# Assessment of Efficiency of Heat Transportation in Indirect Propane Refrigeration System Equipped with Carbon Dioxide Circulation Loop

^{*}

## Abstract

**:**

_{2}as a heat transfer fluid should be designed for operation at maximum refrigeration capacity.

## 1. Introduction

_{2}achieves a heat transfer coefficient that is up to nine times higher than water and brine solutions as working fluids. It should be noted that carbon dioxide has a low critical temperature (−31 °C) and critical pressure at 7.37 MPa, which gives it an advantage and uniqueness because it performs well in supercritical conditions. Zhao et al. [20] proposed empirical correlations for natural circulation mass flux for supercritical CO

_{2}power cycles. The research demonstrated that the pseudo-critical region is the place where the heat transfer process deteriorates. Their results proved that buoyancy forces in a simple circulation loop play a significant role in the heat transfer process. Deng et al. [21] conducted a numerical and experimental study of the application of supercritical CO

_{2}flows. They observed flows under varying output and input conditions and demonstrated that a supercritical loop could offer very fast stabilisation conditions. The system also responded much faster to condenser adjustments compared to the evaporator. In another study [22], using Nusselt number assessment, researchers have proposed working under supercritical conditions but at the lowest possible pressure to achieve more stable operation conditions of the system. Under higher pressures, they observed bidirectional oscillations and under lower pressure conditions, the loop operation led only to unidirectional pulsations. Thimmaiah et al. [23,24] performed a comparative analysis between two different circulation systems. They proposed an NCL with an isothermal heater and cold heat exchanger and a second NCL with a hot and cold heat exchanger. This study demonstrated the system stability conditions with varying temperature and pressure inside the analysed loop. In addition, the results showed that the supercritical NCL system with an isothermal heater is more stable and has fewer fluctuations in flow rate than the subcritical system.

_{2}thermosyphons used in the data centre. They performed a visual experiment and established a calculation model. The results showed that when the diameter is designed to be too small, the system will be operated under overload conditions; however, when the diameter is too big, the system will be in an oscillatory or inactive state. Therefore, the diameters of the loop pipes should be adjusted to actual heat load. Pegallapati et al. [29] presented a dynamic NCL model using CO

_{2}, which was developed by the balance equations for mass, momentum, and energy. They observed that the wall thermal capacity may also be thought of as a crucial factor in the dynamic operation of NCL because it introduces damping to the system which removes the oscillations and increases the time required to reach steady-state conditions. Tong et al. [30] conducted research on the self-regulating performance of CO

_{2}in NCL with two evaporators. The results of this study showed that the difference between the heat transfer loads of the parallel evaporators should be as minimal as possible. Otherwise, it is exceedingly difficult to obtain a self-regulation of the loop system because more mass flux is wasted through the low-power evaporator.

_{2}as a working fluid in refrigeration systems. An appropriate structure is essential for real applications, so the liquid downcomer, pipes’ diameter, and relevant operation parameters must be carefully selected. However, the aspects of the influence of thermal load of the circulation loop on the efficiency of operation of the entire refrigeration system has never been analysed in the literature, which is the most important motivation of the present paper. This paper presents an approach to the analytical modelling of NCL to determine the optimum height of the liquid downcomer for given boundary conditions and operation parameters.

## 2. Calculation Model

_{2}. The unit supplying this circuit is switched on by a signal generated by a pressure alarm pressure switch on the tank, signalling an increase in pressure (usually when the unit does not operate under high external temperature conditions). The second loop is only forced by gravity, where the correct height of the liquid downcomer is essential. An additional issue considered in the system is the possibility of self-regulation of the NCL. Note that the lack of an expansion element reduces investment and operating costs and increases the attractiveness of the system.

