**5. Conclusions**

The point of this research was not to develop a replacement to the universally applicable, commercial heat transfer equipment design packages, such as HTRI Xchanger Suite. On the contrary, the goal was to create a simplified model for heat exchangers representable using sets of interconnected 1-D meshes, which are typically used in high-temperature (i.e., heat recovery) industrial applications and are prone to suffer from operating problems. The model, once finished, should be fast, yet accurate enough, and should provide estimates of not only the flow distribution in the bundle and the tube- and shell-side temperature fields but also the resulting mechanical stress field in the bundle caused by uneven thermal loading. In other words, the aim was to have a supplementary tool which would enable the designer to evaluate in advance, and without any significant effort or time spent, the thermal-hydraulic behavior of the mentioned heat exchangers as well as the likelihood of them suffering mechanical failures under the design operating conditions. In this regard, the FEA-based modelling approach seems to be promising, but a lot of work, as well as a thorough validation, are still needed before it is ready for production use.

The comparison with HTRI was mentioned in this paper solely to present the current capabilities of the model in terms of heat transfer prediction. The discrepancy (or at least a part of it) was very likely caused by the heat transfer coefficients and the hydraulic resistance coefficients being calculated differently. However, the model was designed in such a way that it can easily incorporate any standard method for calculating these coefficients for the simple 1-D mesh elements. More complex flow systems can then be built from these simple elements and the solution strategy remains the same, which ensures scalability of the model.

Considering the fact that shell-side flow velocity fields commonly are not uniform, one of the possible future improvements of the FEA-based model could lie in strictly using a grid of cells in the shell side (in the plane perpendicular to the general direction of flow) instead of only one cell. Another enhancement, which the authors plan to implement, is to make it possible to interface the current computer code with other simulation codes. This would enable the evaluation of flow systems in which some parts are more complex and, therefore, not directly compatible with the simplified mesh elements used by the FEA-based model.

**Author Contributions:** Conceptualization, T.L. and V.T.; methodology, T.L. and V.T.; software, T.L.; validation, V.T. and T.L.; investigation, T.L., V.T., and D.B.F.; resources, Z.J.; writing—original draft preparation, V.T.; writing—review and editing, V.T.; visualization, V.T. and T.L.; supervision, V.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Czech Ministry of Education, Youth, and Sports/EU Operational Programme Research, Development and Education, grant No. CZ.02.1.01/0.0/0.0/16\_026/0008413 "Strategic partnership for environmental technologies and energy production".

**Conflicts of Interest:** The authors declare no conflict of interest.
