Pressure- and Temperature-Driven Flow Through Triangular and Trapezoidal Microchannels

Abstract

A detailed study of pressure- and temperature-driven flows through long channels of triangular and trapezoidal cross sections is carried out. Due to the imposed pressure and temperature gradients there is a combined gas flow consisting of a thermal creep flow from the cold toward the hot reservoir and a Poiseuille flow from the high- toward the low-pressure reservoir. The formulation is based on the linearized Shakhov model subject to Maxwell boundary conditions, and it is solved numerically using a finite-difference scheme in the physical space and the discrete velocity method in the molecular velocity space. The results are valid in the whole range of the Knudsen number. In addition to the dimensionless flow rates, a methodology is presented to estimate for a certain set of input data the mass flow rates and the pressure distribution along the channel. Finally, special attention is given to the case of zero net mass flow and to the computation of the coefficient of the thermomolecular pressure difference.

Acknowledgments

Konstantinos Ritos is a doctoral student at the Mechanical Engineering Department in University of Strathclyde. He obtained a diploma in mechanical engineering from the University of Thessaly (Greece) in 2009. His research is focused on computational micro and nano fluidics.

Yannis Lihnaropoulos is a Ph.D. student at the Mechanical Engineering Department of the University of Thessaly (Greece). He obtained a B.Sc. in mathematics from University of Ioannina (Greece) in 1992 and a postgraduate diploma in mechanical engineering from the University of Thessaly in 2008. He is currently involved with research in rarefied gas flows and kinetic theory.

Steryios Naris holds visiting positions in the Technological Educational Institute of Larisa and in the Department of Mechanical Engineering of the University of Thessaly. He has a degree in mechanical engineering from the Aristotle University Thessaloniki (1998) and M.Sc. (2003) and Ph.D. in microfluidics (2005) from the University of Thessaly. His work is focused on the numerical simulation of nonequilibrium flows. He has 14 journal and more than 35 conference proceedings publications.

Dimitris Valougeorgis is a professor in the Department of Mechanical Engineering of the University of Thessaly in Volos, Greece. He obtained a diploma in mechanical engineering from the Aristotelion University of Thessaloniki, Greece in 1980 and an M.S. and a Ph.D. degree in mechanical engineering from the Virginia Polytechnic Institute and State University in 1982 and 1985, respectively. His research is in kinetic theory of gases, rarefied gas dynamics, and nonequilibrium transport phenomena. He has published about 45 articles in journals and more than 100 articles in proceedings of conferences.