**Flow resistance in the condenser**

_{2}circuit, empirical correlations are used which include the following formulas proposed by Würfel–Ostrowski [31]:

**Flow resistance in the evaporator**

_{i}:

_{l}:

_{2}two-phase mixture shaped by external, as well as interfacial, forces should be considered. Based on the relation proposed by Cheng et al. [34], the vapour quality is determined by the flow structure changes from intermittent to annular flow regimes because of the large difference in velocity between the two phases, resulting in a large inertial force of the vapour phase:

**Flow resistance along the pipeline length**

**Local flow resistance**

## 3. Model Validation

#### 3.1. Validation of Two-Phase Flow Pattern Prediction

_{2}evaporation for various mass velocities in a microchannel. He observed the diverse types of flows, depending on the vapour quality. The flow patterns that were experimentally obtained by Gasche [43] are presented in Figure 3. Note that two-phase pattern boundaries are predicted with the use of the formulated analytical model. As can be seen from the two-phase flow pattern map, the prediction of flow pattern types agrees with the experimental data of Gasche [43], especially for the annular region.

_{2}flow at a high pressure in small-diameter tubes [44]. Figure 4 provides the identified CO

_{2}flow pattern in a 2 mm diameter pipe at a pressure of 5 MPa.

^{2}⋅s and 700 kg/m

^{2}⋅s. Researchers observed the initial flow as bubbly, which is more often attributed to vertical flows and is not highlighted in the proposed flow pattern map. Plug flow has been reported in the literature; hence, in the map, this is shown as a stratified-wavy flow [34]. Accordingly, it can be seen that three of the four points marked on the proposed map agree very well with experimental observations for both mass velocities. The disputed place is the dry-out region. This provides an introduction to the misty region, which is not always highlighted in studies [43]. Therefore, the validation showed that the loop design method proposed in this paper shows its compatibility with other studies available in the literature.

#### 3.2. Validation for Thermal Performance Prediction

_{2}as a working fluid. The research proposed a model with a temperature difference between condensation and evaporation of close to zero. The proposed circulation loop, along with the applied operation parameters, is shown in Figure 5 for a pipeline diameter of 10 mm.

_{2.}In the proposed design method, they presented pipeline diameters for particular heat transfer capacities, which are most optimal from an economic perspective. They also determined the minimum height difference between the heat exchangers. Table 3 presents a comparison of the design recommendations on height difference made by the researchers with the results of the calculations proposed in this article. R134a was chosen for comparison, as a detailed analysis of this fluid was conducted by researchers. The temperature of the R134a was taken as 20 °C and the length of circuit pipeline as 10 m. According to Equation (1), each additional 1 kPa of pressure loss in the loop results in a need to increase the liquid downcomer by 0.083 m. For validation purposes, the condenser flow resistance of 0.7–1.0 kPa and evaporator flow resistance of 3.7–6.0 kPa were assumed. The inaccuracies when determining resistance in the exchangers is crucial to all validation.

## 4. Results and Discussion

_{2}circulation loop.

_{2}as a function of the condensation temperature is presented in Figure 6. The presented results provide information about the maximum allowable total flow resistance of the analysed NCL. The presented results indicate that the effect of CO

_{2}condensation temperature, which may be thought as a kind of free parameter of the analysed refrigeration system, plays a crucial role in the design of this system.

_{2}and, more specifically, its density. It is, therefore, important to consider the condensation parameters at the design stage, as they can significantly affect the system’s stable operation. Due to the gravitational nature of the fluid flow and the lack of influence on the pressure exerted by the liquid column, the flow resistance created in the condenser and on the path between the condenser and the liquefied CO

_{2}tank is negligibly small, as it does not exceed 300 Pa. A suitably designed condenser, using a small amount of refrigerant, ensures the removal of high-heat flux density with a significantly low flow resistance.

_{ideal}for the “ideal cycle” can be determined from equation [20]:

_{2}, the difference in these temperatures is particularly important due to the properties of carbon dioxide. An increase in the temperature difference ${t}_{e}$ and ${t}_{c}$ will necessitate an increase in the liquid downcomer, which can enable NCL operations and achieve self-adjustment of refrigerant mass flux. Therefore, a minimum temperature difference must be achieved to ensure system operation. In addition, the diameter of the pipeline is closely related to temperature differences. Figure 7 shows the calculated dependence of the necessary height difference in the liquid downcomer on the difference between evaporation and condensation temperatures for various pipeline diameters.

