33 - 48
Copyright
© 1976 Cambridge University Press

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References

Batchelor, G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.Google Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.Google Scholar
Batchelor, G. K. 1974 Transport properties of two-phase materials with random structure. Ann. Rev. Fluid Mech. 6, 227–255.Google Scholar
Batchelor, G. K. & Green, J. T. 1972 The determination of the bulk stress in a suspension of spherical particles to order c2. J. Fluid Mech. 56, 401–428.Google Scholar
Cox, R. G., Zia, I. Y. Z. & Mason, S. G. 1968 Particle motions in sheared suspensions. XXV: streamlines around cylinders and spheres. J. Colloid Interface Sci. 27, 7–18.Google Scholar
Ericksen, J. L. 1960 Transversely isotropic fluids. Kolloid-Z. 173, 117–122.Google Scholar
Leal, L. G. 1973 On the effective conductivity of a dilute suspension of spherical drops in the limit of low particle Péclet number. Chem. Engng Comm. 1, 21–31.Google Scholar
Lin, C. J., Peery, J. H. & Schowalter, W. R. 1970 Single shear flow around a sphere: inertia effects and suspension rheology. J. Fluid Mech. 44, 1–17.Google Scholar
Pan, F. Y. & Acrivos, A. 1968 Heat transfer at high Péclet number in regions of closed streamlines. Int. J. Heat Mass Transfer, 11, 439–444.Google Scholar
Robertson, C. R. & Acrivos, A. 1970 Low Reynolds number shear flow past a rotating circular cylinder. Part 1. Momentum transfer. J. Fluid Mech. 40, 685–703.Google Scholar
Rocha, A. & Acrivos, A. 1973 On the effective thermal conductivity of dilute dispersions. General theory for inclusions of arbitrary shape. Quart. J. Mech. Appl. Math. 26, 217–233.Google Scholar