Natural convection of power-law fluids under wall vibrations: A lattice Boltzmann study

The natural convection of non-Newtonian power-law fluids in a rectangular cavity in the presence of wall vibrations has been investigated by the lattice Boltzmann method. The longitudinal and transverse vibrations are applied to the horizontal walls of the cavity separately, and the two vertical walls are set as high and low temperatures, respectively. The velocity fields and temperature distributions of power-law fluids are visualized with respect to the streamlines and isotherm contours. The heat transfer characteristics are interpreted in terms of averaged Nusselt number ((Nu) over bar) near the surface of heated wall. The effects of power-law index n in the range of 0.5-1.2 on momentum transport and heat transfer are investigated for Rayleigh number (Ra) in the range of 10(3)-10(5) and Prandtl number (Pr) of 10. (Nu) over bar near the hot wall is increased significantly with the fluid exponent increase at high Ra, but it is smaller than that without wall vibrations. Moreover, wall vibrations show slight and even no influence on (Nu) over bar of power-law fluids at low Ra. The maximum velocity components of shear-thinning fluids are both decreased under wall vibrations with increasing n, but it is unchanged in shearthickening fluids. The velocity components along the central lines of the cavity are decreased significantly for power-law fluids under wall vibrations. It is concluded that wall vibrations influence the streamlines, isotherm contours, and heat transfer characteristics of power-law fluids significantly at high Ra (similar to 10(5)). In addition, it has been found that the heat transfer rate is decreased as both aspect ratio and Pr increase.