#
Comparative Study of the Thermal and Hydraulic Performance of Supercritical CO_{2} and Water in Microchannels Based on Entropy Generation

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}(sCO

_{2}) close to the pseudocritical point make it possible to replace water as the coolant of microchannels in application of a high heat flux radiator. The computational fluid dynamics (CFD) method verified by experimental data is used to make a comparison of the thermal hydraulic behavior in CO

_{2}-cooled and of water-cooled microchannels. The operation conditions of the CO

_{2}-based cooling cases cover the pseudocritical point (with the inlet temperature range of 306~320 K and the working pressure of 8 MPa), and the water-based cooling case has an inlet temperature of 308 K at the working pressure of 0.1 MPa. The channel types include the straight and zigzag microchannels with 90°, 120°, and 150° bending angles, respectively. The analysis result shows that, only when the state of CO

_{2}is close to the pseudocritical point, the sCO

_{2}-cooled microchannel is of a higher average heat convection coefficient and a lower average temperature of the heated surface compared to the water-cooled microchannel. The entropy generation rate of the sCO

_{2}-cooled microchannel can reach 0.58~0.69 times that of the entropy generation rate for the water-cooled microchannel. Adopting the zigzag structure can enhance the heat transfer, but it does not improve the comprehensive performance represented by the entropy generation rate in the sCO

_{2}-cooled microchannel.

## 1. Introduction

^{2}for a silicon integrated circuit using water as a coolant. Although microchannel heat exchangers have a surprising heat dissipation capacity, they also have high pumping power requirements due to the high flow resistance of the microchannels [9].

_{2}O

_{3}[20], CuO [21], TiO

_{2}[22], Cu-Al

_{2}O

_{3}[23], and ZnO nanofluid [24]. Chein and Chuang [25] studied the performance of a microchannel radiator with a CuO-H

_{2}O mixed coolant. Their research indicates that nanofluids can absorb more heat than water cooling when both are at low flow rates, while in the case of high flow, the thermal performance is mainly determined by the volumetric flow rate, in addition to that the nanoparticles have little effect in this process. Jung and Park [26] conducted an experimental comparative investigation on the thermo-hydraulic performance of Al

_{2}O

_{3}-water nanofluid in microchannels. Their results indicated that the entropy generation rate of nanofluid is 6.3% lower than that of water, while water has a lower flow resistance. The result also indicated that nanofluids present preferable heat transfer characteristics to water, but their channel pressure loss is not dominant compared to that of water.

_{2}is a coolant with excellent potential for application in high heat flux dissipation. As a coolant, CO

_{2}possesses high thermal conductivity and specific thermal conductivity near the pseudocritical point, which is conducive for improving the heat transfer performance [27,28]. Furthermore, as shown in Figure 1, where the data are derived from the RERPROP V9.1 database, the density of CO

_{2}near the pseudocritical point stays close to that of water, but its dynamic viscosity is significantly lower. These thermophysical characteristics of CO

_{2}show the potential to improve flow resistance characteristics while maintaining a heat transfer performance close to that of water. Research in [29,30] both showed that supercritical CO

_{2}(sCO

_{2}) can provide a higher cooling performance with lower channel pressure loss than liquid cooling. Khalesi and Sarunac [31] conducted a good deal of analyses on the development process and conjugated heat transfer in microchannels using supercritical CO

_{2}and liquid sodium as coolants. Their results showed that the sharp change in the thermophysical property of sCO

_{2}near the pseudocritical point will impact the flow and thermo-hydraulic performance in the microchannels, and this effect will be weakened with the operational conditions being further away from the critical point.

