A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section

• Published in: International journal of heat and mass transfer 2007-07, Vol.50 (13), p.2492-2502
• Main Authors: Bahrami, Majid, Michael Yovanovich, M., Richard Culham, J.
• Format: Article
• Language: English
• Subjects: Applied fluid mechanics; Arbitrary cross-section channels; Characteristic length scale; Exact sciences and technology; Fluid dynamics; Fluidics; Fundamental areas of phenomenology (including applications); Laminar fully developed flow; Microchannels; Modeling; Physics; Poisson’s equation; Pressure drop; Saint-Venant
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2006.12.019

This paper outlines a novel approximate solution for determining the pressure drop of fully developed, laminar, single-phase flow in singly connected microchannels of arbitrary cross-section. Using a “bottom-up” approach, it is shown that for constant fluid properties and flow rate in fixed cross-section channels, the Poiseuille number is only a function of geometrical parameters of the cross-section, i.e., perimeter, area, and polar moment of inertia. The proposed model is validated with experimental data for rectangular, trapezoidal, and triangular microchannels. The model is also compared against numerical results for a wide variety of channel cross-sections including: hyperellipse, trapezoid, sine, square duct with two adjacent round corners, rhombic, circular sector, circular segment, annular sector, rectangular with semi-circular ends, and moon-shaped channels. The model predicts the pressure drop for the cross-sections listed within 8% of the values published.