An Analytical Solution for the Steady-State Free Convection Flow of a Nanofluid in a Vertical Channel

Abstract

This research analysed the steady-state free convection flow of a nanofluid in a vertical channel analytically. The nanofluid model used here include the effects of Brownian diffusion and thermophoresis. The solutions for the velocity, temperature and nanoparticle concentration profiles were obtained analytically using separation of variables and integral techniques. Nusselt and Sherwood numbers at the left wall of the channel were determined and discussed in detail. It is observed that the velocity decreases at the hot wall and increases at the cold wall due to increasing Prandtl number parameter. The same behaviour is noticed in the case of the buoyancy ratio, Grashof number, thermophoresis, and Brownian motion parameters. Furthermore, a numerical solution is also obtained and compared with the analytical solution.