A study on the effect of magnetic field and the sinusoidal boundary condition on free convective heat transfer of non-Newtonian power-law fluid in a square enclosure with two constant-temperature obstacles using lattice Boltzmann method

Abstract

In this paper, the flow pattern and thermal characteristics of free convection of a Newtonian magnetohydrodynamic fluid flow inside a square enclosure are compared against two different non-Newtonian power-law (PL) fluids. The enclosure with horizontal insulated walls has two constant-temperature obstacles, while two sidewalls are differentially heated with sinusoidal pattern. Boussinesq approximation is used to consider the effect of hydrodynamic field on the thermal field. The problem is grounded using lattice Boltzmann method, and D2Q9 function is used to describe distribution of the density and energy. The effects of Rayleigh number, PL index, the aspect ratio of constant-temperature obstacles, Hartmann number, and periodicity of sinusoidal boundary condition on the hydrodynamic and thermal characteristics are investigated. The results showed that with increasing Rayleigh number, the Nusselt number increases but with increasing power-law index and Hartmann number, the Nusselt number decreases for shear thinning, Newtonian and shear thickening fluids. In addition, it was shown that increasing the aspect ratio of obstacles increases the Nusselt number. Also, it was reported that the Nusselt number of Newtonian and shear thinning fluids increases with increasing the periodicity of the sinusoidal boundary condition from 2 pi to 4 pi, while it reduces by further increase in periodicity.