Effects of slip velocity and volume fraction of slip spheres on the momentum transfer characteristics of assemblages of slip spheres are numerically investigated. The fluid slip along the surface of the sphere is considered by Navier's linear slip model. The dimensionless governing continuity and momentum equations are solved using a semi-implicit marker and cell method implemented on a staggered grid arrangement in spherical coordinates. The convection and viscous terms of momentum equations are discretized by means of the QUICK scheme and a second-order central differencing scheme, respectively. The present numerical solver is benchmarked via grid independence and comparisons with the existing literature values. Results were obtained over a wide range of pertinent dimensionless numbers such as the Reynolds number, volume fraction of the dispersed phase, and dimensionless slip parameter.
Combined effects of slip velocity and volume fraction of slip spheres on the heat transfer characteristics of multiple slip spheres are numerically investigated within the framework of a free surface cell model combined with a linear slip velocity along the surface of the slip spheres. The governing conservation equations of the mass, momentum, and energy are solved by a segregated approach using a simplified marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates. The convection and diffusion terms of conservation equations are discretized using quadratic upstream interpolation for convective kinematics and second‐order central differencing schemes, respectively. Prior to obtaining new results, this numerical solver is validated by comparison of present results with the existing literature values. Further new results are obtained for a 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 slip parameter, λ: 0.01–100. The effects of these dimensionless parameters on isotherm contours and local and average Nusselt numbers are thoroughly delineated. Finally, a new empirical correlation for the average Nusselt number of multiple smooth slip spheres is proposed on the basis of present numerical results.
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