_{2}coolant can provide a higher cooling performance with a lower channel pressure loss compared to the liquid coolant. However, since the thermophysical properties of CO

_{2}vary sharply near the pseudocritical point, the impact of fluid temperature and pressure change in the microchannel on its thermo-hydraulic performance has not been clearly clarified in existing research. The density of sCO

_{2}is lower than water, and the pump power consumption of the microchannel heat exchanger is also affected by the density of the fluid, which is one of the parameters that affects the comprehensive performance of the microchannel heat exchanger. In high heat flux heat dissipation applications, it is often desirable to achieve better heat transfer performance with smaller package volume and lower flow resistance (pump power consumption). In this paper, the flow and heat transfer performance of water and CO

_{2}coolants in microchannels are comprehensively compared based on the entropy generation rate. Special channels such as zigzag [32], curve [33], and trapezoid [34] are important ways to improve thermal performance in the microchannel. A comparison analysis of the effect of the bend angle on the thermal hydraulic performance is also conducted in this study for water and sCO

_{2}-cooled channels.

## 2. Numerical Method

_{2}are used as coolants to study their thermo-hydraulic performance in microchannels. The numerical simulation employs the software ANSYS fluent V19.0 to solve the conjugate heat transfer problem and the Navier–Stokes equations for the computational domains. The SST-kω model was used to model turbulence. The pressure-based solver with pressure–velocity coupling was used to solve the flow problem through the ANSYS FLUENT package. The thermophysical characteristics of CO

_{2}are based on the NIST real gas model with the REFPROP V9.1 database.

#### 2.1. Physical Model and Boundary Conditions

_{2}work near the pseudocritical point, the outlet pressure of the channels is set at 8 MPa. In this study, a variety of input temperatures (306 K to 320 K) are used to understand the impact of deviation from the pseudocritical point on its thermo-hydraulic performance. Since the temperature and pressure of liquid water have a minor effect on its thermophysical properties, a single inlet temperature (308 K) and a single outlet pressure (0.1 MPa) are adopted. The uniform flow inlet boundary with variation range of mass flux 50~1000 kg/(m

^{2}·s) are adopted for both fluid-type conditions. The heat flux ranges from 40,000 to 120,000 W/m

^{2}for the heated surface on the bottom side of the solid domain, the coupled heat transfer boundary is adopted at the interface between the fluid and solid regions, and the adiabatic boundary is used for the rest surfaces of the solid domain.

#### 2.2. Governing Equations and Data Reduction

#### 2.3. Mesh Description and Independence

#### 2.4. Validation

_{2}as a coolant is detailed in [39]). The comparison result in Figure 5 shows that the numerical result maintained consistency with the experiment data well in the linear flow state when Re < 1500. When Re > 2000, compared with the k-epsilon turbulence model (with maximum relative error 33.8%), the calculation result of the k-omega turbulent model of shear stress transfer (with maximum relative error 13.7%) shows a better consistency with the experiment data. In the transitional region from laminar to turbulent flow, 1500 < Re < 2000, the maximum relative error is 26.5% using laminar models. Since the maximum Reynolds numbers of analysis cases in the following study can reach more than 5000, the k-omega SST model will be adopted for turbulent flow cases.

## 3. Results and Discussions

_{2}, it is apparent that the thermal conductivity of CO

_{2}is lower than that of water by no more than one order of magnitude. Nevertheless, the specific heat capacity of sCO

_{2}shows several orders of magnitude higher than that of water, which is beneficial for its heat transfer performance in microchannels. The dynamic viscosity of sCO

_{2}is also lower than that of water by several orders of magnitude, which is significantly beneficial for its flow characteristics in microchannels. In this analysis, the thermal and hydraulic characteristics of water and sCO

_{2}in straight and zigzag microchannels are compared and analyzed to understand the feasibility of replacing water with sCO

_{2}as a coolant.

#### 3.1. Comparative Study of Straight Channel Cases in Different Mass Flux

_{hsur}, and ${\dot{S}}_{g}$, to analyze the thermal and hydraulic performance of water and sCO

_{2}in microchannels. Six inlet temperatures of 306 K, 307 K, 308 K, 310 K, 315 K, and 320 K are used for the analysis of CO

_{2}. For liquid water, the inlet temperature is 308 K. The inlet mass flux range of the two coolants is 50~1000 kg/(m

^{2}·s). All cases adopt the pressure outlet boundary. The outlet pressure is 8 MPa for CO

_{2}-cooled cases and 0.1 MPa for water-cooled cases. The constant heat flux between 4 and 120 W/cm was adopted for the heat surface of the microchannel.

