Forced convection gaseous slip flow in circular porous micro-channels

Abstract

Laminar forced convection of gaseous slip flow in a circular micro-channel filled with porous media under local thermal equilibrium condition is studied numer- ically using the finite difference technique. Hydrodynamically fully developed flow is considered and the Darcy-Brinkman-Forchheimer model is used to model the flow inside the porous domain. The present study reports the effect of several operating parameters (Knudsen number (Kn), Darcy number (Da), Forchhiemer number (�) , and modified Reynolds number (Re ∗ )) on the velocity slip and temperature jump at the wall. Results are given in terms of the velocity distribution, temperature distri- bution, skin friction (CfRe ∗ ), and the Nusselt number (Nu). It is found that the skin friction is increased by (1) decreasing Knudsen number, (2) increasing Darcy number, and (3) decreasing Forchheimer number. Heat transfer is found to (1) decrease as the Knudsen number, or Forchheimer number increase, (2) increase as the Peclet number or Darcy number increase. Nomenclature C Coefficient in the Forchheimer term Cf Skin friction coefficient Cp Constant pressure specific heat Cv Constant volume specific heat D Diameter of the circular channel Da Darcy number (K/er 2 ) h Local heat transfer coefficient K Intrinsic permeability of the porous medium Kn Knudsen number (λ/r0)