Fully developed nanofluid mixed convection flow in a vertical channel

A closed form analytical solution of laminar mixed convection heat transfer of a nanofluid between two vertical parallel plates, accounting for the effects Brownian motion and thermophoresis, is presented for the fully developed region under thermal boundary conditions of the first and fourth kinds. Four kinds of nano-sized solid particles with varied thermophysical properties suspended in water are considered. Closed form analytical expressions of velocity and temperature fields, pressure gradients, nanoparticle concentration profiles, and Nusslet numbers are illustrated. Effects of the controlling parameters, namely the 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 discussed in detail. It is found that the Nusslet number increases with increases in the buoyancy parameter and volume fraction. However, the pressure drop is found to increase with volume fraction and decrease with the buoyancy parameter. In addition, for upward mixed convection flow, the pressure drop attributed 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-where the buoyancy forces balance the viscous forces-are obtained and presented.