_{2}.

_{2}on the energy efficiency of the entire system, consisted of a propane refrigeration unit and CO

_{2}circulation loop. The assumed height of the liquid downcomer is 4 m, and the diameter of the pipeline is 18 mm. The variable parameter of the refrigeration capacity of the evaporator ranged from 0.50 kW to 10 kW. In Figure 8, prediction results that show the dependence of the mass flux of the working fluid and the temperature difference between the change in heat exchangers for the designed system, depending on the heat load. As noted, as the heat capacity increases, the mass flux of the circulating working fluid increases and the temperature difference increases by increasing the condensation temperature at a constant evaporation temperature. This means that the condenser is responsible for the generation of the pressure that is necessary for the working fluid circulation in the loop. These parameters are responsible for the flow circulation adjustment under a variable heat load (i.e., refrigeration capacity) in the analysed system. This may be thought of as the key aspect in the application of the analysed system.

_{2.}

_{2}circulation loop. The refrigeration unit and circulation loop are coupled in the CO

_{2}condenser, which, in turn, acts as an evaporator for the propane cycle. In practice, this means that, as the condensation temperature of CO

_{2}increases, the evaporation temperature of propane in the plate exchanger should also increase. However, increasing the evaporation temperature of propane refrigeration unit will directly increase the coefficient of performance (COP) of this system, as this is the primary means of improving this indicator, as can be seen from the following formula:

_{in}and specific enthalpy of a saturated vapour at the evaporation temperature h

_{out}in propane refrigeration unit, we can calculate the required mass flux that should be compressed by the compressor:

_{2}were assumed: −20 °C, −10 °C, and 0 °C. The results are shown in Table 4.

_{2}condensation and CO

_{2}evaporation of lower than 2 K have been obtained. Based on these temperature differences, the required mass flux in propane in the propane refrigeration unit, the electrical power consumed by the compressor and the results are shown in the Table 5.

_{2}.

_{2}evaporation temperatures. If the evaporation temperature of CO

_{2}is increased from −20 °C to 0 °C, almost double an increase in efficiency can be seen. This is primarily because the difference in evaporation and condensation temperatures in the propane aggregate decreases and the circuit becomes more efficient. In addition, for higher evaporation temperatures, when the head load of NCL increases, the COP also increases more markedly than at lower temperatures. Thus, in this case, we obtain an appliance with an increased COP that consumes less electricity. For a certain loop design, an increase in heat load increases the efficiency of the NCL that is coupled to the propane refrigeration unit and, similarly, a decrease in heat load decreases the efficiency of the device. This system response shows remarkably interesting results, and this may prove to be an especially important aspect in terms of the such solutions’ applicability in the industry.

## 5. Conclusions

- An analytical model is presented for the design of refrigeration systems with a circulation loop. The model considers the local pressure drop that is particular to the geometry of the loop. The optimum height of the liquid downcomer can be determined, depending on the flow resistance of the entire loop and the diameter of the pipeline.
- The validation of experimental studies shows that the presented model shows reasonable agreement and can be applied to the design of various circulating loop systems. In the validation of two-phase flow pattern prediction, the points on the flow pattern maps overlap by 70% compared with the literature results.
- It has been shown that as the mass flux of CO
_{2}as a working fluid increases, the temperature difference between evaporation and condensation increases, and it becomes necessary to increase the height of the liquid downcomer or increase the diameter of the pipeline. - The effect of a change in the refrigeration capacity of the circulating loop on the COP level of the coupled propane compressor refrigeration system was analysed for the first time. The highest COP was obtained for a CO
_{2}evaporation temperature of 0 °C; then, the COP value was 9.3 for a thermal capacity of 0.5 kW and 11.2 for a thermal capacity of 10 kW. An up to 23% increase in system efficiency was found as the refrigeration capacity of the system increases. Therefore, operation of the indirect refrigeration system with a CO_{2}circulation loop should be avoided with a reduced refrigeration capacity. - Raising the evaporation CO
_{2}temperature in the circulation loop from −20 °C to 0 °C improves the COP of the entire indirect refrigeration system by about 50%. This is of significant importance in terms of the applicability of such systems.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | heat transfer surface area, ${\mathrm{m}}^{2}$ |

