Heat Transfer in Laminar Flow of Bingham Material through an Annulus

Abstract

The heat transfer in fully developed laminar flow of Bingham material in an annulus between two coaxial pipes is discussed. The inner pipe moves parallel to itself and the outer pipe is at rest. Equations for temperature distribution including the effect of dissipation and internal heat generation have been set up and a discussion of the solution is given for the case of small gap approximation. The temperature distributions are found to depend on Bingham number (or the position of yield surface), Brinkman number and the rate of heat transfer at the wall. The effect of dissipation is to increase the temperature at a place and this effect becomes greater as the region of flow becomes narrower. There exists a critical value of the Brinkman number above or below which the cooling or heating of the outer pipe takes place.