A two-phase theoretical study of Al₂O₃-water nanofluid flow inside a concentric pipe with heat generation/absorption

Convective heat transfer and pressure drop characteristics of Al ₂O₃-water nanofluid inside a concentric pipe with constant heat flux boundary conditions at the both walls is investigated theoretically. The employed model for nanofluid includes the two-phase modified Buongiorno model that fully accounts for the effects of nanoparticle volume fraction distribution. Due to the nanoparticles migration in the fluid, the no-slip condition of the fluid-solid interface at the pipe walls is abandoned in favor of a slip condition which appropriately represents the non-equilibrium region near the interface. Governing equations were transformed into a system of ordinary ones via the similarity variables and solved numerically. The effects of heat generation/absorption σ, slip parameter λ, and heat flux ratio ε on nanoparticle volume fraction, velocity, temperature, heat transfer coefficient at both walls, and the dimensionless pressure gradient have been investigated in detail. The results obtained indicated that the nanoparticles move from the wall with higher heating energy towards the wall with lower heating energy (along the temperature gradient) due to the thermophoretic force. This non-uniform distribution of nanoparticles at the cross section of the pipe, pushes the peak of the axial velocity from the wall with lower heating energy towards the wall with higher heating energy. In addition, slip velocity at the pipe walls enhances heat transfer coefficient and increase the dimensionless pressure gradient ratio. Moreover, the changes of the heat transfer coefficient enhancement in the case of heat generation is much more that in the case of heat absorption, for low values of ratio of Brownian diffusivity to thermophoretic diffusivities N_BT.