D | inlet diameter, m |

${D}_{h}$ | hydraulic diameter, m |

Fr | Froude number |

${F}_{WO}$ | constant dependent on the angle of the channel extrusions |

g | gravitational acceleration, $\mathrm{m}/{\mathrm{s}}^{2}$ |

G | mass flux density (mass velocity), kg/(m^{2}⋅s) |

${G}_{pl}$ | single plate width, m |

h | specific enthalpy, J/kg |

H | height of the exchanger plate, m |

k | heat transfer coefficient, W/${\mathrm{m}}^{2}\mathrm{K}$ |

L | length of pipeline, m |

$\mathit{\u1e41}$ | mass flux, kg/s |

${n}_{pl}$ | number of plates of heat exchanger |

${n}_{z}$ | number of parallel fluid streams |

Nu | Nusselt number |

Pr | Prandtl number |

R | thermal resistance in the condenser, K/W |

Re | Reynolds number |

${s}_{pl}$ | distance between plates, m |

${S}_{he}$ | heat exchanger heat transfer surface area, ${\mathrm{m}}^{2}$ |

t | saturation temperature, °C |

Q | thermal capacity, W |

w | velocity, m/s |

We | Weber number |

x | two-phase flow quality |

${X}_{LM}$ | Lockhart–Martinelli parameter |

Greek Symbols | |

$\beta $ | turbulence damping factor |

${\beta}_{t}$ | forced turbulence coefficient |

${\zeta}_{0}$ | coefficient of resistance to flow in a smooth channel |

∆H | liquid downcomer, m |

∆p | pressure drop, Pa |

${\left(\mathsf{\Delta}{p}_{\lambda}\right)}_{L}$ | frictional pressure losses in single-phase fluid flow, Pa |

∆T | temperature difference, K |

$\lambda $ | pressure loss ratio |

ɛ | void fraction |

$\mu $ | dynamic viscosity, Pa⋅s |

⍴ | density, $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${\mathrm{\u2374}}_{r}$ | ratio of liquid and gas density |

${\Phi}_{WO}^{2}$ | two-phase flow multiplier |

${\xi}_{pl}$ | local loss coefficient |

Subscripts | |

av | average |

c | condenser |

e | evaporator |

in | inlet |

ll | flow inside the straight sections of the loop |

lt | the local flow resistances |

out | outlet |

Abbreviations | |

COP | coefficient of performance |

FCL | forced circulation loop |

GWP | global warming potential |

HFC | hydrofluorocarbons |

NCL | natural circulation loop |

ODP | ozone depletion potential |

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**Figure 1.**Schematic of the analysed indirect cooling system with CO

_{2}NCL: 1. propane chiller (R290); 2. plate heat exchanger as evaporator in the propane cycle and condenser in the ${\mathrm{CO}}_{2}$ circulation loop; 3. ${\mathrm{CO}}_{2}$ tank; 4. ${\mathrm{CO}}_{2}$ evaporator; ∆H—height of the liquid downcomer.

**Figure 2.**Schematic of channel section in two-phase separated flow: D—internal channel diameter: ${h}_{l}$—height when filling the channel with liquid; ${P}_{i}$ —the ratio of the length of the fluid interface to the fill height in the channel; ${A}_{l}$ —liquid phase area; ${P}_{l}$ —perimeter of tube wetted by liquid; ${A}_{v}$ —vapour phase surface cross-section area; ${P}_{v}$ —pipe circuit in contact with vapour phase; ${\mathsf{\theta}}_{m}$ —wet angle of the tube perimeter; ${\mathsf{\theta}}_{s}$ —dry angle of the tube perimeter.

