A unified model for Digitized Heat Transfer in a microchannel

Abstract

Digitized Heat Transfer (DHT) is a novel method of adaptive thermal management for high powered devices that uses discrete microdroplets to remove heat. In this paper, the heat transfer characteristics of DHT are investigated for parallel plate and axisymmetric circular microchannels using scale analysis and numerical simulations. DHT in axisymmetric microchannels are also studied using experimental tests. Through scale analysis, it is found that DHT is quantified by the Nusselt number (Nu) and is a function of the Reynolds number (Re), Prandtl number (Pr), nondimensional axial distance (x/DH), and droplet aspect ratio (▪). In simulation and experiment, Nu shows a direct relationship with Re and Pr as well as an inverse relationship with ▪. Using the Graetz problem as a model, new scaling relations are proposed for the axial distance, x, and Nu in an effort to collapse the Nu curves that exist for different flow parameters. To align the characteristic oscillations of Nu found in DHT, x is scaled by the droplet circulation length, Lcirc, to create a new nondimensional axial distance, xcirc=xLcirc. In order to match the overall magnitude, Nu scaling is derived based on the two different modes of heat transfer that occur before and after one circulation length. Prior to one circulation length, heat transfer is characterized by thermal boundary layer growth and the scaling parameter is determined to be f1=RePr▪. After one circulation length, recirculation of heat is dominant and a scaling parameter f2 is found to be a linear function of 1/▪. f2 is modeled by the equation f2=c1▪+c2 where c1 and c2 are dependent on Re and Pr. The two scaling constants are merged using an inverse tangent weighting function (w) so that a fully scaled Nusselt number, Nu∗, is defined by Nu(1/f1)(1-w)-(1/f2)w. Using this unified model, numerical and experimental data are reduced to a single curve that depicts the heat transfer to any digitized flow. In the future, this model will be helpful in comparing various DHT systems as well as enabling the design of powerful and efficient DHT based thermal management systems.