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Research Papers

Analysis of Galinstan-Based Microgap Cooling Enhancement Using Structured Surfaces

[+] Author and Article Information
Lisa Steigerwalt Lam

Mechanical Engineering Department,
Tufts University,
Medford, MA 02155
e-mail: Lisa_Lam@alum.mit.edu

Marc Hodes

Mechanical Engineering Department,
Tufts University,
Medford, MA 02155

Ryan Enright

Thermal Management Research Group,
Efficient Energy Transfer (ηet) Department,
Bell Labs Ireland, Alcatel-Lucent Ireland Ltd.,
Blanchardstown Business & Technology Park,
Dublin 15, Ireland

1Corresponding author.

Manuscript received January 9, 2014; final manuscript received February 11, 2015; published online May 14, 2015. Assoc. Editor: L.Q. Wang.

J. Heat Transfer 137(9), 091003 (Sep 01, 2015) (10 pages) Paper No: HT-14-1013; doi: 10.1115/1.4030208 History: Received January 09, 2014; Revised February 11, 2015; Online May 14, 2015

Analyses of microchannel and microgap cooling show that galinstan, a recently developed nontoxic liquid metal that melts at −19 °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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Figures

Grahic Jump Location
Fig. 1

Surface tension and viscosity for water and Ga-In-Sn ternary alloy. Saturated water properties from Ref. [26]. Ga-In-Sn alloy properties from Ref. [25].

Grahic Jump Location
Fig. 2

Schematic of SS microgap with height H, width w, and length L. The walls of the channel are structured with ridges of width wr and spacing wc+wr arranged parallel to the flow in the x-direction.

Grahic Jump Location
Fig. 3

Schematic of a single unit cell of a parallel ridge SS in a channel. The ridges have a thickness, wr, spacing, wc, and height, h. The maximum deflection of the interface, d, and the advancing contact angle on the wall of the ridge are also shown.

Grahic Jump Location
Fig. 4

NL parameter as a function of surface solid fraction, φs

Grahic Jump Location
Fig. 5

Percent change in thermal resistance of a galinstan SS channel from that of a galinstan classic channel as a function of ridge pitch and solid fraction

Grahic Jump Location
Fig. 6

The maximum pressure which can be supported across the liquid-gas interface versus pitch for a fixed value of φs=0.02 as per Eq. (13). This pressure is used in the classic channel calculations in order to make an equitable comparison.

Grahic Jump Location
Fig. 7

Thermal resistance versus pitch for galinstan in SS channel, φs=0.025, and in classic channel

Grahic Jump Location
Fig. 8

Thermal resistance versus pitch for galinstan and water in SS channel, φs=0.025, and in classic channel. Pressure drop corresponds to Fig. 6 except for that of water in the SS channel.

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