A Numerical Study of Unsteady Natural Convection from Two-Sided Thin Horizontal Isothermal Plates

Unsteady natural convective heat transfer following sudden heating of two-sided, thin isothermal horizontal plates with complex shapes has been numerically studied. The plates were isothermal and exposed to air at ambient conditions. Three different plate shapes were considered. Variations of the heat transfer rates, expressed in terms of the Nusselt number with dimensionless time for various Rayleigh numbers were first obtained with the square root of the plates’ surface area being used as the length scale. Then, the heat transfer rates for steady state were obtained with the same length scale being used. The transient heat transfer rate results showed that depending on the value of the Rayleigh number, the Nusselt number either gradually decreased to a steady state value or first decreased to a minimum and then increased to the steady state value. Similar Nusselt number variation with time were obtained for all plate shapes considered. Now, in studies of steady state natural convective heat transfer rates from horizontal plates with different shapes, it has been found that if 4*Area/Perimeter is used as the length scale in presenting the results, the variation of Nusselt number with Rayleigh number were essentially the same for all shapes considered. Therefore, the unsteady state results obtained in the present study were re-expressed using 4*Area/Perimeter as the length scale and it was found that the variations of Nusselt number with dimensionless time for various Rayleigh numbers for the plate shapes considered, were much closer to each other when 4*area/perimeter was used as the length scale than when the square root of the plate area was used as the length scale.