#### 3.1.1. Pressure Drop

_{2}-cooled microchannel at each inlet temperature. Obviously, this is in line with our predictions. This is because the dynamic viscosity of water at room temperature is significantly higher than that of sCO

_{2}with its condition close to the pseudocritical state. For sCO

_{2}-cooled cases in this comparison analysis, the channel ΔP increases with increasing T

_{in}. This is because the ΔP through the microchannel is influenced by the dynamic viscosity and density of the coolant. These two thermophysical parameters both decrease with increasing T

_{b}, but the influence of density change takes the lead.

_{2}-cooled one. This is also because the density and dynamic viscosity of CO

_{2}change drastically with temperature near the pseudocritical point, especially density, which is much more sensitive to the temperature compared to the water. Similar conclusions also appeared in [30].

#### 3.1.2. Average Heat Convection Coefficient

_{2}-cooled cases with low mass flux (<250 kg/(m

^{2}·s)). This is because the bulk temperature T

_{b}of the fluid increases significantly relative to T

_{in}at low mass flow, resulting in a large deviation in T

_{b}from the pseudocritical temperature (T

_{m}= 307.75 K at 8 MPa) for CO

_{2}. This will lead to a sharp deterioration in the thermophysical (thermal conductivity and specific heat) properties of CO

_{2}. As the contour diagram in Figure 8 shows, the temperature change in the fluid along the channel decreases with the increase in G. Figure 7 also shows that h of water and CO

_{2}both gradually increase with the increasing G, but the growth rate of the CO

_{2}-cooled case is larger. As G increases, the temperature variation of the CO

_{2}fluid along the flow path becomes smaller, making its deviation from the pseudocritical point smaller. In this high mass flux condition, the h for water-cooled channels is not as good as h for the CO

_{2}-cooled channels in the cases where the T

_{in}is close to T

_{m}(T

_{in}= 306 K, 307 K, 308 K, 310 K). For CO

_{2}-cooled cases, the highest value, and the highest rate of increase in h, occur at T

_{in}= 308 K, which is closest to T

_{m}. This is because the closer the state of CO

_{2}is to the pseudocritical point, the better its thermophysical properties, and the more intense the change in its thermophysical properties.

#### 3.1.3. Average Temperature of the Heated Wall

_{hsur}of the CO

_{2}-cooled and water-cooled microchannels. In this analysis, T

_{in}= 308 K, q

_{w}= 40,000 W/m

^{2}, P

_{out}= 8 MPa for the sCO

_{2}case, P

_{out}= 0.1 MPa for the water case, and G = 50~500 kg/(m

^{2}·s). It also shows that the T

_{hsur}of the water-cooled channel is lower than that of the CO

_{2}-cooled channel only at an extremely low mass flux. This is also caused by the large deviation in the temperature of the CO

_{2}fluid from T

_{m}under low mass flux conditions, resulting in the deterioration of its thermophysical properties and the weakening of the heat transfer performance. This impact will gradually decrease with increasing mass flux. When G > 100 kg/(m

^{2}·s), T

_{hsur}of the CO

_{2}-cooled channel will be lower than that of the water-cooled channel. When G > 300 kg/(m

^{2}·s), the average temperature difference in the heated surface between the two coolant-based cooling cases tends to be stable, and values of T

_{hsur}of the CO

_{2}-cooled channel are 0.5~0.7 K lower than those of the water-cooled channel.

#### 3.1.4. Entropy Generation Rate

_{2}as coolants at mass flux between 50~1000 kg/(m

^{2}·s) against different inlet temperatures (CO

_{2}: 306 K, 307 K, 308 K, 310 K, 315 K, 320 K; water: 308 K).

