Abstract
In the present 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 non-linear and non-monotonic 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 multi-mode temperature profiles. The Conduction-Convection Parameter and the heat generation intensity have a profound effect on the solution structure and the stability since multi-mode 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.
