*2.1. Inclusion of Heat Transfer into the Model*

The main shortcoming of the original, flow-only version of the Finite Element Analysis (FEA)-based model was its inability to properly evaluate tube bundles in which heat transfer could not be neglected. Given the intended purpose of the model (that is, usage in engineering practice), this functionality had to be implemented.

Please note that heat transfer was not, strictly speaking, evaluated using FEA. However, the temperature fields in the tube side and the shell side were still obtained using a system of linear equations generated as shown in the following text, and this system was then solved in the usual manner. It was assumed that the temperature profile between two end nodes of an edge was continuous and was given by the mean temperatures on control volume cross-sections, which were perpendicular to the corresponding edge. The iterative solver then worked similarly to any other segregated solver. First, the fluid flow (FEA-based) submodel was solved under the assumption of a constant temperature field. Next, the heat transfer submodel was solved under the assumption of a constant velocity field. This was followed by the update of the fluid physical properties and other necessary post-iteration tasks, and then the fluid flow submodel was solved again. This iterative procedure was repeated until convergence was reached.

Even though the heat transfer submodel was not using FEA, the corresponding mesh on which the temperature field was calculated can be constructed in a similar manner. In the fluid flow mesh, the field to be calculated was described by total pressures in the nodes. The temperature field can be described analogously with the difference being that every edge had its own temperature in the node. Figure 3 shows the two meshes and the differences between meshes.

**Figure 3.** Comparison of the fluid flow mesh (left) and the temperature mesh (right). The fluid flow mesh consists of 8 edges with 8 nodes total, and there are 8 unknown pressures (in the green nodes, some of which are shared between edges); in the temperature mesh, there are 2 × 8 = 16 nodes and, therefore, 16 unknown temperatures.

As mentioned before, the temperatures were calculated using a set of linear equations. From Figure 3 it is clear that a flow system consisting of *n* edges will feature 2*n* node temperatures and, therefore, 2*n* linear equations were required. There were three classes of temperature-related equations that were used in the model:

