## 3 Results
Figure 8 shows the water temperature distributions in the microchannels for the bottom temperature \(T_{s0}=360\) K and the inlet velocity \(v_{0}=0.1\) m/s. The temperature increases along the flow. It is clearly visible that increasing the number of zigzag pattern segments improves the heat exchange between the solid and the water flowing inside the microchannel. Each bend of the microchannel causes the flowing water to mix (Figure 4), resulting in improved heat transfer. Figure 5: Pressure drop. Figure 6: Power, \(P\), used to force the flow. Figure 7: Darcy friction factor, \(f\). Figure 9 shows the average temperature of the outlet water for all considered cases. For all microchannels, increasing the bottom temperature, \(T_{s0}\), increases the outlet temperature. Increasing the flow rate in a straight microchannel significantly reduces the outlet temperature of the fluid. However, this effect becomes more pronounced with the introduction of zigzag bends; for higher flow velocities, the outlet temperature notably increases. While this trend holds true across all cases, it is especially evident in microchannels with zigzag shapes, where the influence of the number of zigzag segments on the outlet temperature is more marked. Figure 10 shows the heat flux carried away by the fluid, \(\dot{Q}\), (Equation (21)) for all considered cases. When the flow velocity is low, the differences in heat transfer between the various microchannel shapes are not substantial. The total heat transfer is understandably dependent on the bottom temperature, \(T_{s0}\). However, at higher flow velocities, the number of zigzag segments increasingly affects the amount of heat transferred. Enhancing the number of these segments has been shown to improve the microchannel's heat dissipation capability. Figure 8: Temperature distribution along the microchannels for bottom temperature at 360 K and inlet velocity 0.1 m/s. Figure 9: Average outlet fluid temperature, \(T_{f}\)  
Figure 11 shows the averaged heat transfer coefficient, \(\alpha\), (Equation (27)) for all considered cases. As you can see, this coefficient practically does not depend on the bottom temperature, \(T_{s0}\). However, an increase in flow velocity results in an almost linear increase in the coefficient for all microchannels. The greater the number of microchannel segments, the greater the increase in the heat transfer coefficient. Figure 11: Averaged heat transfer coefficient, \(\alpha\). Figure 10: Heat flux, \(\dot{Q}\). Heat transfer from a solid to a fluid can also be described by the dimensionless Nusselt number (Equation (28)). The Nusselt number shown in Figure 12 has exactly the same properties as the heat transfer coefficient, i.e., it does not depend on the temperature, but it varies with the flow velocity and the number of zigzag segments. The obtained values of Nusselt number are several times higher compared to those obtained experimentally by Gaikwad and Nalawade (Gaikwad). This is due to the greater amplitude of the grooves compared to [Gaikwad] as well as the greater number of zigzags. These geometric differences result in increased flow disturbance and consequently, improved heat transfer. It should be noted that the flow velocity has a large influence on heat transfer. The Nusselt number changes several times with the increase in flow velocity. This type of effect was observed, among others, by [PERSON] et al. (2020). Figure 13 shows the quality factor, \(\eta\). This factor is the ratio of the heat flux during cooling to the power needed to force the flow (Equation (29)). The higher the value of the coefficient, the better the performance of the microchannel from the point of view of comparing the energy taken out in the form of heat with the energy used to forcing the flow. The coefficient values for all cases are greater than \(10^{5}\), which means that the energy needed to force the flow is negligibly small compared to the heat released. So, all microchannels perform a cooling function well. Figure 12: Nusselt number, Nu.