*3.3. Turbulent Heat Transfer*

Figure 7 shows turbulent heat flux contours. It is well known that turbulent heat flux is an important factor in determining heat transfer [18,19]. The turbulent heat flux was large near the two edges of the rib and around *x/e* = 4 near the wall. For all heat flux ratios, the distribution of turbulent heat flux was similar, but when the thermal conductivity ratio decreased, the value of turbulent heat flux decreased and the distribution of turbulent heat flux became spatially uniform. As shown in Figure 3, when the heat conduction ratio decreased, the temperature distribution on the fluid side became uniform and the turbulent heat transfer decreased. In particular, the peak of the turbulent heat flux near the wall disappeared for K\* < 10.

**Figure 7.** Turbulent heat flux *θ v* contours for (**a**) K\* = 566.26, (**b**) K\* = 100.00, (**c**) K\* = 10.00, and (**d**) K\* = 1.00.

Locally, the turbulent heat flux near the rib varied with the thermal conductivity ratio. As evident in Figure 7a,b, when the thermal conductivity ratio was large, the turbulent heat flux at the front face of the rib was almost uniform. On the other hand, when the thermal conductivity ratio was small, the effect of the corner vortex relatively increased, resulting in the turbulent heat flux at the corner exceeding that at the edge. Consequently, the heat transfer distribution near the rib varied with the thermal conductivity ratio (Figure 6).

Figure 8 shows temperature fluctuations inside the solid wall. As explained in the introduction, the thermal condition of the solid wall is an important factor in determining convective heat transfer. In particular, in the turbulent flow section, temperature fluctuations in the solid are important along with thermal resistance. When the thermal conductivity ratio exceeds 1, most temperature fluctuations are caused by turbulent flows in the fluid region. At K\* = 100, the temperature fluctuation at the upstream edge of the rib reaches 2%. When K\* is 10 or higher, the temperature fluctuation inside the solid increases with the thermal resistance of the solid. When the thermal conductivity ratio is 1, the effect of the flow on convective heat transfer decreases and the temperature fluctuation in the fluid region weakens. Consequently, the temperature fluctuation in the solid region becomes similar to that in the fluid region. Furthermore, the depth at which temperature fluctuations occur inside the solid becomes smaller than that for K\* = 10 or 100. When the thermal conductivity ratio is 1, the influence of the corner vortices becomes significant, and therefore, the maximum temperature fluctuation occurs at the corners of the rib.

**Figure 8.** Temperature fluctuations (*θ*rms) for (**a**) K\* = 566.26, (**b**) K\* = 100.00, (**c**) K\* = 10.00, and (**d**) K\* = 1.00.
