I previously made about three years ago two posts about coupled natural circulation loops. These were the results of initial investigations and badly incomplete. This new post brings a degree of completion to those analyses. The original two posts can be discarded.
I have finally pushed through the analysis of two configurations of coupled natural circulation loops; (1) the energy source and energy sink are represented by constant-temperature heat reservoirs and, (2) the energy source is a constant-temperature energy reservoir and the sink is represented by a heat exchanger. The second is a little more representative of physical-domain applications. Additional initial investigations of the most general case having heat exchangers at both the source and sink indicate an almost intractable algebra problem.
These more nearly complete analyses give the temperature distributions interior to the systems in terms of the boundary conditions, as it should. Systems of four equations for the four unknown interior temperatures that requires iterative solution for applications is obtained.
The nomenclature is somewhat complex and the algebra, while straightforward, is tedious.
A file in which the analyses are summarized is NewSimple2Loops07.
I think these results have not appeared in the literature. All comments on the correctness of the results will be appreciated.