Laminar natural convection of power-law fluids in a square enclosure submitted from below to a uniform heat flux density

Two-dimensional steady-state simulations of laminar natural convection of non-Newtonian power-law fluids in square enclosures heated through the lower horizontal wall have been carried out for constant wall heat flux boundary conditions. The effects of power-law index n on heat and momentum transport have been analysed for nominal values of Rayleigh number (Ra) in the range 103-105 and a Prandtl number (Pr) range of 10-106. It has been demonstrated that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number for both Newtonian and power-law fluids. Moreover, Nu¯ values obtained for power fluids with n < 1 (n > 1) are greater (smaller) than that obtained in the case of Newtonian fluids with the same nominal Rayleigh number Ra due to strengthening (weakening) of convective transport. The effects of convection strengthen with increasing Ra for a given set of values of Pr and n, which is reflected in the increasing trend of Nu¯ with increasing Ra. By contrast, the Prandtl number is shown to have marginal influence on Nu¯. In addition a detailed comparison has been undertaken between these new results for the case of heating from below with existing results for the sidewall heating case. It has been found that Nu¯ in the differentially heated horizontal wall configuration assumes smaller values than in the differentially heated vertical wall configuration for a given set of values of n and Prandtl number in shear-thinning fluids (i.e. n < 1) for high values of Ra, whereas Nu¯ values remain comparable for both differentially heated vertical and horizontal wall configurations for the Newtonian (i.e. n = 1) and shear-thickening fluids (i.e. n > 1). However for small values of Rayleigh number, Nu¯ attains greater values in the differentially heated horizontal wall configuration for Newtonian (n = 1.0) and shear-thinning (n < 1) fluids. In contrast, Nu¯ assumes higher values in the differentially heated vertical sidewall configuration for shear-thickening fluids(n > 1) for small values of Ra. Detailed physical explanations have been provided for the observed Ra, Pr and n dependences of Nu¯. A new correlation has been proposed for Nu¯ for natural convection of power-law fluids in square enclosures heated from below subjected to constant heat fluxes. The new correlation is shown to satisfactorily capture both the qualitative and quantitative behaviour of Nu¯ in response to the changes in Ra, Pr and n obtained from simulation data.