**Figure 3.**CO

_{2}two-phase flow pattern map based on own prediction: A—annular flow; D—dry-out region; I—intermittent flow; M—misty flow; S—tratified flow; SLUG—slug flow; SW—stratified-wavy flow; The experimental data observed by Gasche [43]: 1,2—slug flow; 3—slug/annular flow; 4,5—annular flow.

**Figure 4.**CO

_{2}two-phase flow pattern map based on own prediction, where: A—annular flow; D—dry-out region; I—intermittent flow; M—misty flow; S—stratified flow; SLUG—slug flow; SW—stratified-wavy flow. The experimental data observed by Ozawa et al. [44]: 1—bubbly flow; 2—slug/annular flow; 3—annular flow; 4—misty flow; 5—plug flow; 6—slug flow; 7—annular flow; 8—misty flow.

**Figure 5.**Operation parameters of the NCL in the experimental investigations, acc. to [10].

**Figure 6.**Predicted hydrostatic pressure of the column of liquid at the loop of height of 4 m for various condensation temperatures.

**Figure 8.**Effect of heat load on mass flux and required temperature difference between condenser and evaporator.

**Figure 9.**Schematic diagram of propane refrigeration unit equipped with a CO

_{2}circulation loop: 1—propane condenser with fan; 2—expansion valve; 3—plate heat exchanger as evaporator in the propane cycle and condenser in the ${\mathrm{CO}}_{2}$ circulation loop; 4—compressor; 5—${\mathrm{CO}}_{2}$ tank; 6—${\mathrm{CO}}_{2}$ evaporator.

**Figure 10.**Effect of CO

_{2}evaporation temperature and heat load of NCL on COP of propane refrigeration unit.

**Table 1.**Loss coefficients for selected loop components acc. to [32].

Regular 90° flanged elbows | 0.30 |

Regular 90° threaded elbows | 1.50 |

Long radius 90° flanged elbows | 0.20 |

Long radius 90° threaded elbows | 0.70 |

Line flow flanged tees | 0.20 |

Line flow threaded tees | 0.90 |

Union threaded | 0.08 |

**Table 2.**Assumed CO

_{2}condenser and evaporator geometries (based on existing plate heat exchangers) acc. to [45].

CO_{2} Condenser | CO_{2} Evaporator | ||
---|---|---|---|

Angle of embossing of the channels of adjacent plates ϒ | 60°/30° | Angle of embossing of the channels of adjacent plates ϒ | 30°/30° |

${F}_{WO}$ | 0.10 | ${F}_{WO}$ | 0.10 |

p | 0.30 | p | 0.40 |

${\lambda}_{WO}$ | 1.0 | ${\lambda}_{WO}$ | 0.86 |

H [m] | 0.50 | H | 0.30 |

${d}_{h}$[m] | 0.002 | ${d}_{h}$ | 0.0018 |

Plate width [m] | 0.145 | Plate width | 0.150 |

Heat transfer area [m^{2}] | 1.015 | Heat transfer area | 1.80 |

Predicted flow resistance depends on mass flux in terms of 0.005–0.05 kg/s [kPa] | 0.67–1.64 | Predicted flow resistance depends on mass flux in terms of 0.005–0.05 kg/s [kPa] | 3.59–10.26 |

**Table 3.**Comparison of model prediction with experimental results of Yang X. et al. [46].

Q | Diameter of Pipe | Experimental Loop Height and Pressure Losses | Calculated Loop Height and Pressure Losses |
---|---|---|---|

4000 W | 12.7 mm | 0.65 m; 7.83 kPa | 0.89 m; 10.72 kPa |

8000 W | 15.9 mm | 0.75 m; 9.04 kPa | 0.94 m; 11.33 kPa |

10,000 W | 19.1 mm | 0.40 m;4.82 kPa | 0.65 m; 7.83 kPa |

**Table 4.**Calculation results of propane evaporator/CO

_{2}condenser and resulting circulation CO

_{2}loop temperature difference.

