Natural convection of Carreau–Yasuda non-Newtonian fluids in a vertical cavity heated from the sides

This paper reports a numerical study of natural convection in a vertical enclosure filled with a non-Newtonian fluid. Thermal boundary conditions of the Neumann type are applied on the vertical walls of the enclosure while the horizontal ones are assumed adiabatic. A Carreau–Yasuda model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the shear thinning fluids. The governing parameters for the problem are the thermal Rayleigh number RaRa, Prandtl number PrPr, power-law index nn, aspect ratio AA and parameters of non–Newtonian fluid model. A semi-analytical solution, valid for an infinite layer (AA ≫ 1), is derived on the basis of the parallel flow approximation. The influence of the constitutive Carreau–Yasuda equation parameters on the fluid flow, temperature field and heat transfer is discussed in detail. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations. The results reveal the strong influence of the pseudoplastic behavior of a non-Newtonian fluid on its natural convection heat transfer within the enclosure. Results are also obtained by considering the same phenomenon on the basis of the power law model. A comparison is made between the predictions of the two rheological models.