_{2}-cooled microchannel is lower than that of the water-cooled microchannel at relatively large mass flux in the case of T

_{in}= 306 K, 307 K, and 308 K, and the lowest ${\dot{S}}_{g}$ curve occurs when T

_{in}= 308 K. For the cases with T

_{in}= 315 K and 320 K, the ${\dot{S}}_{g}$ of the CO

_{2}-cooled microchannel is higher than that of the water-cooled microchannel due to the large deviation from the pseudocritical point. It also means that the comprehensive performance of the microchannels can be improved on the basis of maintaining the state of CO

_{2}close to the pseudocritical point.

_{in}= 308 K to ${\dot{S}}_{g,water}$ in Figure 10b also shows that under the current working condition, when G < 250 kg/(m

^{2}·s) the performance of the CO

_{2}-cooled channel is not as good as that of the water-cooled channel, and when G > 500 kg/(m

^{2}·s) using sCO

_{2}as a coolant can decrease the ${\dot{S}}_{g}$ to 0.58~0.69 times of the water-cooled straight microchannel.

_{2}-cooled cases within the current analyzed mass flux range. This is because as the mass flux increases, as shown in Figure 11a,b, for both the water-cooled and CO

_{2}-cooled channels, the ${\dot{S}}_{g,\Delta T}$ shows a decreasing trend due to the increasing heat convection coefficient in the microchannel, and ${\dot{S}}_{g,\Delta P}$ shows a increasing trend due to the increasing channel pressure drop. The total entropy generation rates ${\dot{S}}_{g}$ for both water-cooled and CO

_{2}-cooled cases decrease first, then increase continuously with the increasing G.

#### 3.2. Comparative Study of Straight-Channel Cases in Different Heat Flux

_{2}coolant, it is essential to maintain the CO

_{2}state close to the pseudocritical point. With the increase in q

_{w}, the temperature change in the fluid along the channel will increase, causing the fluid state to deviate more from the pseudocritical point. This section studies the effect of heat flux (q

_{w}) on the h, $\Delta P$, and ${\dot{S}}_{g}$ of straight microchannels cooled by water and CO

_{2}for three different mass fluxes (500, 1000, 1500 kg/(m

^{2}·s)) at T

_{in}= 308 K, P

_{out}= 8 MPa for the sCO2 case, and P

_{out}= 0.1 MPa for the water case.

#### 3.2.1. Average Heat Convection Coefficient

_{w}on heat transfer performance for both water-cooled and CO

_{2}-cooled channels. It can be seen from the result that the change in q

_{w}has little impact on h for water-cooled cases. This is because the change in coolant T

_{b}caused by the increase in q

_{w}has little effect on the thermophysical properties (specific heat and thermal conductivity) of the water. For the sCO

_{2}coolant, however, as T

_{in}= 308 K, the fluid state is near the peak position of the curves of thermal conductivity and specific heat capacity. At this position, the values of both thermal conductivity and specific heat capacity decrease dramatically as temperature deviates from the T

_{m}(307.75 K at 8 MPa). When q

_{w}continuously increases at a fixed mass flux, the deviation in T

_{b}from T

_{in}will increase, and the thermophysical properties of CO

_{2}will deteriorate. As a result, the h of the CO

_{2}-cooled channel decreases rapidly with the increase in q

_{w}.

#### 3.2.2. Pressure Drop and Pumping Power

_{w}on channel pressure drop (ΔP) and pump power consumption (W), respectively. As shown in Figure 13a, the $\Delta P$ of the water-cooled channel is significantly higher than that of the CO

_{2}-cooled channel. This result also shows that the variation in q

_{w}has little impact on the channel pressure drop in water-cooled cases. However, for the CO

_{2}-cooled channel, the ΔP curves show a slight upward trend as q

_{w}increases. This is caused by the increase in T

_{b}of CO

_{2}, which will lead to a decrease in the density and dynamic viscosity of CO

_{2}. The influence of these two parameters on the channel ΔP is opposite and the combined effect is that the ΔP of the CO

_{2}-cooled channel increases slightly with increasing q

_{w}. Although the ΔP in the water-cooled channel is higher, the difference in pump power consumption between the CO

_{2}-cooled and water-cooled channels is relatively small under the same mass flux, as shown in Figure 13b, because of the lower density of the CO

_{2}compared to water.

