*3.1. Code Validation Study*

Figure 2a shows the time-averaged streamline in the ribbed channel. Similar to the streamlines [40] obtained with experimental data, recirculating cells exist behind the rib, and there is a secondary vortex between the recirculation flow and the back of the rib. There is a vortex on the front side of the rib and there is a separation bubble on the top side of the rib. While the LES-predicted flow field was almost identical to that observed in the experiment, the corner vortices occurring before and after the rib were predicted to be slightly larger compared with those in the experiment. This appears to be because of the difference between the blockage ratio and the channel aspect ratio. In the time-averaged temperature distribution under isothermal conditions (Figure 2b), a high-temperature region was formed behind the rib since heat transfer was not active.

**Figure 2.** Time-averaged flow and thermal fields for the isothermal wall: (**a**) comparison of timeaveraged streamlines with particle image velocimetry measurement data of Casarsa et al. [40], (**b**) the time-averaged temperature field, and (**c**) the Nusselt number ratio on the channel wall between ribs.

Figure 2c shows a comparison of the heat transfer coefficient distribution at the channel wall with those in the literature (see Table 1). The heat transfer coefficient was compared with the Nusselt number ratio, where *Nu*<sup>0</sup> is the Nusselt number of a smooth channel wall obtained using the following Dittus–Boelter correlation:

$$Nu\_0 = 0.023 \, Re^{0.8} \, Pr^{0.4}.\tag{7}$$

When wall conduction was considered (red solid line in Figure 2c), the local heat transfer change slightly decreased compared with that obtained through locally isothermal analysis (black dotted line in Figure 2c). Among the experimental data, it was in good agreement with that of Liou et al. [6] (green square), who adopted the same blockage ratio (=0.1). The results of Cukurel et al. [14,15] compared together had a blockage ratio of 0.3, and the pink triangle and blue circle show iso-flux and conjugate results, respectively. Although not as quantitatively consistent as [6], the tendency of the convective heat transfer to be higher than the conjugate heat transfer in the range of 2 < *x/e* < 4 and the reversal of this tendency downstream are identical to those in the present study.
