Fully Developed Mixed Convection Flow of a Nanofluid in a Vertical Channel

A closed form analytical solution of laminar mixed convection heat transfer of nanofluid inside two vertical parallel plates taking into account the Brownian motion and thermophoresis effects is presented in the fully... [ view full abstract ]

A closed form analytical solution of laminar mixed convection heat transfer of nanofluid inside two vertical parallel plates taking into account the Brownian motion and thermophoresis effects is presented in the fully developed region under the thermal boundary conditions of first and fourth kinds. Four different kinds of nano-sized solid particles which have different thermophysical properties suspended in water are considered. Closed form analytical expressions of velocity and temperature fields, pressure gradient, nanoparticle concentration profiles, and Nusslet number are illustrated. The effects of controlling parameters, namely buoyancy parameter, thermal conductivity solid/fluid ratio, and volume fraction on the hydrodynamic and heat transfer parameters such as pressure gradient and Nusslet number are in detail discussed. It is found that the Nusslet number increases with increasing buoyancy parameter and volume fraction. However, the pressure drop is found to increase with volume fraction and decrease with buoyancy parameter. In addition, the results show that, for upward mixed convection flow, the pressure drop due to the addition of nano-sized solid particles into the base fluid can be overcome by the buoyancy forces. The critical values of the buoyancy parameter at which the buoyancy forces balance the viscous forces are obtained and presented.