# Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) has been used widely in the refrigeration system due to its good thermophysical properties and is classified as A1 safety level by ASHRAE [5]. Moreover, the utilization of supercritical R744 overwhelmed the inefficiency problems in refrigeration cycles at high temperatures since it has a low critical temperature [6]. The low critical temperature anticipates smooth variation in the thermophysical properties, resulting in a stable operation of the PHE. Recently, Elbarghathi et al. [5] presented a transcritical R744 refrigeration cycle that utilizes the supercritical phase of R744 at the gas cooler and the subcritical R744 at the evaporator. In these applications, the supercritical R744 temperature is relatively high and distant from the critical point, making it suitable for use as a heat source for different applications of PHE.

_{2}as a heat source for recently manufactured eco-friendly refrigerants, which will be helpful for designing and developing refrigeration cycles.

## 2. System Description

## 3. Theoretical Analysis

#### 3.1. Data Reduction

_{pl}and A

_{eff}are the number of plates and the effective area, respectively. The effective area includes the effect of Chevron corrugation on the total area exposed to the working fluids by multiplying the plate (A

_{pl}) area by the enlargement factor (∅) [4], as shown below:

_{pl}are the fouling factor and the plate thermal conductivity, respectively, while h

_{c}and h

_{h}are the convection coefficient of the cold and hot fluids, respectively. The convection coefficients can be estimated from Nusselt number (Nu) as:

_{hy}is the channel hydraulic diameter.

_{m}is the mean vapor quality of the vaporization process, which is equal to 0.5 when the process starts from the saturated liquid line to the saturated vapor line.

#### 3.2. Calculation Procedure

- The inputs are the cold stream inlets, outlets temperature, and hot stream pressure.
- The cold stream pressure was estimated according to the refrigerant name (N) and the specified saturation temperature.
- The cold stream enthalpies were evaluated for the artificial inlet and outlet for each cold stream.
- Then, the heat rate (Q) was estimated for each artificial section by multiplying the total mass flow rate by the enthalpy difference.
- The hot stream temperatures were evaluated using the R744 inlet temperature and the heat rate.
- Thereafter, the dimensionless numbers were evaluated. Re, We, Bd, and Bo were evaluated for the cold stream, while for the hot stream, Re and Gr were evaluated. Since the boiling number requires information from the heat flux and the overall heat transfer coefficient, as shown in Equation (7), a loop was set to iteratively solve Equations (5) and (7).
- Once the boiling number difference condition is achieved, the effectiveness, convection coefficients, and pressure drops will be evaluated and saved. Then, the calculation proceeds with the following flow rate or the number of plates. Finally, the mentioned steps were repeated for different inputs and refrigerants.

## 4. Discussion

#### 4.1. Effect of the Number of Plates

^{−1}for four different types of HFOs: R1234yf, R1234ze(E), R1234ze(Z), and R1233zd(E). Figure 3 illustrates the cold stream liquid-phase convection coefficients versus the number of plates from 10 to 109. For all cases, the liquid-phase convection coefficient has the same tendency to decrease from around 700 to 170 W m

^{−2}K

^{−1}. For a number of plates lower than 40, the liquid-phase convection coefficient has a steep slope, and then this slope becomes more horizontal at a higher number of plates. This tendency is due to the change in Reynold’s number as the velocity and the channel mass flux decrease with the increasing number of plates. Moreover, the type of refrigerant has a negligible effect on the liquid-phase convection coefficients, since the viscosities and conductivities differ slightly.

^{−2}K

^{−1}and from 4175 to 1766 W m

^{−2}K

^{−1}for R1234yf and R1234ze(E), respectively. In contrast, the two-phase convection coefficient for R1234ze(Z) and R1233zd(E) was approximately five times lower than R1234yf and R1234ze(E). The R1234ze(Z) and R1233zd(E) have considerably lower two-phase convection coefficients due to their higher energy of vaporization, which leads to lower heat fluxes, lower boiling numbers, and lower overall heat transfer coefficients. On the other hand, the two-phase convection coefficient for R1234ze(E) was 8% higher than R1234yf.

^{−2}K

^{−1}due to the differences in bond number. The bond number is mainly a function of the surface tension, and it is assumed to be constant during the vaporization process for each refrigerant. For all curves, the slope becomes more horizontal with the increasing number of plates due to the decrement in the cold channel mass flux and Reynolds number. However, the estimated two-phase convection coefficients are in good agreement with the experimental data performed by Longo et al. [10,11].

^{−2}K

^{−1}. The other HFOs have a lower two-phase convection coefficient by 28%, 38%, and 47% for R1234ze(E), R1234ze(Z), and R1233zd(E), respectively. Compared to the liquid-phase convection coefficients, higher differences in the gas-phase convection coefficients were observed. This effect is due to considerably lower values of thermal conductivities and viscosities at the gas phase. However, the slopes of the plotted curves for the two-phase convection coefficients become more horizontal as the number of plates increases, especially for the number of plates higher than 60.

