Abstract
Steady two-dimensional natural convection in the annulus formed by confocal elliptic cylinders oriented at an arbitrary angle a with respect to the gravity force is formulated in terms of an elliptic coordinate system. The method of spectral series expansion is used to reduce the governing coupled partial differential equations to three sets of second-order ordinary equations. These equations are truncated and then numerically integrated using COLSYS, [1] a finite-element collocation code for boundary value differential equations. Overall equivalent conductivities for the inner surface are determined for the eases with: Rayleigh number based on the gap width, Ra L = 100,1000, and 10000; eccentricity of the inner ellipse, e = 0.0,0.5 and 1.0; Prandtl number, Pr = 0.7; and various angles of orientation, a, of the elliptical annulus with respect to gravity. The special case of e = 1.0, corresponding to the convective flow within the annulus formed by an ellipse surrounding a flat plate is investigated in detail. The results are presented in terms of fluid flow patterns, isotherms, graphs ofvorticity and local Nusselt numbers on the plate's surface for various values of alpha.
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