External Conjugate Boiling on Channels. A Graetz Problem With Multiple Solutions

Abstract

In this study, a conjugate laminar Graetz problem in a channel with wall conduction is theoretically studied. The heat exchanger under consideration utilizes a hot fluid stream with embedded heat sources in the internal side of the channel and a boiling liquid at the external side. Because of the nonlinear and nonmonotonic boiling curve, a complex and interesting solution structure exists. When the wall conduction is accounted for the problem admits multiple solutions. For a certain range of the conduction–convection parameter and the heat generation intensity up to five solutions have been determined featuring stable single and multimode temperature profiles. The conduction–convection parameter and the heat generation intensity have a profound effect on the solution structure and the stability since multimode solutions are becoming unstable allowing only the single mode profiles to be stable. An important finding is that when the boiling heat flux is directly imposed as a boundary condition, neglecting wall conduction, it is not possible to capture the multiplicity since a unique temperature profile is predicted. The model developed is applicable to typical heat exchangers with phase change in general and to cryogenic applications in particular where there is a significant temperature difference between the boiling point of the cryogenic liquid and the inlet temperature of the hot fluid in the exchanger.