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Advances in Mechanical Engineering
Volume 2012 (2012), Article ID 481280, 8 pages
Research Article

Slip Flow in Elliptic Microducts with Constant Heat Flux

Department of Industrial Engineering, University of Parma, Parco Area delle Scienze 181/A, 43124 Parma, Italy

Received 28 April 2012; Revised 6 September 2012; Accepted 10 September 2012

Academic Editor: C. T. Nguyen

Copyright © 2012 Marco Spiga and Pamela Vocale. 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.


This paper outlines a numerical model for determining the dynamic and thermal performances of a rarefied fluid flowing in a microduct with elliptical cross-section. A slip flow is considered, in laminar steady state condition, in fully developed forced convection, with Knudsen number in the range 0.001−0.1, in H1 boundary conditions. The velocity and temperature distributions are determined in the elliptic cross-section, for different values of both aspect ratio γ and Knudsen number, resorting to the Comsol Multiphysics software, to solve the momentum and energy equations. The friction factors (or Poiseuille numbers) and the convective heat transfer coefficients (or Nusselt numbers) are calculated and presented in graphs and tables. The numerical solution is validated resorting to data available in literature for continuum flow in elliptic cross-sections (Kn = 0) and for slip flow in circular ducts ( ). A further benchmark is carried out for the velocity profile for slip flow in elliptical cross-sections, thanks to a recent analytical solution obtained using elliptic cylinder coordinates and the separation of variables method. The Poiseuille and Nusselt numbers for elliptic cross-sections are discussed. The results may be used to predict pressure drop and heat transfer performance in metallic microducts with elliptic cross-section, produced by microfabrication for microelectromechanical systems (MEMS).