Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip

Hodes, Marc; Lam, Lisa Steigerwalt; Cowley, A.; Enright, Ryan; MacLachlan, Scott

doi:10.1115/1.4029818

Cited by 22 publications

(21 citation statements)

References 11 publications

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“…Thermocapillary stress for flow over ridged surfaces has been considered by Baier et al (2010) and recently by Hodes et al (2015a), and evaporation/condenstaion investigated by Hodes et al (2015b). However, all previous work on heat transfer (including that mentioned in the previous paragraph) has assumed a flat meniscus.…”

Section: Introductionmentioning

confidence: 94%

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

2016

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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 de-wetted (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 to ridge period are compared to numerical solutions of the dual series. 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 useful for engineering applications.

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Section: Introductionmentioning

confidence: 94%

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

2016

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“…We also assume that the evaporation and condensation along the liquid-gas interface are negligible due to the extremely low vapor pressure of galinstan (p v < 10 À6 Pa at 500 C) [5]. In the case of water, evaporation and condensation may have a significant and beneficial effect on slip lengths [29], but we do not address this here. We further assume that for the purposes of calculating hydrodynamic and thermal slip lengths the liquid-gas interface is flat.…”

Section: Problem Formulationmentioning

confidence: 99%

“…(29) where Kn 0 ¼ 0. Values for the caloric resistance with a fully developed flow assumption and with an apparent friction factor assumption are listed in Table 5 for Table 5 Entrance length and f app Re Dh values from Eq.…”

Section: Galinstanmentioning

confidence: 99%

Analysis of Galinstan-Based Microgap Cooling Enhancement Using Structured Surfaces

Lam

Hodes

Enright³

2015

Journal of Heat Transfer

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Analyses of microchannel and microgap cooling show that galinstan, a recently developed nontoxic liquid metal that melts at À19 C, may be more effective than water for direct liquid cooling of electronics. The thermal conductivity of galinstan is nearly 28 times that of water. However, since the volumetric specific heat of galinstan is about half that of water and its viscosity is 2.5 times that of water, caloric, rather than convective, resistance is dominant. We analytically investigate the effect of using structured surfaces (SSs) to reduce the overall thermal resistance of galinstan-based microgap cooling in the laminar flow regime. Significantly, the high surface tension of galinstan, i.e., 7 times that of water, implies that it can be stable in the nonwetting Cassie state at the requisite pressure differences for driving flow through microgaps. The flow over the SS encounters a limited liquid-solid contact area and a low viscosity gas layer interposed between the channel walls and galinstan. Consequent reductions in friction factor result in decreased caloric resistance, but accompanying reductions in Nusselt number increase convective resistance. These are accounted for by expressions in the literature for apparent hydrodynamic and thermal slip. We develop a dimensionless expression to evaluate the tradeoff between the pressure stability of the liquid-solid-gas system and hydrodynamic slip. We also consider secondary effects including entrance effects and temperature dependence of thermophysical properties. Results show that the addition of SSs enhances heat transfer.

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“…Lam et al [14] derived expressions for the thermal slip length for isoflux and isothermal parallel ridges accounting for small meniscus curvature. Hodes et al [15] captured the effects of evaporation and condensation along menisci on the thermal slip length for isoflux ridges. Lam et al [16] developed expressions for the Nusselt number for Couette flow as a function of the slip lengths for various boundary conditions.…”

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confidence: 99%

Solution of the Graetz–Nusselt Problem for Liquid Flow Over Isothermal Parallel Ridges

Karamanis

Hodes

Kirk

et al. 2017

Journal of Heat Transfer

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We consider convective heat transfer for laminar flow of liquid between parallel plates that are textured with isothermal ridges oriented parallel to the flow. Three different flow configurations are analyzed: one plate textured and the other one smooth; both plates textured and the ridges aligned; and both plates textured, but the ridges staggered by half a pitch. The liquid is assumed to be in the Cassie state on the textured surface(s), to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. Heat is exchanged with the liquid either through the ridges of one plate with the other plate adiabatic, or through the ridges of both plates. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). Axial conduction is neglected and the inlet temperature profile is arbitrary. We solve for the three-dimensional developing temperature profile assuming a hydrodynamically developed flow, i.e., we consider the Graetz-Nusselt problem. Using the method of separation of variables, the thermal problem is essentially reduced to a two-dimensional eigenvalue problem in the transverse coordinates, which is solved numerically. Expressions for the local Nusselt number and those averaged over the period of the ridges in the developing and fully developed regions are provided. Nusselt numbers averaged over the period and length of the domain are also provided. Our approach enables the aforementioned quantities to be computed in a small fraction of the time required by a general computational fluid dynamics (CFD) solver.

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Effect of Evaporation and Condensation at Menisci on Apparent Thermal Slip

Cited by 22 publications

References 11 publications

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

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

Analysis of Galinstan-Based Microgap Cooling Enhancement Using Structured Surfaces

Solution of the Graetz–Nusselt Problem for Liquid Flow Over Isothermal Parallel Ridges

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