Start-up slip flow in a microchannel with a rectangular cross section

• Published in: Theoretical and computational fluid dynamics Vol. 29; no. 5-6; pp. 351 - 371
• Main Authors: Avramenko, A. A., Tyrinov, A. I., Shevchuk, I. V.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2015; Springer; Springer Nature B.V
• Subjects: Asymptotic properties; Classical and Continuum Physics; Computational fluid dynamics; Computational Science and Engineering; Eigenfunctions; Engineering; Engineering Fluid Dynamics; Flow pattern; Fluid dynamics; Fluid flow; Fourier analysis; Hydraulics; Mathematical analysis; Mathematical models; Microchannels; Momentum equation; Original Article; Pressure; Pressure drop; Self-similarity; United States; Slip flow; Lie group; Lattice Boltzmann; Nusselt number; Microchannel
• ISSN: 0935-4964; 1432-2250
• DOI: 10.1007/s00162-015-0361-x

The paper outlines results of the theoretical study of an incompressible fluid flow in a rectangular microchannel subject to a sudden time-dependent pressure drop. The momentum equation together with the independent and dependent variables was reduced to a self-similar form by means of the symmetry analysis. The problem was solved using two analytical approaches, the Fourier method and the method of eigenfunction decomposition, as well as numerically by means of the lattice Boltzmann method. The unsteady two-dimensional velocity profiles in the microchannel were predicted using the infinite series and validated against the numerical solution. As expected, the flow pattern asymptotically attains the fully developed state, which is reached more rapidly for smaller Knudsen numbers. The analytical solution yielded expressions for the calculation of the hydraulic resistance coefficient.