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Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

Published online by Cambridge University Press:  07 December 2016

Toby L. Kirk ,
Marc Hodes  and
Demetrios T. Papageorgiou
Toby L. Kirk*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Marc Hodes
Affiliation:
Department of Mechanical Engineering, Tufts University, Medford, MA 02155, USA
Demetrios T. Papageorgiou
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.

JFM classification

Convection: Convection Micro-/Nano-fluid dynamics: Microfluidics Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 811 , 25 January 2017 , pp. 315 - 349
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Copyright
© 2016 Cambridge University Press 

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