Analytical Solution of a Steady Non-Reacting Laminar Fluid Flow in a Channel Filled With Saturated Porous Media with Two Distinct Horizontal Impermeable Wall Conditions

Abstract

An analysis of the study of momentum and heat transfer characteristics of a non-reacting Newtonian viscous incompressible laminar fluid flow in a channel filled with saturated porous media with both isothermal and isoflux boundary conditions has been carried out.  The dimensionless non-linear coupled ordinary differential equations governing the flow and the heat transfer characteristics are solved analytically using the method of undetermined coefficients. Details of velocities and temperature fields for various values of the emerging parameters of the steady solutions of the problems are presented using contour graphs. It was shown that the porous medium may be used to control the flow in a saturated porous media using less permeable materials which offer greater resistance to the boundary-layer momentum development. It was further revealed that increase in porous media permeability and decrease in ratio of viscosities, help to enhance the fluid flow; however the input of the viscous term on the flow behaviour is insignificant for extremely lower values of Darcy number. It was also shown that the fluid temperature is more influenced in isothermal and isoflux processes if the Darcy number, Da, or Brinkman number, Br, or both are increased and if the ratio of viscosities M, is decreased.

Keywords: laminar flow, porous medium, impermeable walls, isothermal, isoflux)