Correlations for Nusselt Number in Free Convection from an Isothermal Inclined Square Plate by a Numerical Simulation
Jasim Abdulateef,
Ayad Hassan
Issue:
Volume 3, Issue 2, March 2015
Pages:
8-18
Received:
4 April 2015
Accepted:
12 April 2015
Published:
7 May 2015
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.
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 vortic...
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