Herschel-Bulkley fluid flow within a pipe by taking into account viscous dissipation

The present numerical study deals with the analysis of thermal characteristics during the flow of an incompressible Herschel-Bulkley fluid of constant physical and rheological properties. The flow takes place within a pipe, of circular cross section, maintained at uniform wall temperature. Because of the viscous character of this kind of fluid, viscous dissipation is taken into account. The effect of this parameter is analyzed for various values of the fluid index flow and the Herschel-Bulkley number. The governing equations are resolved by means of the finite volume method and using the SIMPLER algorithm and the line by line method. The results reveal that heat transfer is significantly underestimated when viscous dissipation is neglected, particularly for shear-thinning fluids and for high values of the Herschel-Bulkley number. In addition, heat transfer is more important in the case of heating and the curves display a discontinuity, and negative values of Nusselt number are obtained.