Influences of Boundary Conditions on Laminar Natural Convection of Bingham Fluids in Rectangular Enclosures With Differentially Heated Side Walls

Abstract

Two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated side walls have been conducted for a range of different aspect ratios (height/length) for both constant wall temperature and constant heat flux boundary conditions. The rectangular enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield-stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number in the range 104–106 and the aspect ratio range 1/8 to 8 for a single nominal Prandtl number (= 500). It is found that the mean Nusselt number increases (decreases) with increasing values of Rayleigh (Bingham) number irrespective of the boundary condition. For the constant wall temperature boundary condition, the aspect ratio at which the maximum mean Nusselt number occurs is found to decrease with increasing Rayleigh number. In contrast, the value of mean Nusselt number increases monotonically with increasing aspect ratio in the case of the constant wall heat flux boundary condition. Detailed physical explanations are provided for these aspect ratio effects. New correlations are proposed for the mean Nusselt number in both the constant wall temperature and wall heat flux boundary conditions, which are shown to satisfactorily capture the simulation results.