The effective thermal conductivity of sheared suspensions

Formal expressions are derived for the effective thermal conductivity K ij 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 K ij (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.