$\mathbf{Parameters}\mathbf{of}\mathbf{the}\mathbf{Condensation}\mathbf{C}{\mathbf{O}}_{\mathbf{2}}\mathbf{side}\mathbf{\to}\mathbf{-}\mathbf{20}\mathbf{\xb0}\mathbf{C}$ | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$\mathbf{[}\frac{W}{{m}^{2}K}]$ | $\mathrm{U}\left[\frac{W}{{m}^{2}K}\right]$ | ΔT°C |

14,820 | 2.23 | 0.029 | 2.98 | 3.59 | 170.5 | 5754 | 1543.2 | 1.67 |

Parameters of the evaporation R290 side | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{R}290}\left[\frac{W}{{m}^{2}K}\right]$ | ||

5710 | 1.75 | 0.036 | 2.99 | 3.59 | 76.13 | 2227 | ||

$\mathbf{Parameters}\mathbf{of}\mathbf{the}\mathbf{condensation}\mathbf{C}{\mathbf{O}}_{\mathbf{2}}$ side→−10 °C | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$\mathbf{[}\frac{W}{{m}^{2}K}]$ | $\mathrm{k}\left[\frac{W}{{m}^{2}K}\right]$ | ΔT °C |

16,657 | 2.2 | 0.028 | 2.98 | 3.59 | 183.25 | 5613.9 | 1658.4 | 1.56 |

Parameters of the evaporation R290 side | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{R}290}\left[\frac{W}{{m}^{2}K}\right]$ | ||

6190 | 2.16 | 0.036 | 2.98 | 3.59 | 90.95 | 2509.2 | ||

$\mathbf{Parameters}\mathbf{of}\mathbf{the}\mathbf{condensation}\mathbf{C}{\mathbf{O}}_{\mathbf{2}}$ side→0 °C | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$\mathbf{[}\frac{W}{{m}^{2}K}]$ | $\mathrm{k}\left[\frac{W}{{m}^{2}K}\right]$ | ΔT °C |

18,662 | 2.27 | 0.027 | 2.98 | 3.59 | 201.01 | 5549.38 | 1855.29 | 1.39 |

Parameters of the evaporation R290 side | ||||||||

Re | Pr | ${\zeta}_{0}$ | ${\beta}_{t}$ | $\beta $ | Nu | ${k}_{\mathrm{R}290}$$\mathbf{[}\frac{W}{{m}^{2}K}]$ | ||

6684 | 2.95 | 0.035 | 2.98 | 3.59 | 113.01 | 2993.92 |

Evaporation Temperature of CO_{2} → −20 °C | |||||
---|---|---|---|---|---|

Heat Load of NCL [kW] | Mass Flux of CO_{2} [kg/s] | Evaporation Temperature of Propane [°C] | Mass Flux of Propane [kg/s] | Enthalpy Difference ∆h [kJ/kg] | Power of the Compressor P [kW] |

500 | 0.00177 | −21.37 | 0.00650 | 64.19 | 0.414 |

1500 | 0.00531 | −20.77 | 0.00652 | 62.86 | 0.410 |

2500 | 0.00885 | −20.07 | 0.00654 | 62.05 | 0.406 |

3500 | 0.01240 | −19.37 | 0.00655 | 61.23 | 0.401 |

4500 | 0.01593 | −18.67 | 0.00657 | 60.42 | 0.397 |

5500 | 0.01947 | −17.97 | 0.00658 | 59.61 | 0.392 |

6500 | 0.02301 | −17.17 | 0.00660 | 58.68 | 0.387 |

7500 | 0.02655 | −16.37 | 0.00661 | 57.75 | 0.382 |

8500 | 0.03009 | −15.57 | 0.00663 | 56.83 | 0.377 |

9500 | 0.03363 | −14.77 | 0.00665 | 55.91 | 0.372 |

10,000 | 0.03541 | −14.27 | 0.00666 | 55.33 | 0.369 |

Evaporation temperature of CO_{2}→ −10 °C | |||||

Heat load of NCL [kW] | Mass Flux of CO_{2} [kg/s] | Evaporation temperature of propane [°C] | Mass flux of propane [kg/s] | Enthalpy difference ∆h [kJ/kg] | Power of the compressor P [kW] |

