Numerical analysis of conjugate natural and mixed convection heat transfer of nanofluids in a square cavity using the two-phase method

In the present study, the problem of conjugate natural and mixed convection of nanofluid in a square cavity containing several pairs of hot and cold cylinders is visualized using non-homogenous two-phase Buongiorno's model. Such configuration is considered as a model of heat exchangers in order to prevent the fluids contained in the pipelines from freezing or condensing. Water-based nanofluids with Cu, Al₂O₃, and TiO₂ nanoparticles at different diameters ($25\text{nm}?d_p?145\text{nm}$) are chosen for investigation. The governing equations together with the specified boundary conditions are solved numerically using the finite volume method based on the SIMPLE algorithm over a wide range of Rayleigh number (${10}^4?\mathit{Ra}?{10}^7$), Richardson number (${10}^{-2}?\mathit{Ri}?{10}^2$) and nanoparticle volume fractions ($0?\phi ?5\%$). Furthermore, the effects of three types of influential factors such as: orientation of conductive wall, thermal conductivity ratio ($0.2?K_r?25$) and conductive obstacles on the fluid flow and heat transfer rate are also investigated. It is found that the heat transfer rate is significantly enhanced by incrementing Rayleigh number and thermal conductivity ratio. It is also observed that at all Rayleigh numbers, the total Nusselt number rises and then reduces with increasing the nanoparticle volume fractions so that there is an optimal volume fraction of the nanoparticles where the heat transfer rate within the enclosure has a maximum value. Finally, the results reveal that by increasing the thermal conductivity of the nanoparticles and Rayleigh number, distribution of solid particles becomes uniform.