**Appendix A**

In the appendix, more consideration for the heat transfer coefficients is described. According to Figure 8a, the heat transfer coefficients increase linearly with the flow rate. As described in Section 2.4, the calculation performed with the 3D model, in which the uniform temperature of 26 ◦C was set to the liquid–solid cross-sectional boundary, and the temperature on the inlet boundary is 25 ◦C. The results are given under the various flow rate conditions where the range of the flow rate is from 0 l/min to 1 l/min. The heat transfer coefficients are calculated by the results and Equation (12).

According to the right side of Equation (12), the normal directional heat flux on the liquid–solid cross-section *qn* is the only component which is dependent on the flow rate. Figure A1b shows the normal directional heat flux profile under the various flow rate. On the curve line the values increase linearly with the flow rate though the values do not vary on the straight line. It is considered that this is because of the variation of temperature due to the flow bias in the curve channel. From Figure A1d,f, in the curve channel the variation of temperature and velocity in the vicinity of the boundary is larger. On the other hand, from Figure A1c,e, in the straight channel the variation of them is smaller. Because the normal directional heat flux is influenced significantly from the temperature in the vicinity of the boundary, the fact can be the main factor to increase the normal directional heat flux and the heat transfer coefficients.

**Figure A1.** (**a**) The overview of the data output lines, and under the various flow rate (**b**) the normal directional heat flux profile on the outer line, the temperature profile on (**c**) the inner line I and (**d**) the inner line II, and the velocity profile on (**e**) the inner line I and (**f**) the inner line II.
