*3.4. Instantaneous Thermal Fields*

Figure 9 shows instantaneous temperature fields near the rib. When the thermal conductivity ratio was large, the temperature inside the solid wall exceeded that of the fluid at all interfaces (Figure 5). In those cases, the difference between the bulk temperature of the fluid and the temperature on the solid surface was large (Figure 5), and therefore, the cold core fluid impinging became an important heat transfer mechanism.

However, as the thermal resistance of the solid increased (K\* ≤ 10), the temperature difference between the fluid and the solid decreased. Consequently, the impingement of the fluid did not significantly influence the convective heat transfer in the near-upstream region of the rib. In this case, the corner vortex at the upstream corner of the rib induced a temperature change and reduced the local thermal resistance, resulting in the convective heat transfer increasing near both corners of the rib. In particular, the effect of the secondary vortex generated after the rib was very different when the thermal conductivity ratio was small. As shown in Figure 9c, the fluid heated by the channel wall was supplied to the downstream face of the rib by the recirculation flow and the secondary vortex. Consequently, the heat transfer rate at the downstream face of the rib was negative. In the temperature field of Figure 9d, compared with the temperature field of Figure 9c, it is evident that the isotherms are more concentrated near the surface as the relative thermal resistance of the solid increases. Consequently, the top surface of the rib is not heated and remains cold, and the cold flow over the rib takes heat from the rib and the hot fluid behind the rib.

**Figure 9.** Instantaneous thermal fields near the rib for (**a**) K\* = 566.26, (**b**) K\* = 100.00, (**c**) K\* = 10.00, and (**d**) K\* = 1.00.

Figure 10 shows the local heat transfer distribution obtained for the instantaneous temperature field. Here, A, B, C and D represent the upstream corner, upstream edge, downstream edge, and downstream corner of the rib, respectively. At K\* = 566.26, the cold fluid flowing along the wall collides with the rib, greatly promoting heat transfer to the upstream face of the rib. This can be confirmed by the repeated occurrence of high heat transfer after the corner at the location of the streak with a high heat transfer coefficient on the channel wall based on A, which corresponds to the upstream corner of the rib. At edge B, as the flow separates and recombines, spots with high heat transfer coefficient occur on the downstream side of the top of the rib. The downstream face of the rib is partially supplied with recombined cold fluid and has a high heat transfer coefficient, but the overall heat transfer is greatly reduced compared with the upstream face. In the downstream corner D, a locally negative heat transfer coefficient (white area in the contour) is observed. For K\* = 100, the above-mentioned trend is maintained, but the heat transfer coefficient is reduced overall.

As the thermal conductivity ratio decreases (K\* ≤ 10), the heat transfer rate decreases and becomes uniform overall. As the heat transfer rate decreases, the area of negative heat transfer (the white area in Figure 10) also widens. In the case of K\* = 10 (Figure 10c), a negative heat transfer coefficient appears on the downstream side and along the downstream corner (D). For K\* = 1, it appears along the downstream corner (C) but not at the downstream corner. This appears to be because the cold fluid flowing over the top of the rib cools the rib, as discussed in the context of Figure 9.

**Figure 10.** Instantaneous local heat transfer: (**a**) K\* = 566.26; (**b**) K\* = 100.0; (**c**) K\* = 10.0; and (**d**) K\* = 1.0.