^{−2}K

^{−1}. However, the hot fluid convection coefficient decreases by 62% at the number of plates that is equal to 60, and a slight decline was estimated at a number of plates equal to 110. This decline becomes more stable due to the decrement in Reynolds number and the continuous increase in the Grashof to Reynolds number ratio. The acquired results were calculated at CO

_{2}mean temperature of around 90 °C, which is in good agreement with the experiment performed by Zendehboudi et al. [6]. Furthermore, the CO

_{2}has a relatively higher temperature than the critical one (31 °C), which provides a more stable PHE operation.

^{−1}at 10 plates to 31.5 kPa m

^{−1}at 109 plates. At a number of plates equal to 10, the total pressure drops to 21, 25, and 28 kPa m

^{−1}for R1234ze(E), R1234ze(Z), and R1233zd(E), respectively. In contrast, at a number of plates higher than 60, the R1234ze(E), R1234ze(Z), and R1233ze(E) have a 50%, 65%, and 68% smaller total pressure drop than R1234yf, respectively. On the other hand, R1234ze(Z) and R1233zd(E) have a total pressure drop higher than R1234ze(E) for a number of plates lower than 16 and 22, respectively. First, it should be noted that the two-phase pressure drop dominates the overall pressure drop since it is more turbulent. According to Amalfi et al. [3], the vaporization process is turbulent even at low vapor quality for a bond number higher than 4. Moreover, the two-phase pressure is directly proportional to the Bond number and inversely proportional to the Weber number. Both numbers are strongly dependent on the used refrigerant surface tension. However, the highest pressure was observed for R1234yf since it has the lowest value of Weber number. In contrast, R1233zd(E) had similar values of Weber number, but its pressure drop is considerably lower since it has the lowest bond number, which indicates that it is the least turbulent fluid of the used HFOs. In addition, the R1234ze(E) has the highest Weber and Bond numbers, but its Bond number is considerably higher than the other fluids. Therefore, it has the lowest total pressure drop at a low number of plates and a relatively high-pressure drop at an increased number of plates. The estimated pressure drops are in good agreement with the experiment performed by Longo et al. [10,11] and indicate that an insignificant pressure drop change was observed for a number of plates higher than 40.

^{−1}at a number of plates equal to 10 and 109, respectively. In the case of R1234ze(E), R1234ze(Z), and R1233zd(E), the total hot stream pressure drop declined by 6%, 14%, and 15%, respectively, compared to R1234yf. These differences in pressure drop resulted due to the fact that the CO

_{2}temperature drop depends on the cold fluid energy of vaporization. The higher the required vaporization energy, the higher the CO

_{2}temperature drop, higher CO

_{2}viscosity, and lower Reynolds number. The highest temperature drop was observed for R1234ze(Z), and the lowest was found at R1234yf. Generally, the total hot pressure drop has an insignificant variation at a number of plates higher than 50, in which the hot stream Reynolds number converges, as well. The estimated pressure drop is in good agreement with the data evaluated by Zendehboudi et al. [6].

_{2}can be used as a heating source for different types of recently produced HFOs at a wide range of plates. The following sections illustrate the effect of different boundary conditions: The hot stream pressure effect and the cold stream superheating temperature effect at various cold channel mass fluxes. In contrast, the impact of the cold stream saturation temperature was ignored as it is insignificant, as reported by Longo et al. [10,11]. For the following sections, the plate heat exchanger is considered to have 40 plates, since at a higher number of plates, insignificant variations were observed for effectiveness, pressure drop, and heat transfer coefficients.

#### 4.2. Effect of Hot Stream Inlet Pressure

^{−2}s

^{−1}, at hot stream inlet pressures of 10 and 12 MPa, and cold stream superheating temperature difference of 3 K. At 12 MPa hot stream pressure, R1234ze(E) has the highest two-phase convection coefficient increasing from 927 to 3315 W m

^{−2}K

^{−1}. In contrast, the other cold fluids have heat transfer coefficients by less than 14%, 57%, and 73% at the highest channel mass flux, and less than 18%, 56%, and 76% at the lowest channel mass flux for R1234yf, R1234ze(Z), and R1233zd(E), respectively. A similar tendency was revealed at 10 MPa hot stream pressure; the R1234ze(E) has a concave curve for the two-phase convection coefficient, increased from 829 to peak at 2601 W m

^{−2}K

^{−1}then decreased to 2551 W m

^{−2}K

^{−1}. Similar concave curves appeared for R1234ze(E) and R1233zd(E), but with convection coefficients lower by 56%, 73%, and 86%, 83% at the lowest and highest channel mass flux, respectively. Meanwhile, for R1234yf, the two-phase convection coefficient at 10 MPa increased continuously from 927 to 3315 W m

^{−2}K

^{−1}. As previously mentioned, R1234ze(E) has the highest two-phase convection coefficient since it possesses the highest bond number. Generally, the two-phase convection coefficient is higher at higher pressure due to the elevated values of heat flux and boiling number. In addition, the concave shape of the curve is due to the significant decrease in the hot stream temperature and the convergence of the overall heat transfer coefficient to a constant value. At the peak, the overall heat transfer coefficients do not change significantly. Then, the significant reduction in the two-phase convection coefficient occurs when the CO

_{2}temperature gets closer to the cold stream saturation temperature, leading to a considerable decrease in the heat flux and boiling number, as shown in Equation (7).

