Analysis of a Non-Reacting Laminar Fluid Flow with Viscous Dissipation through a Porous Channel Formed by Two Parallel Horizontal Permeable Walls

Abstract

The analytical solutions for the steady momentum and heat transfer of a non-reacting Newtonian viscous incompressible laminar fluid flow in a channel filled with saturated porous media with isothermal and isoflux heating walls were reported. The problem was studied under the viscous dissipation and suction/injection. The effects of various emerging parameters involved in the steady solution of the problem are discussed using contour graphs. It was revealed that with the imposition of suction/injection (Re ? 0) on the walls, the velocity close to the wall suction of the channel increases faster as compared to the opposite wall injection as Da increases as well as the ratio of viscosities M decreases. It was further shown that the fluid temperature is more influenced in isothermal process if either the Darcy number Da, or Brinkman number Br, or wall suction Reynolds number, Re or the three parameters are increased and either the ratio of viscosity M, or Peclet number Pe, or the wall injection Reynolds number, Re or the three parameters are decreased. With the same imposition in isoflux heating process, the fluid temperature distribution is more enhanced with increase in values of Pe or Br and decrease in values of M or wall suction/injection Reynolds numbers Re or the two emerging parameters respectively, while the effect of Darcy number Da on the flow results in an anomalous phenomenon in temperature distribution in the presence of suction Reynolds number Re.

Keywords: laminar flow, non-reacting fluid, suction/injection, isothermal, isoflux