Scaling of Nusselt Number for Digitized Heat Transfer at All Axial Distances Available to Purchase

The heat generation rates of modern electronic systems have increased to a point where conventional forms of thermal management are no longer sufficient. In this paper, Digitized Heat Transfer (DHT) is examined as one of the proposed solutions for high heat flux thermal management. Nusselt number is used to quantify the heat transfer capabilities of the flow while Re, Pr, x/H, and droplet aspect ratio are identified as the relevant nondimensional parameters that influence the shape and magnitude of Nu throughout a heated channel. With the intention of providing a single curve to represent the heat transfer in any digitized flow, a scaling constant, f₂, for Nu at axial distances greater than one circulation length is found. This scaling is combined with a previously identified scaling constant for the first circulation length using an inverse tangent weighting function. The two different scalings are applied to the Nu curve for heat transfer to a digitized flow and the result is a single curve that can approximately predict Nu at any axial position if the flow parameters are known. From the fitting functions identified, it is found that extremely long droplets will exhibit higher steady state Nu that is at least three times greater than the Nu value of the equivalent continuous flow.