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research-article

Nusselt Numbers for Poiseuille Flow over Isoflux Parallel Ridges for Arbitrary Meniscus Curvature

[+] Author and Article Information
Simon Game

Department of Mathematics, Imperial College London, London SW7 2AZ, UK
s.game14@imperial.ac.uk

Marc Hodes

Department of Mechanical Engineering, Tufts University, Medford, MA 02155
marc.hodes@tufts.edu

Toby Kirk

Department of Mathematics, Imperial College London, London SW7 2AZ, UK
toby.kirk12@imperial.ac.uk

Demetrios Papageorgiou

Department of Mathematics, Imperial College London, London SW7 2AZ, UK
d.papageorgiou@imperial.ac.uk

1Corresponding author.

ASME doi:10.1115/1.4038831 History: Received August 01, 2017; Revised November 13, 2017

Abstract

We numerically compute Nusselt numbers for laminar, hydrodynamically and thermally fully-developed Poiseuille flow of liquid in the Cassie state through a parallel plate-geometry microchannel symmetrically textured by a periodic array of isoflux ridges oriented parallel to the flow. Our computations are performed using an efficient, multiple domain, Chebyshev collocation (spectral) method. The Nusselt numbers are a function of the solid fraction of the ridges, channel height to ridge pitch ratio and protrusion angle of menisci. Significantly, our results span the entire range of these geometrical parameters. We quantify the accuracy of two asymptotic results for Nusselt numbers corresponding to small meniscus curvature, by direct comparison against the present results. The first comparison is with the exact solution of the dual series equations resulting from a small boundary perturbation. The second comparison is with the asymptotic limit of this solution for large channel height to ridge pitch ratio.

Copyright (c) 2017 by ASME
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