Effects of temperature-dependent viscosity on natural convection in a porous cavity with a circular cylinder under local thermal non-equilibrium condition

In the present work, the influences of exponentially temperature-dependent viscosity on free convection in a porous cavity with a circular cylinder under local thermal non-equilibrium (LTNE) condition are investigated numerically via lattice Boltzmann (LB) method. To incorporate the LTNE effects, the temperature evolution equations are constructed by adding some unified source terms, which also preserve the parallel computation feature of the standard LB method. The effects of several physical parameters, including viscosity variation index (n), Rayleigh number (Ra), Darcy number (Da), ratio of fluid-to-solid thermal conductivity (lambda) and inter-phase heat transfer coefficient (H) on flow and heat transfer characteristics are numerically studied. The numerical results show that as the LTNE parameters increase (i.e., H and lambda), the solid heat transfer rate increases dramatically, while few changes are found for the heat transfer rate of fluid. Additionally, we find that for most given parameters, both the heat transfer rate of fluid and solid are generally decreased with the increase of n, while for relatively small values of H and lambda, the heat transfer coefficient of solid phase depends little on the value of n. Further, the impacts of the porosity (epsilon) as well as the aspect ratio (F) are also considered.