Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 568345, 14 pages
Research Article

Analytic Approximations for the Flows and Heat Transfer in Microchannels between Two Parallel Plates

Mathematics Department, Faculty of Science, Helwan University, Cairo 11795, Egypt

Received 19 October 2011; Revised 15 December 2011; Accepted 15 December 2011

Academic Editor: Anuar Ishak

Copyright © 2012 A. El-Nahhas. This 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.


We consider the nonlinear problem for the flow of Newtonian fluid in a microchannel between two parallel plates with the effects of velocity slip, viscous dissipation, and temperature jump at the wall. This problem is modelled by both the Navier-Stokes equation and energy equation with two thermal boundary conditions related to the two cases: the constant wall temperature (CWT) and the constant heat flux (CHF). The homotopy analysis method is applied via a polynomial exponential basis to obtain analytic approximations for this problem. A rarefaction effects on the velocity profile and the flow friction are investigated. Also, as a result of the application, the effects, on the Nusselt number Nu, with variation in Brinkman number Br and Knudsen number Kn for both (CWT) case and (CHF) case are discussed.