Reliable compartmental models for double-pipe heat exchangers: An analytical study

In this work, the analytical properties of the heat exchanger infinite-dimensional dynamic model are discussed. More importantly, those of a 2nd-order lumped-parameter model using the logarithmic mean temperature difference (LMTD) as driving force are derived and shown to agree with those of the former. Three essential aspects are focused: existence and uniqueness of solutions, equilibrium states, and stability properties. The results developed in this work are intended to supply a solid support for the reliability on the use of the kind of simple compartmental model that is treated. This is specially addressed to works where it is not the quantitative solutions but the qualitative behavior that is important, like modelling and simulation of heat exchanger networks and complex industrial processes where heat exchangers are involved.