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Heat transfer in laminar Couette flow laden with rigid spherical particles

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations using a direct-forcing immersed boundary method to account for the dispersed phase. A volume of fluid approach is employed to solve the temperature field inside and outside of the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed. In addition, an average composite diffusivity can be used to predict the effective diffusivity of the suspension the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, saturating at higher volume fractions. By phase-ensemble averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated to fluid and particle velocity. We also show that the heat conduction in the solid phase reduces when increasing the particle Reynolds number and so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increase the total heat transfer.