Heat Transfer in the Non-Newtonian Axisymmetric Flow in the Neighborhood of a Sudden Contraction

The flow pattern at low Reynolds number in the neighborhood of a sudden contraction is very sensitive to the mechanical behavior of the flowing fluid. A large extensional viscosity leads to vortex enhancement in the corner region of the flow of a non-Newtonian fluid in such geometry. In the corresponding flow of a Newtonian fluid, these vortices are much weaker and smaller. Moreover, the extension-thickening behavior of most polymeric liquids leads to higher viscous dissipation effects in the predominantly extensional flow, as compared to typical shear flows. The flow and temperature fields for this problem have been obtained from numerical integration of the conservation equations, aiming at applications related to extrusion and capillary rheometry of polymeric liquids. To account for the flow dependence of the stress tensor, a generalized Newtonian model has been employed, including the dependence of the viscosity function on both the second and the third invariants of the rate-of-deformation tensor. The numerical solutions have been obtained via a finite-volume method. The case of a 4:1 circular contraction was investigated, with uniform temperature distribution at the solid boundaries. The fluid inlet temperature is equal to the temperature at the walls, so that thermal gradients in the fluid are due to viscous dissipation effects only. Comparisons between Newtonian and non-Newtonian results showed that the combined effect of viscous dissipation and enhancement of vortex activity significantly affects the temperature field. The practical significance of the results is discussed for extrusion processes and capillary rheometry.