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NATURAL CONVECTION BETWEEN TWO CONFOCAL ELLIPTICAL TUBES USING SPECTRAL METHOD

DOI: 10.1615/ICHMT.2008.CHT.350
20 pages

Fathi Mahfouz
Mechanical Engineering Department, UET, Taxila, Pakistan. On leave from Menoufia University, Egypt

Abstract

In this paper, the transient and steady natural convection in an elliptical annulus has been numerically investigated. The annulus, which is the space between two confocal, concentric elliptic tubes, is placed horizontally and the resulting laminar natural convection flow is predicted at different annulus orientations. The full governing equations are solved numerically using Fourier Spectral method. The process of heat convection within the annulus is dependent on Rayliegh number, Prandtl numbers, angle of inclination of minor axes to gravity vector, ratio of outer tube major axis to inner tube major axis and the axes ratio of the inner tube. The Prandtl number and inner tube axis ratio are fixed at 0.7 and 0.5, respectively. The Rayleigh number has assigned two values of 104 and 105, the major axes ratio is varied up to 3 while the angle of orientation of the minor axes is varied up to 90. The results for local and average Nussult numbers are obtained and discussed together with the details of both flow and thermal fields. For certain isothermal heating boundary conditions the study has shown an optimum value for major axes ratio at which the heat transfer through the annulus is minimum.

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