Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Abstract

Thermal convection for an incompressible Herschel-Bulkley fluid along an annular duct, whose inner cylinder is rotating and outer is at rest, is analyzed numerically and experimentally. The outer cylinder is heated at constant heat flux density and the inner one is assumed adiabatic. The first part of this study deals with the effect of the rheological behavior of the fluid and that of the rotation of the inner cylinder on the flow field and heat transfer coefficient. All the physical properties are assumed constant and the flow is assumed fully developed. The critical Rossby number Ro c = (R 1Ω/U d) c , for which the dimension of the plug flow is reduced to zero is determined with respect to the flow behavior index, the radius ratio and the Herschel-Bulkley number for axial flow. The rotation of the inner cylinder induces a decrease of the axial velocity gradient at the outer cylinder thereby reducing the heat transfer between the heated wall and the fluid. The second part of this study introduces the variation of the consistency K with temperature and analyzes the evolution of the flow pattern and heat transfer coefficient along the heating zone. Two cases are distinguished depending on the Rossby number: (i) Ro < Ro c, the plug flow dimension increases along the heating zone; (ii) Ro < Ro c , the decrease of K with temperature leads to the reappearance of the plug flow. For high angular velocities, it is possible to have a plug zone attached to the outer cylinder. Finally, a correlation is proposed for the Nusselt number. It shows clearly that the effect of thermodependency of K on the heat transfer becomes more important with increasing rotational velocity of the inner cylinder.