## 3 Results and Discussions
### U-Shaped Channel with a Smaller Temperature Difference  
This part describes the heat transfer and the flow characteristics in the U-shaped channel, at the temperature boundary conditions of 283 K on the wall and 300 K of the incoming fluid at the inlet. Figure 9 shows the pressure and the vorticity magnitude at the middle-height plane of the channel. The inlet-outlet pressure drop values show no change as the wall temperature changes, compared to Figure 4. However, the vorticity values change. At the lower flow rate, the vorticity shows a narrower minimum zone compared to the one in the more cooled fluid, meaning that the fluid in this case is less rigid since the fluid is less cooled and thus the viscosity is smaller. At the higher flow rate, the maximum vorticity is larger than that in which the fluid cools more, again showing that the fluid is less rigid. Another noticeable phenomenon is that, at both lower and higher flow rates, the vorticity is less symmetric than that of the more cooled fluid, which also reflected this. From the streamlines, vorticity, and velocity magnitudes/vectors displayed in Figure 10, the less cooled fluid shows a more asymmetric vorticity distribution at both flow rates. Moreover, the flow turns more gently and the maximum velocity zone is more oblique, together with the later overlap of the streamlines in the curved part, meaning that the deflection of the less cooled fluid is easier and smoother. As the flow is faster, it seems that the maximum velocity zone is even oblique. The disappearing velocity vectors at the  
Figure 7: The velocity magnitude and the velocity vector arrows at the five sections of the U-shaped channel. The first row shows the data at the inlet velocity of 0.5 m/s with no temperature difference. The second row shows the results at the inlet velocity of 0.5 m/s but at the temperature conditions of 273 K on the wall and 300 K of the incoming fluid at the inlet. The third row shows the results at the inlet velocity of 1 m/s with no temperature difference. The fourth row shows the results at the inlet velocity of 1 m/s but at the temperature conditions of 273 K on the wall and 300 K of the incoming fluid at the inlet. strongly curved points indicate that there should be a strong cross-section secondary flow at these positions. Figure 8: The vorticity magnitude and the projected streamlines at the five sections of the U-shaped channel. The first row shows the data at the inlet velocity of 0.5 m/s with no temperature difference. The second row shows the results at the inlet velocity of 0.5 m/s but at the temperature conditions of 273 K on the wall and 300 K of the incoming fluid at the inlet. The third row shows the results at the inlet velocity of 1 m/s with no temperature difference. The fourth row shows the results at the inlet velocity of 1 m/s but at the temperature conditions of 273 K on the wall and 300 K of the incoming fluid at the inlet. Figure 9: The pressure and the vorticity magnitude at the middle-height plane of the U-shaped channel. The pressure is displayed in the left column, and the vorticity magnitude is displayed in the right column. The upper row shows the data at the inlet velocity of 0.5 m/s at the temperature conditions of 283 K on the wall and 300 K of the incoming fluid at the inlet. The lower row shows the results at the inlet velocity of 1 m/s at the temperature conditions of 283 K on the wall and 300 K of the incoming fluid at the inlet. The temperature profiles at the five sections and the outlet plane of the U-shaped channel are shown in Figure 11. Overall, compared to the cases of the larger temperature difference, the distribution is more symmetrical because of fewer heat transfer processes, and at the higher flow rate, it is even more symmetrical. Again, at the beginning of the bend, the temperature at the inner wall side is higher due to the inner-wall-pointed velocities (Figure 12), and thus the heat is transferred from the outer wall to the inner wall.