Effects of Brownian diffusion and thermophoresis on the laminar forced convection of a nanofluid in a channel

A steady laminar forced convection in a parallel–plane channel using nanofluids is studied. The flow is assumed to be fully developed, and described through the Hagen–Poiseuille profile. A boundary temperature varying with the longitudinal coordinate in the thermal entrance region is prescribed. Two sample cases are investigated in detail: a linearly changing wall temperature, and a sinusoidally changing wall temperature. A study of the thermal behavior of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. The numerical solution is obtained by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). With reference to both the wall temperature distributions prescribed along the thermal entrance region, the governing equations have been solved separately both for the fully developed region and for the thermal entrance region. The analysis shows that if a linearly varying boundary temperature is assumed, for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. On the other hand, in case of a longitudinally periodic boundary temperature, nonhomogeneities in the nanoparticle concentration distribution arise, which are wrongly neglected whenever the homogeneous model is employed.