#### 3.2.3. Entropy Generation Rate

_{w}on entropy generation rate ${\dot{S}}_{g}$ is presented in Figure 14. It can be seen from the comparison result that with the increase in heat flux density, the ${\dot{S}}_{g}$ of both the water-cooled channel and the CO

_{2}-cooled channel show an upward trend, but the increase rate of the CO

_{2}-cooled channel is higher. This means that the irreversible loss of the CO

_{2}-cooled channel is more affected by the heat flux. It can also be seen from the comparison of the curves that the accelerating upward trend of ${\dot{S}}_{g}$ with the increase in q

_{w}for the CO

_{2}-cooled microchannel is more significant. This is because an increase in q

_{w}leads to a greater deviation from the pseudocritical point of the CO

_{2}fluid state, which will also weaken the heat transfer performance of the channel.

#### 3.3. Comparative Analysis of Zigzag Channels

_{2}. In this comparative analysis, four inlet temperatures (T

_{in}= 308, 310, 315, and 320 K) and a fixed outlet pressure of P

_{out}= 8 MPa are considered for the CO

_{2}-cooled channel. For the water-cooled microchannel cases, fixed T

_{in}= 308 K and P

_{out}= 0.1 MPa are used, and G = 50~500 kg/(m

^{2}·s) and q

_{w}= 40,000 W/m

^{2}are set for both water-cooled and CO

_{2}-cooled cases.

#### 3.3.1. Comparative Study of h under Different Angles of Bend in The Zigzag Channel

_{2}-cooled and water-cooled channels with four different bending angles, including the straight channel (θ = 180°). The h of the water-cooled channel for all four bending angle channel types is greater compared to the CO

_{2}-cooled channel under low mass flux. This means that the heat transfer performance of CO

_{2}is worse than that of water at a relatively low mass flux. This is because the lower mass flux will aggravate the deviation in the T

_{b}and T

_{w}from the T

_{in}of the CO

_{2}fluid, resulting in a greater deviation in the state of CO

_{2}from the pseudocritical point. The thermophysical parameters (specific heat and thermal conductivity) of CO

_{2}are greatly reduced.

_{2}-cooled channel is higher than that of the water-cooled channel for all four bending angle channel types. This result means that the increase in mass flux has a greater impact on h of the CO

_{2}-cooled channel than on the water-cooled one. This is because increasing the mass flux not only increases the Re of the microchannel and enhances turbulence, but also makes the T

_{b}of CO

_{2}closer to T

_{m}, and the heat transfer performance can be further improved.

_{2}-cooled and water-cooled microchannels of zigzag type, respectively. Obviously, the comparison results in these figures indicate that for both CO

_{2}-cooled and water-cooled microchannels, reducing the turning angle is conducive to enhancing heat transfer. However, the comparison result also shows that the existence of bends has a more significant impact on the water-cooled channel. Compared to the straight channel case, the h of the zigzag channel with θ = 150° increases significantly. However, the improvement in heat transfer performance of water-cooled cases by further reducing θ is no longer as significant as the transition from straight to zigzag type.

_{2}-cooled channel, the heat transfer enhancement effect produced by using a zigzag channel instead of the straight channel is not as great as that of the water-cooled channel. This is because the sCO

_{2}-cooled straight channel has a thinner thermal boundary layer than the water-cooled straight channel, as illustrated in Figure 17c,d, and the variation in the thickness of the thermal boundary layer caused by the bending in the channel is not as significant as that of the water-cooled channel.

#### 3.3.2. Comparative Study of ${\dot{S}}_{g}$ under Different Angles of Bend in the Zigzag Channel

_{2}-cooled microchannel in different θ cases.

