PREDICTION OF THREE DIMENSIONAL NATURAL CONVECTION FROM A HORIZONTAL ISOTHERMAL SQUARE PLATE

Abstract

A theoretical study of a three-dimensional natural convection heat transfer from an isothermal horizontal square plate, with upper and lower heated surfaces is present. The transient Navier–Stokes and energy equations were solved by using finite deference method (F.D.M). The complete Navier–Stokes equations are transformed and expressed in terms of vorticity–vector potential and solved using an Alternating Direction Implicit (ADI) method for the parabolic portion of the problem, and Successive Over–Relaxation (SOR) method for the elliptic portion .A computer program in (FORTRAN 77) was built to carry out the solution. The numerical results were obtained for laminar flow range of Grashof number up to (105) in up ward–facing and downward–facing with Prandtl number of (0.72). The results of local Nusselt number have maximum values at the outer edge of plate for two cases upward and downward facing heating.
The comparison of the results of average Nusselt number with numerical data for downward facing and experimental data for upward facing shows acceptable agreement. It may be noted that the present data are generally different with experimental data, since the available data are extrapolated to high Grashof number. Thus the deviation may be large with present data.