A Numerical Study of Unsteady Natural Convective Heat Transfer From Thin, Two-Sided Heated Horizontal Plates of Various Shapes

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Bandyopadhyay, Koustav
Natural convection , horizontal plates , transient natural convection , unsteady , two-sided , length scale
In this study, natural convective heat transfer from thin, two-sided, horizontal flat plates has been numerically investigated. The objective of the study is to explore the mechanics of unsteady natural convection at various Rayleigh numbers. The influence of varying the characteristic length scales, i.e., the width of the plate, the square root of the single-side surface area, and 4 times the total area divided by the total perimeter (4A/P) was studied. Ansys FLUENT was used to conduct the numerical simulations. The Boussinesq approximation was used, where the thermal properties of the air were kept constant, except for density, which decreased with an increase in temperature. Laminar and Standard k-epsilon turbulence models were used for computing the flow-coupled heat transfer in the laminar and turbulent flow regimes. The results of the study showed that at lower Rayleigh numbers, the heat transfer was primarily through conduction. At higher Rayleigh numbers, the heat transfer was first initiated through conduction, and as the temperature of the air increased, the density decreased and the air moved upwards, giving rise to convective flow. Varying the characteristic length scales showed that when the width of the plate was used, the transient Nusselt number profiles for different shapes, were very different. When square root of the area was used as the length scale, the transient Nusselt number variations for different plate shapes were closer to each other, but still had significant differences. However, when 4A/P was used as the length scale, the Nusselt number variations for plates of different dimensions, areas, and shapes overlapped with each other at lower Rayleigh numbers. The difference between the Nusselt number profiles increased at higher Rayleigh numbers, where the flow around the plates became turbulent. In the turbulent flow regime, using 4A/P as the length scale did not produce a common shape and size independent Nusselt number variation for different shapes. However, when the transient Nusselt number profile was normalized with the respective steady state Nusselt number from the different shaped plates, substantial overlap between the Nusselt number profiles was observed. This indicated that using 4A/P as the characteristic length scale, a general shape and size independent Nusselt number profile can be obtained at lower Rayleigh numbers and a general shape and size independent normalized Nusselt number profile can be obtained at higher Rayleigh numbers.
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