Thermal convection for a thermo-dependent yield stress fluid in an axisymmetric horizontal duct

This paper deals with the combined forced and free convection heat transfer of a yield stress fluid in a horizontal duct heated uniformly with a constant heat flux density. It is assumed that (i) the rheological behavior of the fluid can be described by the Herschel–Bulkley model and that the consistency K* varies with temperature T*, as K* = a exp(−bT*); (ii) the variation of the fluid density ρ  , with temperature, ρ=ρe(1-β(T∗-Te∗)), is considered important only in the buoyancy term and (iii) the Péclet number is sufficiently large so that it is possible to resort to an asymptotic solution. The aim of this study is to quantify the effect of the rheological properties on the magnitude of the secondary flows induced by the thermo-dependency of K* and ρ. Expressions for local Nusselt number and wall shear stress are given. Finally, to be consistent with the variation along the duct of the axial velocity in the central zone around the axis, due to the thermo-dependency of K* or ρ, the pseudo-plug zone and pseudo-yield surface notions are introduced. Some characteristics of the stresses distribution within the pseudo-plug zone are discussed.