Heat Transfer for Annular Flow in Microchannel Bends: A Free Energy Minimization Model for Square Channels

For annular liquid-vapor two-phase flow in straight microchannels, effects of gravity are generally small compared to viscous and/or inertia forces. In serpentine evaporator or condenser passages with semicircular return bends, the bend radius may be so small that large centrifugal body forces are generated as the fluid flows through the bend region of the passage. This paper summarizes a model analysis based on the premise that flow morphology in the bend is dictated by radial acceleration forces and the thermodynamic Second Law requirement that the established two-phase flow morphology minimizes the free energy at the local temperature and pressure. An analytical model is derived relating the dependence of the free energy on vapor core geometry, and the geometry that minimizes free energy is determined numerically. This provides a prediction of the mean thickness of the liquid surrounding the vapor core, and the mean heat transfer coefficient for annular flow vaporization or condensation, as a function of flow parameters and physical properties. When this relation is cast in dimensionless form, the effect of centrifugal acceleration is quantified in terms of a Weber number (We) that represents the ratio of centrifugal body force to surface tension force. The analysis indicates that centrifugal acceleration acts to displace the vapor towards the inside of the curved passage and distort the liquid-vapor interface. Displacement occurs at any level of acceleration. Significant distortion is found to occur only for We > 1. The effects of these morphology changes on heat transfer are analyzed and the implications of these predictions for designing microchannel evaporators and condensers are explored.