Heat Transfer from Slip Spheres to a Shear-Thickening Fluid: Effects of Slip Velocity and Particle Volume Fraction

Numerical simulations are performed to study the effects of tangential slip velocity and volume fraction of slip spheres on the heat transfer characteristics of assemblages of slip spheres to a shear-thickening fluid of n = 1.4. Navier's linear slip velocity boundary condition is applied at the fluid-solid interface and free surface cell model is used to estimate the effects of the adjacent particles. The governing equations are solved using a segregated approach. First continuity and momentum equations are numerically solved using a finite difference method based simplified marker and cell (SMAC) semi-implicit algorithm implemented on a staggered grid arrangement in spherical coordinates. To solve energy equation fully converged flow field is used as input. The present numerical solver is validated by comparison of present literature results with the existing literature values. Further new results obtained in the range of conditions as Reynolds number, Re: 0.1 – 200; Prandtl number, Pr: 1 – 100; volume fraction of slip spheres, Φ: 0.1 – 0.5 and a dimensionless slip parameter, λ: 0.01 – 100. Finally influence of these pertinent dimensionless parameters on isotherm contours and surface and average Nusselt numbers are thoroughly delineated.