Heat exchangers immersed in solar thermal storage tanks to charge and/or discharge energy from the tank provide several benefits over conventional systems that rely on pressurized tanks or pumps. The present study builds on a recent experimental study of heat transfer to an immersed heat exchanger with different baffle and shroud geometries (Nicodemus et al., Solar Energy, 157:911-919, 2017). A simple straight geometry was found to provide more benefit than a more complex geometry, in which the baffle underneath the heat exchanger narrows relative to the shroud around the heat exchanger. In this study, we propose an axi-symmetric model of a two-loop heat exchanger in order to investigate the mechanisms by which the straight baffle-shroud improves the heat transfer relative to the complex baffle-shroud. Further, we compare results of the two-loop model to a one-loop representation of the heat exchanger in order to determine whether or not a model with more fidelity to realistic storage systems better predicts experimental performance. Both the two-loop and one-loop models yield higher heat transfer with the straight baffle-shroud and confirm that the improved heat transfer in the straight baffle-shroud geometries is due to higher velocities around the heat exchanger relative to those in the complex baffle-shroud geometries, consistent with the experiments. However, the one-loop model significantly underestimates the differences between the baffle-shrouds relative to the experimental results. Since the two-loop model more accurately captures the fluid dynamics in the tank and better predicts the heat transfer and rate of energy discharge, it is an appropriate tool for future studies of immersed heat exchanger performance.