High-Order Algorithm for Simulating Heat Transfer in Complex Yield-Stress Fluid Flows

This paper examines the numerical simulation of non-isothermal flows of Herschel-Bulkley fluids under stick-slip boundary conditions and a constant wall temperature. To solve the governing equations, we propose a decoupled transient solution algorithm utilizing high-order time-stepping methods based on the Taylor-Galerkin approach combined with pressure correction in a finite element framework. This numerical approach exhibits high accuracy in achieving convergence. The results obtained for the steady-state solution emphasize the significant impact of temperature changes on the flow pattern. Their effect on the topology of yielded and unyielded regions, along with the efficiency of heat transfer and the friction factor of Fanning as functions of yield stress, power-law index, Reynolds number, and Péclet number, underscores the significant interaction among these parameters. Notably, the effects of stick-slip conditions are particularly pronounced at the transition to the slipping zone within the singularity. Here, a peak in the shear rate is observed, leading to significant changes in the stress distribution within the channel. Moreover, the numerical method was validated in good agreement with previous numerical findings.