Numerical simulation of free convection within an eccentric annulus filled with micropolar fluid using spectral method

摘要

In this paper, the problem of natural convection in a circular eccentric annulus filled with micropolar fluid has been numerically investigated using Fourier Spectral Method. The annulus inner wall is heated and maintained at constant temperature while the outer wall is cooled and kept at constant temperature. The full governing equations of momentum, angular momentum and energy have been solved to give the details of flow and thermal fields. The heat convection process in the annulus is mainly controlled by Rayleigh number Ra, Prandtl number Pr, radius ratio Rr, eccentricity, e and material parameters of micropolar fluid. The material parameters are dimensionless spin gradient viscosity λ, dimensionless micro-inertia density B and dimensionless vortex viscosity D. This study considers Ra up to 5 × 104 and the eccentricity is varied between −0.6 and +0.6 while dimensionless material parameters D of micropolar fluid is considered between 0 and 10. Both Pr, and Rr are fixed at 0.7, 2.6, respectively while B and λ are assigned the value of 1. The study considers the effect of controlling parameters on flow and thermal fields with emphasis on the effect of these parameters on mean Nusselt number. The study has shown that for certain controlling parameters the heat transfer in the annulus is minimum at a certain eccentricity. The study also has shown that as parameter D increases the rate of heat transfer through the annulus decreases.