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A NUMERICAL STUDY OF NATURAL CONVECTIVE HEAT TRANSFER FROM AN INCLINED ISOTHERMAL PLATE WITH A "SINUSOIDALLY WAVY" SURFACE

Patrick H. Oosthuizen
Dept. of Mechanical and Materials Engineering, Queen's University Kingston, Ontario Canada K7L 3N6

Jane T. Paul
Department of Mechanical and Materials Engineering, Queen's University, Kingston, Ontario, Canada K7L 3N6

Abstract

Natural convective heat transfer from a wide isothermal plate which has a "wavy" surface, i.e. a surface which periodically rises and falls, has been numerically studied. The surface waves run in the horizontal direction, i.e., are normal to the direction of flow over the surface. Attention has been restricted to the case where the waves have a sinusoidal cross-sectional shape. The plate is, in general, inclined to the vertical with consideration being given both to inclination angles at which the heated plate is facing upwards and to inclination angles at which the heated plate is facing downwards. The range of Rayleigh numbers considered extends from values that for a non-wavy vertical plate would be associated with laminar flow to values that would be associated with fully turbulent flow. The flow has been assumed to be steady and fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq approximation. The Reynolds averaged governing equations in conjunction with a standard k-epsilon turbulence model with buoyancy force effects accounted for have been used in obtaining the solution. The governing equations have been solved using the commercial CFD code FLUENT© . The solution has the following parameters: i) the Rayleigh number based on the height of the heated plate, ii) the Prandtl number, iii) the ratios of the amplitude of the surface waviness and of the pitch of the surface waves to the height of the plate, and iv) the angle of inclination of the plate to the vertical. Results have been obtained for a Prandtl number of 0.74 and for amplitude and pitch ratios of 0.1. The effects of Rayleigh number and angle of inclination on the mean and local surface Nusselt numbers have been numerically studied.

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