Hindawi Publishing Corporation Journal of Fluids Volume 2013, Article ID 604893, 9 pages http://dx.doi.org/10.1155/2013/604893 Research Article Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid Yazan Taamneh 1 and Reyad Omari 2 1 Department of Mechanical Engineering, Tafla Technical University, P.O. Box 179, Tafla 66110, Jordan 2 Department of Mathematics, Al-Balqa Applied University, Irbid University College, P.O. Box 19117, Irbid 19110, Jordan Correspondence should be addressed to Yazan Taamneh; taamneh@daad-alumni.de Received 18 May 2013; Accepted 5 October 2013 Academic Editor: Ciprian Iliescu Copyright © 2013 Y. Taamneh and R. Omari. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Tis study aims to numerically examine the fuid fow and heat transfer in a porous microchannel saturated with power-law fuid. Te governing momentum and energy equations are solved by using the fnite diference technique. Te present study focuses on the slip fow regime, and the fow in porous media is modeled using the modifed Darcy-Brinkman-Forchheimer model for power- law fuids. Parametric studies are conducted to examine the efects 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. Tis efect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the efect of power law index vanishes. Te 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 efects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little. 1. Introduction Fluid fow 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 feld of microscale heat transfer have existed. However, microchannels are now used in several industries and equip- ment such as cooling of electronic package, microchannel heat sinks, microchannel heat exchanger, microchannel fab- rication, and cooling, and heating of diferent devices [1–5]. One of the major difculties in trying to predict the gaseous transport in micron sized devices can be attributed to the fact that the continuum fow assumption implemented in the Navier-Stokes equations breaks down when the mean free path of the molecules () is comparable to the characteristic dimension of the fow domain. Under these conditions, the momentum and heat transfer start to be afected by the discrete molecular composition of the gas and a variety of noncontinuum or rarefaction efects are likely to be exhibited such as velocity slip and temperature jump at the gas-solid interface. Velocity profles, fuid fow rate, boundary wall shear stresses, temperature profles, heat transfer rates, and Nusselt number are all infuenced by the noncontinuum regime. However, there is a certain limit of the channel size with which one can still apply Navier-Stokes equations with some modifcations on the boundary conditions [6]. Tis is the case when Knudsen number (Kn) is in the range 0.001 ≤ Kn ≤ 0.1, and the fow under such condition is called slip- fow. Knudsen number is defned as the ratio of the molecular mean free path to the characteristic length of the system. It is also used to measure of the degree of rarefaction of gases encountered in fows through narrow passages, and also to measure the degree of the validity of the continuum model. Te continuum model is valid for very small Knudsen number fows (Kn < 10 −3 ). While the Knudsen number increases, the rarefaction efects become more pronounced,