Numerical heat transfer during Herschel–Bulkley fluid natural convection by CVFEM

Abstract

Numerical prediction of heat transfer by natural convection of a Herschel-Bulkley non-Newtonian fluid inside a square cavity has been computationally analyzed. Unsteady 2D fluid mechanics and heat transfer were described in terms of the non-linear coupled continuity, momentum and heat equations. These equations were solved by the control volume finite element method (CVFEM) with Gauss-Seidel/System Over-Relaxation coupling algorithm. The effect of the Ra, Pr, Bn and the rheological behavior index (n) on the non-Newtonian fluid thermal and momentum behavior were studied. The non-Newtonian fluid flow was described by the rheological model of Herschel-Bulkley. Results for the streamlines and isotherms along the enclosure walls are presented. It was found that the effect of the Pr and Bn is more important when the Ra is lower (103). In addition, the behavior index had a significant effect on the CPU time for the different studied cases.