Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid

This study aims to numerically examine the fluid flow and heat transfer in a porous microchannel saturated with power-law fluid. The governing momentum and energy equations are solved by using the finite difference technique. The present study focuses on the slip flow regime, and the flow in porous media is modeled using the modified Darcy-Brinkman-Forchheimer model for power-law fluids. Parametric studies are conducted to examine the effects of Knudsen number, Darcy number, power law index, and inertia parameter. Results are given in terms of skin friction and Nusselt number. It is found that when the Knudsen number and the power law index decrease, the skin friction on the walls decreases. This effect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the effect of power law index vanishes. The numerical results indicated also that when the power law index decreases the fully-developed Nusselt number increases considerably especially, in the limit of high permeability, that is, nonDarcy regime. As far as Darcy regime is concerned the effects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little. 1. Introduction Fluid flow and heat transfer in porous media has been a subject of continuous interest during past decades because of the wide range of engineering applications. In addition to conventional applications including solar receivers, building thermal insulation materials, packed bed heat exchangers, and energy storage units, new applications in the emerging field of microscale heat transfer have existed. However, microchannels are now used in several industries and equipment such as cooling of electronic package, microchannel heat sinks, microchannel heat exchanger, microchannel fabrication, and cooling, and heating of different devices [1–5]. One of the major difficulties in trying to predict the gaseous transport in micron sized devices can be attributed to the fact that the continuum flow assumption implemented in the Navier-Stokes equations breaks down when the mean free path of the molecules (λ) is comparable to the characteristic dimension of the flow domain. Under these conditions, the momentum and heat transfer start to be affected by the discrete molecular composition of the gas and a variety of noncontinuum or rarefaction effects are likely to be exhibited such as velocity slip and temperature jump at the gas-solid interface. Velocity profiles, fluid flow rate, boundary wall shear stresses, temperature profiles, heat