Analytical Solution for Fully Developed Flows of Nanofluids in Mixed-Convection Zone Within Vertical Channels

摘要

In this paper, a closed-form analytical solution is presented for a fully developed mixed-convection laminar flow of nanofluids between two vertical parallel plates. The Buongiorno model, which considers the Brownian motion and thermophoresis force, is employed to investigate the hydrodynamic and heat transfer behavior of the nanofluid flow. The equations for the conservation of mass, momentum, energy, and the nanoparticle concentration field have been analytically solved, and expressions for the velocity, temperature, and nanoparticle concentration profiles as well as for the Nusselt number are given. The results show that in addition to the mixed-convection buoyancy parameter (Gr/Re), the immersed-particle buoyancy parameter additionally enriches the momentum and enhances the heat transfer inside the channel. Moreover, in the mixed-convection regime, in contrast to the case of forced convection, the heat transfer rate decreases sharply and then gradually as the solid/fluid thermal conductivity ratio increases. The present results contradict the prevailing perception that higher thermal conductivities of nanoparticles are always desirable and boost heat transfer. The study findings will be helpful in selecting an appropriate nanoparticle material that would provide a high heat transfer rate based on the application's thermal conditions.