*3.1. Simple Cross-Flow Tube Bundle Heat Exchanger from the Literature*

The example discussed here was taken from [44] and involves an air-to-water heat exchanger from Figure 7. Its parameters are listed in Table 2 together with the data obtained using the present model and HTRI Xchanger Suite 8.0.1 [45]. The computational time needed by the present model to automatically create the necessary meshes, reach in 46 major iterations the results mentioned below, and export all the solution data into Kitware ParaView for visualization purposes was ca. 15 s on an average desktop computer with the Intel Core i-5 2500K CPU. The ranks of the matrices used in the model were ca. 800 and ca. 1600 in case of fluid flow and heat transfer, respectively.

**Figure 7.** The evaluated air-to-water heat exchanger (please note that the tubes are shown as unfinned for clarity even though the exchanger used rolled helical fins in the heated portion of the bundle). The dimensions of the air duct were 0.56 × 0.5 × 1.0 m (width × height × length).

**Table 2.** Parameters of the air-to-water heat exchanger (for the remaining construction data, etc., please see [44]) and the corresponding results obtained using the present model and HTRI Xchanger Suite ("HTRI XS").


<sup>1</sup> Tube side (water); <sup>2</sup> Shell side (air).

In order to minimize the number of sources of discrepancies, the necessary heat transfer coefficients were calculated by the present model using the equations mentioned in the literature [44]. The results should, therefore, have been identical, yet they were not. The reason for the difference became clear once one noticed that, in [44], the iterative computation was stopped while the difference between the hot and the cold heat duties was still relatively large. In fact, should one carry out the heat balance for the data from the literature, one would get the actual water heat duty of 150.3 kW (as listed among the results) while for air the duty would be 149.9 kW. There may also be another reason for the discrepancies in the data, namely the fact that, in [44], the computation was done using average temperatures, average fluid physical properties, etc. for the entire tube side and shell side.

Considering the differences between the values provided by the present model and the data yielded by HTRI Xchanger Suite, these most likely stemmed from the software package using much more accurate equations for obtaining the heat transfer coefficients. It, therefore, is entirely possible that with different equations the results obtained using the present model would be much closer to the data from HTRI Xchanger Suite. In any case, this supports the notion that any such tool or model can only be as good as the equations internally utilized by it.

To demonstrate the level of detail of the solution data provided by the developed software, the water and air temperatures were exported (together with the respective geometry, which used only plain tubes to improve clarity) into Kitware ParaView. The resulting combined plot is shown in Figure 8.

**Figure 8.** Visualization generated in Kitware ParaView of the bundle in the air duct (some faces are culled). These were colored by the tube-side (water) and the shell-side (air) temperatures obtained using the FEA-based model.