_{2}-cooled microchannel of straight type and zigzag type with θ =150°, as shown in Figure 18a,b, the ${\dot{S}}_{g}$ shows a decreased trend as G increases from 50 to 500 kg/(m

^{2}·s), which means that the decreasing amplitude of thermal entropy generation caused by the increasing flow flux is greater than the increasing amplitude of flow entropy generation. For the CO

_{2}-cooled microchannel of zigzag type with θ =120° and θ =90°, as shown in Figure 18c,d, the ${\dot{S}}_{g}$ curve presents a U shape. The minimum value of ${\dot{S}}_{g}$ occurs when G is between 250 and 300 kg/(m

^{2}·s). With the decrease in θ of the zigzag microchannel, the proportion of the flow entropy generation in total entropy generation becomes larger. Figure 18 also shows that when T

_{in}= 310, 315, and 320 K, ${\dot{S}}_{g}$ of the CO

_{2}-cooled case is larger than that of the water-cooled case in the whole analysis flow flux range for all straight and zigzag microchannels. In this case, there is no advantage in using CO

_{2}to replace water as a coolant. When T

_{in}= 308 for straight type and zigzag type with θ =150°, the ${\dot{S}}_{g}$ of the CO

_{2}-cooled microchannel is lower than that of the water-cooled channel under high-flow flux conditions.

_{2}-cooled microchannel with T

_{in}= 308 K, respectively. It can be seen from the analysis result that in water-cooled cases, the zigzag channel with θ = 150° has the best comprehensive performance (lowest valve of ${\dot{S}}_{g}$), followed by θ = 120° and straight channels, and the zigzag channel with θ = 90° is the worst. For the cases of sCO

_{2}-cooled channels, the ${\dot{S}}_{g}$ of the straight channel and zigzag channel with θ =150° is better, and with a reduction in the value of θ, the ${\dot{S}}_{g}$ of the zigzag channel gradually increases. This analysis result also shows that although the existence of bends in the microchannel can improve the h of the sCO

_{2}-cooled microchannel, it is not beneficial to its comprehensive performance evaluated by ${\dot{S}}_{g}$. However, the existence of obtuse bends in the channel can improve the comprehensive performance to some extent for the water-cooled microchannel.

## 4. Conclusions

_{2}-cooled and water-cooled straight and zigzag (θ = 90°, 120°, and 150°) microchannels. The mass flux (G) ranges from 50 to 1000 kg/(m

^{2}·s) and the heat flux (q

_{w}) ranges from 40,000 to 120,000 W/m

^{2}for both coolant-based cooling cases. The inlet temperature (T

_{in}) for CO

_{2}-cooled microchannels ranges from 306 K to 320 K with the operating pressure 8 MPa, which covers the pseudocritical point. The inlet temperature of the water-cooled microchannel is 308 K with the operating pressure 0.1 MPa. The following conclusions were obtained:

_{2}has advantages over water in thermal and hydraulic performance in microchannels due to its excellent thermophysical properties nearby the pseudocritical point. Taking sCO

_{2}as a coolant makes it possible to reduce the average temperature of the heating surface (T

_{hsur}) to 0.5~0.7 K and enhance the heat transfer performance in contrast to water. The entropy generation rate (${\dot{S}}_{g}$) of the straight microchannel cooled with sCO

_{2}can reach 0.58~0.69 times the one cooled with water.

_{2}replacing water as the coolant can improve microchannel thermal and hydraulic performance, but the premise lies in adopting a reasonable inlet temperature, working pressure, and adequate channel mass flux according to the heat load to keep the CO

_{2}state near the pseudocritical point.

