Numerical and experimental investigation of heat transfer within the first circulation length of a digitized flow

In this paper, the heat transfer to a hydrodynamically developed digitzed flow in a microchannel is studied with a specific emphasis on the dynamics occuring near the start of a heated region. The nondimensional parameters governing the phenomena are identified and the relations among them are presented. It is shown that the relevant nondimensional parameters are Nu, x/D, L_d/D, Re, and Pr while ignoring the air gap between droplets. Currently, Digitized Heat Transfer (DHT) is most commonly presented as Nu with respect to equation. This approach is reexamined and it is shown that equation is a parameter uniquely suited to heat transfer in a continuous flow and not appropriate for DHT. Based on two dimensional Cartesian and axisymmetric numerical simulations, a new model is proposed where heat transfer rate in DHT is presented as Nu√(AR/Pe) vs x/(2L_d+D) where AR = L_d/D is the droplet aspect ratio. Using this scaling, the Nu within the first circulation length of a translating droplet converges for all AR and Pe values greater than 1. Experimental trials are conducted to verify trends observed in numerical simulations. It is confirmed that increases in Pe cause an overall increase in Nu and that the proposed scaling is applicable to digitized flows with liquid fractions less than one. Furthermore, it is found that the relative size of the gas bubbles compared to the liquid droplets can have an effect on local heat transfer rate where larger gas bubbles result in a lower Nu.