Rayleigh–Bénard Power-Law Fluid Convection in Rectangular Enclosures

Abstract

The influences of the aspect ratio (ratio of height to length) on the laminar Rayleigh–Bénard convection of power-law fluids in rectangular enclosures have been numerically investigated for the constant wall heat flux boundary condition for horizontal walls. The steady-state simulations have been conducted for a range of aspect ratios of 0.25 to 4, a nominal Rayleigh number range of to , and a power-law index of 0.6 to 1.8 for a representative single value of the nominal Prandtl number (). It has been found that convective transport weakens with an increasing aspect ratio and thermal conduction dominates thermal transport for tall enclosures. Moreover, the critical Rayleigh number for the onset of convection increases with increasing values of the power-law index and aspect ratio for both shear-thinning and Newtonian fluids. Thermal convection, irrespective of the value of the aspect ratio, has been found to augment with an increasing (decreasing) Rayleigh number (power-law index) due to strengthening of the buoyancy force in comparison to viscous resistance with an increasing Rayleigh number (shear-thinning behavior with decreasing power-law index). The simulations revealed that the flow patterns and mean Nusselt number are dependent on the initial condition, and it is possible to obtain different steady-state solutions for different initial conditions. The numerical findings have been explained with the help of scaling arguments and, in turn, have been used to propose a correlation for the mean Nusselt number.