Free Convection from an Elliptic Tube with its Major Axis Vertical and Placed in a Micropolar Fluid

Abstract

Abstract:- In this paper free convection from a horizontal isothermal elliptic tube placed in a micropolar fluid with its major axis vertical is investigated. The governing equations are based on the conservation of mass, linear momentum, angular momentum and energy. The full governing equations written in stream function-vorticity formulation are solved numerically using the Spectral method based on Fourier series expansion. Beside the classical controlling parameters (Rayleigh number, Prandtl number and ellipse axis ratio) the effect of the material parameters of the micropolar fluid are also considered. These parameters are the vortex viscosity, micro-inertia density and spin gradient viscosity. In comparison with Newtonian fluids, the study has shown that micropolar fluids display a clear reduction in heat transfer rate. The study shows also that the effect of vortex viscosity is the most significant material parameter on heat transfer rate. Key-Words:- Micropolar – free convectioon – elliptic- tube – vortex viscosity- microrotation

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