Analysis of Galinstan-Based Microgap Cooling Enhancement Using Structured Surfaces

Abstract

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.

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

“…Superhydrophobic surfaces, i.e., those with hydrophobic micro-and/or nanoscale protrusions, are of interest in the context of liquid flow through microchannels, especially in direct liquid cooling applications as a means to reduce flow and thus caloric resistance [1]. When criteria are met [1,2], the solid-liquid interfaces are confined to the tips of the structures, forming a composite interface along with the liquid-gas interfaces (menisci), as per Fig. 1, and the liquid is said to be in the unwetted or Cassie state [3,4].…”

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

“…The practical interest lies in, e.g., the thermal management of electronics via microchannel cooling of microprocessors whereby transfer of heat from the solid substrate (silicon) to a liquid coolant is desired, with as little thermal resistance as possible. A significant portion of the total thermal resistance is the caloric resistance of the coolant attributable to the energy required to increase its bulk temperature as it flows through the microchannel (Tuckerman & Pease 1981;Hodes et al 2014;Lam et al 2015). The structured walls increase the mass flow rate, and thus decrease the caloric resistance.…”

Nusselt Numbers for Thermally Developing Couette Flow With Hydrodynamic and Thermal Slip

“…Understanding these interactions is of importance in the design of microfluidic and nanofluidic platforms for use in a variety of application areas, including biotechnology [2], thermal management of electronics [3] and energy [4]. Structured surfaces (SSs), e.g., superhydrophobic surfaces or superoleophobic surfaces are a class of surfaces engineered on the microscale and nanoscale that resist wetting and decrease hydrodynamic drag.…”