Steady State Heat Transport by Microbubble Dispersions Mediating Convection With Phase Change Dynamics

A new theory for additional heat transfer convected by a dispersed phase of microbubbles was posited recently. An additional convection term in the heat transport equation reflects the latent heat of vapor of the liquid carried by the microbubbles from hot zones that vaporize more liquid to cold zones where condensation releases the latent heat. This theory was shown to be consistent with analysis of observations of freezing times measured by in the original Mpemba effect study, by inferring heat transfer coefficients fitted by Newton’s law of cooling. In this paper, the scaling analysis, leading to the proposition that the additional heat flux is proportional to the phase fraction of microbubbles, is tested by steady state solutions of the canonical hot wall / cold wall buoyant convection problem. For phase fractions 0.02 and 0.1, the maximum ratio of additional Nusselt number emergent is five, occurring in the microfluidic regime. Increasing the characteristic length of the domain maintains the monotonicity of the increase in additional Nusselt number ratio over the case of no microbubbles present. The additional heat transfer due to the microbubble dispersion, ranging from 5-50%, is found to be nearly proportional to the microbubble phase fraction for the range of 0.02 to 0.2. However, larger characteristic lengths introduce insufficient heat flux from the hot wall to maintain a “driven cavity” flow structure, so that the steady state structure that emerges is a stable stratification with thin boundary layers near the hot and cold walls, with weak shear flow convection. The stable stratification resultant at higher characteristic lengths suppresses the additional heat flux due to microbubble mediation, but only moderately deviating from proportionality.