Numerical Simulation of Steady and Unsteady Mixed Convection from Tubes of Elliptic Cross-section

Abstract

The problem of two-dimensional laminar mixed convection (forced and free convection) from a tube of elliptic cross-section has been numerically simulated for the cases when the approaching flow is either steady or fluctuating. The elliptic cross-section is flexible enough to simulate the circular tube or to approach the flat plate depending on the ratio between its minor and major axes. The numerical scheme is developed in a way to cover the special cases of steady and unsteady flows, parallel and counter flows, forced convection as well as mixed convection flows. The tube is assumed to have an isothermal surface and is placed in an unsteady but uniform stream. The free-stream fluctuations are represented by periodic (sinusoidal) fluctuations superimposed on the average stream velocity. The resulting velocity and thermal fields are obtained by solving the conservation equations of mass, momentum and energy. The main parameters involved are the tube axis ratio, Reynolds number, Grashof number, Prandtl number, frequency parameter and the relative amplitude of fluctuations. Results will be presented for some steady flow cases covering the parallel, cross and counter flow configurations as well as the fluctuating flow cases with emphasis on the effects of the amplitude and frequency of free-stream fluctuations on the local and average Nusselt numbers. The average flow Reynolds number ranges from 50 to 500, the frequency parameter ranges from π/4 to π and the relative amplitude ranges from 0.25 to 1.0. The study revealed that the effect of fluctuations on the time-average Nusselt number becomes more pronounced with increasing Reynolds number. It also revealed that the rate of heat transfer increases with the increase of the amplitude of fluctuations but decreases with the increase of frequency. The details of flow and thermal fields will be presented in the form of local and average Nusselt number variations as well as streamline and temperature contours for some selected cases.