The mechanism by which thermal coupling leads to an asymptotic maldistribution stability boundary for flow boiling in parallel channels

Abstract

Phase change heat transfer processes are attractive for the efficient thermal management of advanced semiconductor devices, with flow boiling in parallel microchannel heat sinks being one promising solution. However, there are several implementation challenges associated with two-phase flow in parallel microchannels, particularly flow maldistribution, which can adversely affect performance and reliability. Two-phase flow models can be useful in predicting and understanding the instability mechanisms that leads to maldistribution, such that parametric performance trends and safe regions of operation can be identified. Channel-to-channel thermal coupling has been shown to alleviate maldistribution, but it is not yet understood why this effect is limited to some critical lateral thermal conductance above which there is no further benefit. In the current work, a two-phase flow model with a lumped thermal capacitance representation of the heat sink wall is developed to identify the mechanism for this asymptotic maldistribution stability boundary for thermally coupled microchannels. The lumped model allows the nature of stability boundary to be explained via a scaling analysis of the eigenvalues. In such systems, it is identified that a single eigenvalue determines the occurrence of flow maldistribution. Scaling analysis shows that, for small values of thermal conductance, this eigenvalue becomes a quadratic function of thermal coupling, which enhances the stability of microchannels and moves the stability boundary. However, for large values of thermal conductance, the eigenvalue is dependent only on the fluid properties, leading to a limit at which thermal coupling can no further improve stability or affect the stability boundary. The lumped model developed in this work enables mechanistic understanding of the role of channel-to-channel thermal coupling on mitigating flow maldistribution and therefore may offer important guidance on the design of flow boiling systems and heat sinks.