Abstract
This paper presents a numerical study on three-dimensional transient natural convection from an inclined isothermal square plate. The finite difference approach is used to solve the governing equations, in which buoyancy is modeled via the Boussinesq approximation. The complete Navier-Stokes equations are transformed and expressed in term of vorticity and vector potential. The transformed equations are solved using alternating direction implicit (ADI) method for parabolic portion of the problem and successive over relaxation (SOR) for the elliptic portion. Solutions for laminar case are obtained up to Grashof number of 5x104 as well as the inclination angles were varied from 0o to 180o with 30o intervals, and the Prandtl number of 0.7 is considered. The results are shown in terms of isothermal plots, and the local and average Nusselt numbers are also presented. The simulation results show that the main process of heat transfer is conduction for Grashof number less than 103 and convection for Grashof number larger than 103. It is also found that, the values of Nusselt number show fairly large dependence on inclination angle and there is a significant difference in heat transfer rates between the upward and downward orientation. The average Nusselt number increases to 20% at the vertical position compared to horizontal position then decreases with increasing inclination of plate at downward orientation. Based on the results obtained, correlations have been proposed to evaluate the Nusselt numbers of both upward and downward orientation. Validations of the present results are made through comparison with available numerical and experimental data, and a good agreement was obtained.
Highlights
The clarification of flow and heat transfer mechanisms of natural convection in square plates-which is often observed in many science and engineering applications such as in printed circuit board (PCB), solar cell, and thin film manufacturing chamber - is very important for both industrial applications and academic research [1]
The results showed that, four distinct flow regions appeared, consisting of a two-dimensional laminar boundary layer region near the leading edges, a transitional region characterized by a three-dimensional flow separation and by the attachment of ambient fluid onto the heated surface downstream of the flow separation, a fully turbulent region, and a collision region near the plate centerline
Temperature fields, local and average Nusselt Number distribution over the heated surface are examined for Grashof numbers and inclination angles ranged from 103 to 5x104 and from 0o to 180o, respectively
Summary
The majority of the studies available in the literature on natural convection heat transfer from horizontal rectangular plates facing upwards have been carried out experimentally, by using air or water as working fluid [2,3,4,5,6,7,8,9,10]. Further heat transfer results for rectangular surfaces were found by Lewandowski and Kubski [4]. Kitamura and Kimura [5] conducted an experimental study of natural convection in water from slender rectangular plates heated with uniform heat flux and equipped with fences at both longer sides to inhibit side flows, obtaining a two-dimensional flow field over the plates.
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