Influence of viscosity variations on the forced convection flow through two types of heterogeneous porous media with isoflux boundary condition

A theoretical analysis of fully developed forced convection flow through a heterogeneous porous medium with isoflux boundary condition is carried out by invoking a varying viscosity model to determine its effect on the resulting heat and fluid flow characteristics. Two different types of permeability and thermal conductivity variations, in the transverse direction of the channel, are accounted for in the analysis, viz., continuous weak and step-wise variations. Analytical solutions are obtained and graphical illustrations are presented to reveal the influence of thermal conductivity, permeability and viscosity variations. The results indicate that the viscosity variations have significant effect on the resulting heat transfer characteristics interpreted in terms of the Nusselt number. Moreover, the results reveal that the heat transfer rate decreases with the increase of permeability ratio for strong viscosity variations, which cannot be captured if a constant viscosity model is assumed.