Study of cooling with solidification of a laminar thermodependent Herschel-Bulkley fluid flow in a convectively cooled annular duct

This article presents a numerical analysis of cooling with solidification for laminar Herschel-Bulkley fluid flow in an annular duct. The outer cylinder is subject to uniform cooling with the surrounding sink temperature below the freezing temperature of the fluid. The inner cylinder is considered adiabatic. It is assumed that all the physical properties of the fluid except the consistency K are constant. The K-T relation used is K = a exp (-bT). Under this cooling condition, the thermal entrance region consists of two parts. The first one is a liquid - solidification free zone. The second one corresponds to the region where the solidification grows inward along the annular duct. The problem is governed by nine independent dimensionless numbers. Here, we focus on the effect of the rheological parameters and the thermo-dependency of K on the dynamic and thermal Fields. The effects of the rheological parameters are analyzed through the flow behavior index n, and the relative dimension of the plug core flow ap(e). Concerning the K-T variation effects, they can be described by the Pearson number Pn. Numerical results are obtained for the liquid-solidification free length z(f), liquid-solid interface profile, pressure drop, axial velocity evolution, plug core dimension and local Nusselt number. They indicate how the effect of Pn depends on ap(e) and n.