Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls

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In this study, two-dimensional steady-state simulations of laminar natural convection of Newtonian fluids in rectangular enclosures with differentially heated side walls have been conducted. Two Prandtl numbers Pr=0.71 and 7.0 – typical values for air and water – and a range of different aspect ratios AR(=H/L where H is the enclosure depth and L is the enclosure width) ranging from 1/8 to 8 for constant heat flux boundary conditions are investigated for Rayleigh numbers in the range 104–106. To demonstrate the difference between the aspect ratio effects between the constant wall temperature and constant wall heat flux boundary conditions, simulations have also been carried out for the same range of numerical values of Rayleigh number for the constant wall temperature boundary condition. It is found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number for both constant wall temperature and constant heat flux boundary conditions. The effects of aspect ratio AR have also been investigated in detail and it has been found that the effects of thermal convection (diffusion) strengthens (weakens) with increasing aspect ratio and vice versa, for a given set of nominal values of Rayleigh number and Prandtl number for both types of boundary conditions. In the case of constant wall temperature boundary condition, the mean Nusselt number increases up to a certain value of the aspect ratio ARmax but for AR>ARmax the mean Nusselt number starts to decrease with increasing AR. In contrast, the mean Nusselt number is found to increase monotonically with increasing AR for the constant wall heat flux boundary condition in the range of values of aspect ratio, Rayleigh number and Prandtl number considered in this study. Detailed physical explanations are provided for the observed phenomenon. Suitable correlations are proposed for the mean Nusselt number Nu¯ for both constant wall temperature and wall heat flux boundary conditions which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu¯ for the range of Rayleigh number and aspect ratio considered here.