Analysis of the Forced Convection in a Porous Channel Saturated by a Nanofluid: Effects of Brownian Diffusion and Thermophoresis

Abstract

The Darcy-Graetz problem for a channel filled by a nanofluid saturated porous medium is studied. The flow is assumed to be fully developed, and a boundary temperature linearly varying with the longitudinal coordinate in the thermal entrance region is prescribed. A study of the thermal behaviour of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. For the model of the nanofluid, both thermophoresis and Brownian diffusion are taken into account. The governing equations have been solved separately for the fully developed region and for the thermal entrance region. With reference to the fully developed region the solution has been obtained analytically, while for the thermal entrance region it has been obtained numerically, by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). The analysis shows that for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. Indeed, the homogeneous model could be employed effectively, since the effects of thermophoresis and Brownian diffusion are negligible.