_{2}-cooled case, the straight channel had the best comprehensive performance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | area (m^{2}) | Greek symbols | |

C | wet circumference (m) | $\rho $ | density (kg/m^{3}) |

${d}_{h}$ | hydraulic diameter (m) | $\mu $ | dynamic viscosity (Pa·s) |

$\overrightarrow{g}$ | gravity vector (m/s^{2}) | θ | bend angle |

G | mass flux (kg/(m^{2}·s)) | ||

h | average heat convection coefficient (W/(m^{2}·K)) | Subscripts | |

k | thermal conductivity (W/(m·K)) | b | bulk |

$\dot{m}$ | mass flow rate (kg/s) | eff | effective |

Nu | Nusselt number | hsur | heated surface |

P | pressure (Pa) | in | inlet |

$\Delta P$ | pressure difference (Pa) | m | pseudocritical point |

q | heat flux (W/m^{2}) | out | outlet |

Q | heat (W) | t | turbulent |

Re | Reynolds number | w | wall |

${\dot{S}}_{g}$ | entropy generation rate (W/K) | ||

T | temperature (K) | ||

$\overrightarrow{v}$ | velocity vector (m/s) |

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**Figure 1.**Thermophysical properties of CO

_{2}at different working pressure (7.5, 8.0, and 9 MPa). (

**a**) Specific heat; (

**b**) thermal conductivity; (

**c**) dynamic viscosity; (

**d**) density.

**Figure 5.**Validation with experimental data [38].

**Figure 10.**Comparison results of the entropy generation rate in different G: (

**a**) ${\dot{S}}_{g}$; (

**b**) ${S}_{g,C{O}_{2}}/{S}_{g,water}$.

**Figure 11.**Effect of G on ${\dot{S}}_{g,\Delta P}$, ${\dot{S}}_{g,\Delta T}$, and ${\dot{S}}_{g}$: (

**a**) water-cooled channel (T

_{in}= 308 K, P

_{out}= 0.1 MPa); (

**b**) CO

_{2}-cooled channel (T

_{in}= 308 K, P

_{out}= 8 MPa).

**Figure 13.**Effect of q

_{w}on $\Delta P$ and pumping power consumption: (

**a**) pressure drop; (

**b**) power.

**Figure 16.**Comparison of the effect of bend angle on h: (

**a**) water-cooled channel; (

**b**) CO

_{2}-cooled channel (T

_{in}= 308 K).

**Figure 17.**Velocity vector diagram of the cross section of microchannel (G = 500 kg/(m

^{2}·s), T

_{in}= 308 K): (

**a**) water-cooled straight channel; (

**b**) water-cooled zigzag channel (θ = 150°); (

**c**) CO

_{2}-cooled straight channel; (

**d**) CO

_{2}-cooled zigzag channel (θ = 150°).

**Figure 18.**Comparison of ${\dot{S}}_{g}$: (

**a**) straight channel; (

**b**) θ = 150°; (

**c**) θ = 120°; (

**d**) θ = 90°.

**Figure 19.**Comparison of the effect of bend angle on ${\dot{S}}_{g}$: (

**a**) channel cooled by water; (

**b**) channel cooled by CO

_{2}(T

_{in}= 308 K at P

_{out}= 8 MPa).

Coolants | G (kg/(m^{2}·s)) | P_{out} (MPa) | Q_{w}(W/m^{2}) | T_{in} (K) |
---|---|---|---|---|

sCO_{2} | 50~1000 | 8 | 40,000~120,000 | 306, 307, 308, 310, 315, 320 |

water | 50~1000 | 0.1 | 40,000~120,000 | 308 |

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**MDPI and ACS Style**

Tu, Y.; Zeng, Y.
Comparative Study of the Thermal and Hydraulic Performance of Supercritical CO_{2} and Water in Microchannels Based on Entropy Generation. *Entropy* **2022**, *24*, 1312.
https://doi.org/10.3390/e24091312

**AMA Style**

Tu Y, Zeng Y.
Comparative Study of the Thermal and Hydraulic Performance of Supercritical CO_{2} and Water in Microchannels Based on Entropy Generation. *Entropy*. 2022; 24(9):1312.
https://doi.org/10.3390/e24091312

**Chicago/Turabian Style**

Tu, Yi, and Yu Zeng.
2022. "Comparative Study of the Thermal and Hydraulic Performance of Supercritical CO_{2} and Water in Microchannels Based on Entropy Generation" *Entropy* 24, no. 9: 1312.
https://doi.org/10.3390/e24091312