Effects of viscous and darcy dissipation on fully developed natural convection flow in a composite channel partially filled with porous material: Homotopy perturbation method (HPM)

A steady natural convection flow in a composite channel partially filled with porous material is investigated analytically in this paper. In this respect, the effects of heat generation due to viscous dissipation and darcy dissipation were considered in the energy equations of the porous region and that of clear fluid region. In addition, the Brinkmann extended Darcy model was applied to model the flow in the porous region. The coupled system of nonlinear ordinary differential equations that governed the flow is solved by the homotopy perturbation method. The analytical solution results for velocity, temperature, and Nusselt number are provided and analyzed. The investigation reveals that increase in the thickness of the porous region hampers the hydrodynamics while it promotes the thermodynamics within the composite channel.

Automated summary

This paper analytically investigates a steady natural convection flow in a composite channel partially filled with porous material. The effects of heat generation due to viscous dissipation and darcy dissipation were considered in the energy equations of the porous region and clear fluid region. The Brinkmann extended Darcy model was applied to model the flow in the porous region. The analysis reveals that the increase in the thickness of the porous region hampers the hydrodynamics while promoting the thermodynamics within the composite channel.