500 | 0.00193 | −11.24 | 0.00672 | 51.96 | 0.349 |

1500 | 0.00580 | −10.64 | 0.00673 | 51.29 | 0.345 |

2500 | 0.00967 | −9.94 | 0.00675 | 50.49 | 0.341 |

3500 | 0.01353 | −9.24 | 0.00676 | 49.70 | 0.336 |

4500 | 0.01740 | −8.54 | 0.00678 | 48.90 | 0.332 |

5500 | 0.02127 | −7.84 | 0.00680 | 48.11 | 0.327 |

6500 | 0.02514 | −7.04 | 0.00681 | 47.32 | 0.322 |

7500 | 0.02900 | −6.24 | 0.00683 | 46.42 | 0.317 |

8500 | 0.03287 | −5.44 | 0.00685 | 45.52 | 0.312 |

9500 | 0.03674 | −4.54 | 0.00687 | 44.51 | 0.306 |

10,000 | 0.03867 | −4.04 | 0.00689 | 43.95 | 0.303 |

Evaporation temperature of CO_{2}→0°C | |||||

Heat load of NCL [kW] | Mass Flux of CO_{2} [kg/s] | Evaporation temperature of propane [°C] | Mass flux of propane [kg/s] | Enthalpy difference ∆h [kJ/kg] | Power of the compressor P [kW] |

500 | 0.02170 | −1.09 | 0.00696 | 40.55 | 0.282 |

1500 | 0.00650 | −0.51 | 0.00698 | 39.91 | 0.279 |

2500 | 0.01083 | +0.21 | 0.00700 | 39.15 | 0.274 |

3500 | 0.01516 | +0.91 | 0.00701 | 38.35 | 0.269 |

4500 | 0.01949 | +1.61 | 0.00703 | 37.58 | 0.264 |

5500 | 0.02382 | +2.31 | 0.00705 | 36.78 | 0.259 |

6500 | 0.02815 | +3.01 | 0.00707 | 36.05 | 0.255 |

7500 | 0.03248 | +3.81 | 0.00709 | 35.18 | 0.249 |

8500 | 0.03681 | +4.61 | 0.00711 | 34.31 | 0.244 |

9500 | 0.04114 | +5.51 | 0.00714 | 33.34 | 0.238 |

10,000 | 0.04331 | +6.01 | 0.00713 | 33.88 | 0.234 |

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**MDPI and ACS Style**

Pawłowski, M.; Gagan, J.; Butrymowicz, D.
Assessment of Efficiency of Heat Transportation in Indirect Propane Refrigeration System Equipped with Carbon Dioxide Circulation Loop. *Sustainability* **2022**, *14*, 10422.
https://doi.org/10.3390/su141610422

**AMA Style**

Pawłowski M, Gagan J, Butrymowicz D.
Assessment of Efficiency of Heat Transportation in Indirect Propane Refrigeration System Equipped with Carbon Dioxide Circulation Loop. *Sustainability*. 2022; 14(16):10422.
https://doi.org/10.3390/su141610422

**Chicago/Turabian Style**

Pawłowski, Mateusz, Jerzy Gagan, and Dariusz Butrymowicz.
2022. "Assessment of Efficiency of Heat Transportation in Indirect Propane Refrigeration System Equipped with Carbon Dioxide Circulation Loop" *Sustainability* 14, no. 16: 10422.
https://doi.org/10.3390/su141610422