Impact of the Nusselt and Rayleigh Numbers on Heat Transfer in Rectangular Enclosure

Abstract

In this study, effect of the Nusselt and Rayleigh numbers on heat transfer in rectangular enclosure is investigated. The governing equations along with the boundary conditions are non-dimensionalized and discretized. The average Nusselt numbers (N u) for fluids of water (P r = 7) and air (P r = 0.7) at different Rayleigh numbers (Ra) are calculated. Details of empirical correlations used for calculating the average Nusselt numbers (N u) for specific fluids are presented. Mode of heat transfer in rectangular enclosure for suitable Nusselt and Rayleigh number is determined. Different factors which induce heat transfer in the rectangular enclosure are investigated. For each of these factors, appropriate numerical data is derived and elucidated. The numerical values of N u are obtained as less than 1 at different Rayleigh numbers in Ra < 1708. It is determined that the average Nusselt numbers for water (P r = 7) and air (P r = 0.7) increases curved linearly. For different Rayleigh numbers in Ra > 1708, it is found that the average Nusselt numbers for water (P r = 7) and air (P r = 0.7) increases linearly. At Ra = 1708, the critical Rayleigh number, the fluid layer remains stable and hence quiescent. The transfer of heat from the top wall to the bottom wall within the enclosure is by conduction for liquid (water, P r = 7) and through conduction and radiation for gas (air, P r = 0.7).