Numerical Simulation of Buoyancy-Induced Micropolar Fluid Flow between Two Concentric Isothermal Spheres

Natural convection heat transfer between two differentially heated concentric isothermal spheres utilizing micropolar fluid is investigated numerically. The two-dimensional governing equations are discretized using control volume method and solved by employing the alternating direction implicit scheme. Results are presented in the form of streamline and temperature patterns, local and average Nusselt numbers, over the heated and cooled boundaries for a wide range of Rayleigh numbers, Prandtl numbers and dimensionless vortex viscosity   , v K dimensionless micro- inertia density   , v B and microrotation boundary condition (n) for radius ratio of 2. The goal of this work is to investigate heat transfer characteristics of natural convection in the annulus between concentric spheres using micropolar theory. It is shown that micropolar fluids give lower heat transfer values than those of the Newtonian fluids. It is also found that the average Nusselt number increases with increasing Rayleigh and Prandtl numbers. On the other hand, it is disclosed that increasing the vortex viscosity reduces the heat transfer rate. The results are compared with the data available in the open literatures, and an excellent agreement was obtained. Finally, a correlation between the average Nusselt number, Rayleigh number and material parameter   K v is presented.