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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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