*3.3. Effect of dh on the Channel Flow and Heat Transfer Performance*

In this comparative evaluation study, three different *dh* of 1.17, 2, and 4 mm are used. The other geometric factors *Lp* and *θ* are set to 4.5 mm and 115◦, respectively and remain unchanged. The channel has an inlet mass flux of *G* = 200 kg/m2-s, an outlet pressure of *Pout* = 8 MPa, and a wall heat flux of *Qw* <sup>=</sup> ±12 kw/m2-k. The bulk temperature *Tb* of CO2 varies between 280 K and 360 K, covering the pseudocritical temperature *Tm*.

With the reduction of channel *dh*, the distance from the mainstream region to the wall also decreases, which is theoretically conducive to the heat transfer performance, and there are indeed such conclusions in the study on the thermal performance of the straight channel in [24,31]. Nonetheless, for the zigzag channels, the heat convection coefficient *h* does not show an obvious increasing trend with the decrease of *dh*. It can be seen from Figure 11 that h and Δ*P* increase significantly as *dh* changes from 4 mm to 2 mm, especially in the heating cases. However, when *dh* changes from 2 mm to 1.17 mm, neither *h* nor Δ*P* show significant change. This is different from the conclusion in the semicircular straight channel study.

Through the previous analysis cases, we found that the separation of boundary layer promotes the mixing and diffusion in the fluid and enhances the heat transfer performance of the zigzag channel. However, on the other hand, it will also reduce the effective heat transfer area of the wall, which is disadvantageous to the heat exchange. Figure 12 shows us another possible scenario. As for the *dh* = 4 mm diameter case, the boundary layer separation area accounts for a large proportion of the total heat exchange area and the weakening effect of the separation of boundary layer on heat transfer becomes dominant. It can also be seen from Figure 13 that the local heat convective coefficient of the *dh* = 4 mm channel has not been obviously enhanced on the windward side compared to the *dh* = 1.17 mm and *dh* = 2 mm channels.

As can be also seen from Figure 12, the boundary layer separation effect is weakened with the decrease of the *dh.* In the *dh* = 1.17 mm and *dh* = 2 mm diameter cases, the boundary layer separation area will not account for as large a proportion of the total wall area as that presented in *dh* = 4 mm case, which means that the boundary layer separation has a positive effect on the heat transfer performance of the 1.17 mm and 2 mm channels. When *Lp* >> *dh*, this positive effect is enhanced with the increase of *dh*. At the same time, there is an opposite influence whereby the heat transfer will be weakened with the increase of *dh* due to the increasing distance between mainstream region and the wall. The combination

of these two effects makes the convective heat transfer coefficient close for the 1.17 mm and 2 mm channels.

**Figure 11.** Effect of *dh* on flow and heat transfer performance: (**a**) *h* of cooling case; (**b**) Δ*P* of cooling case; (**c**) *h* of heating case; (**d**) Δ*P* of heating case.

**Figure 12.** Velocity vector along the zigzag channel with *dh* of 1.17 mm, 2 mm, and 4 mm.

**Figure 13.** Local heat transfer coefficient of the zigzag channel with *dh* of 1.17 mm, 2 mm, and 4 mm.

All three geometric parameters produce effects on the flow and heat transfer performance of the zigzag channel and have a certain regularity. When the size of *dh* is close to *Lp*, the wall separation caused by channel turning will not strengthen the heat transfer performance. For industrial design, from the point of view of enhancing heat transfer, the *Lp* should be significantly larger than *dh* for the zigzag channels.
