Mixed convective heat transfer from a permeable square cylinder: A lattice Boltzmann analysis

The flow and mixed convection heat transfer from a two-dimensional porous square cylinder under the influence of aiding buoyancy in an infinite stream are analysed employing a mesoscopic approach. Reynolds number (Re) and Darcy number (Da) considered in this study vary from 2 to 40 and 10-6 to 10-2, respectively. The flow and heat transfer characteristics at the Prandtl number value of 0.71 (air) is compared for three different values of Richardson number (Ri) i.e. 0, 0.5 and 1. The numerical experiments in this study are carried out by using Lattice Boltzmann technique with two distribution functions. The BGK collision operator with Darcy-Forchheimer and Boussinesq force terms are added to the LB collision equation. Mach number annealing process is also carried out to accelerate the simulations. Flow and heat transfer characteristics are found to be a function of non-dimensional permeability (Da), buoyancy condition and Reynolds number. It is observed that a monotonous reduction occurs in the wake length and drag coefficient values at higher permeability levels. Whereas, aiding buoyancy depicts a pronounced reduction in wake length and an increment in drag coefficient values. The heat transfer enhancement ratio for all surfaces of the cylinder and mean Nusselt number were calculated to compare the thermal behaviour at various Ri and Da values. A significant augmentation in heat dissipation is reported for increasing values of Ri and/or Da. The percentage increment in mean Nusselt number at Re = 40, Da=10-2 is found to be 18% and 34% for Ri = 0.5 and 1, respectively with reference to the forced convection case. Also, heat transfer is maximum at Da=10-2 and Ri = 1 for the flow regime considered in this study. Correlations for mean Nusselt number, valid for the range of parameters considered in the present study, are also provided. The key results obtained from this study can be helpful for further research in different realms of engineering sciences, especially thermal engineering, aided by porous media modeling approach.