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In this paper, Buongiorno’s mathematical model is adopted to simulate both natural con- vection and mixed convection of a nanofluid in square porous cavities. The model takes into account the Brownian diffusion and thermophoresis effects. Both constant and varia- ble temperatures are prescribed at the side walls while the remaining walls are maintained adiabatic. Moreover, all boundaries are assumed to be impermeable to the base fluid and the nanoparticles. The governing equations are transformed to a form of dimensionless equ- ations and then solved numerically using the finite-volume method. Thereafter, effects of the Brownian diffusion parameter, the thermophoresis number, and the buoyancy ratio on the flow strength and the average Nusselt number as well as distributions of isocontours of the stream function, temperature, and nanoparticles fraction are presented and discussed.

Natural and mixed convection of a nanofluid in porous cavities: critical analysis using Buongiorno’s model