_{2}can be used as a heat source with a good range of hot stream pressures. Lower pressures than 10 Mpa for the hot stream were not investigated in this study to maintain the hot stream temperature as high as possible than the cold stream saturation temperature, which provides a wider range of applicable cold flow rates. At the same time, the saturation temperature of the cold stream is considered relatively high to adapt to a wider range of applications, such as ejector cooling systems, where it requires a relatively high temperature inside the ejector mixing chamber to avoid condensation.

#### 4.3. Effect of Superheat

^{−2}s

^{−1}, at hot stream inlet pressures of 10 MPa, and cold stream superheating temperature difference of 5 and 20 K. At the 5 K cold stream superheating difference, the highest two-phase convection coefficients were observed for R1234ze(E) from 826 to 2553 W m

^{−2}k

^{−1}. At the same time, it was lower for other cold fluids by 18%, 56%, and 73% at 0.1 Kg m

^{−2}s

^{−1}cold channel mass flux, and lower by 12%, 61%, and 75% at 6.8 Kg m

^{−2}s

^{−1}cold channel mass flux for R1234yf, R1234ze(Z), and R1233zd(E), respectively. Meanwhile, at 20 K cold stream superheating difference, the two-phase convection coefficient decreased maximally by 16%, 14%, 53%, and 26% for R1234ze(E), R1234yf, R1234ze(Z), and R1233zd(E), respectively. Compared to the hot stream pressure effect, the difference in convection coefficients due to the superheating difference is relatively small. However, these differences occurred due to lower heat fluxes in the two-phase region, since the gas phase covered areas that were significantly increased with the superheating temperature difference [9]. Moreover, the concave curves appeared at 20 K since it corresponds to a higher CO

_{2}temperature drop. According to the estimated two-phase convection coefficients, the CO

_{2}can operate as a hot fluid for PHE on a wide range of superheating temperatures, making it applicable for high-temperature applications.

## 5. Conclusions

_{2}can be used efficiently as a heat source for plate heat exchangers with different eco-friendly refrigerants.

- The estimated results at various numbers of plates are in good agreement with data from the literature for both cold and hot streams. Moreover, the effectiveness, pressure drops, and heat transfer coefficients vary smoothly or slightly at different hot stream pressures, cold fluid superheating temperatures, and cold channel mass fluxes.
- The cold stream liquid-phase and gas-phase convection coefficients decrease with the increasing number of plates by 40%, when the number of plates changed from 40 and 50 to 109 for liquid-phase and gas-phase, respectively.
- The cold stream two-phase convection coefficients decrease with the increasing number of plates. This decline in the convection coefficient becomes insignificant for the number of plates higher than 40 and lower by 31% when the number of plates changed from 40 to 109. Moreover, the two-phase convection coefficients were more sensitive to the hot stream inlet pressure than the cold stream superheating temperature difference.
- The CO
_{2}convection coefficients are almost identical regardless of the used cold fluid. Moreover, slight differences were observed with the changing hot-stream pressure. In addition, when the number of plates changed from 40 to 109, the CO_{2}convection dropped by 34%, which is relatively low compared to the variation at a lower number of plates. - The two-phase flow dominates the cold stream pressure drop since it is more turbulent. Moreover, the pressure drop in the two-phase region is influenced mainly by the turbulence (Bond number) and the surface tension forces (Weber number), which are a function of the used fluid type since the Reynolds numbers were identical for the used cold fluids. On the other hand, the CO
_{2}pressure drop has a similar tendency regardless of the used fluid. However, for both streams, an insignificant variation in the pressure drop was observed at a number of plates higher than 40.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 10.**Cold stream liquid-phase and gas-phase convection coefficients at various cold channel mass fluxes.

**Figure 11.**Cold stream two-phase convection coefficient at various cold channel mass fluxes and different superheating temperature differences.

Geometrical Parameter | Value |
---|---|

Effective flow length L | 485 mm |

$\mathrm{Plate}\mathrm{thickness}{\mathrm{t}}_{\mathrm{pl}}$ | 0.6 mm |

$\mathrm{Port}\mathrm{diameter}{\mathrm{D}}_{\mathrm{po}}$ | 55 mm |

$\mathrm{Corrugation}\mathrm{angle}\mathsf{\beta}$ | 60° |

$\mathrm{Plate}\mathrm{Pitch}\mathrm{Pi}$ | 2.8 mm |

Mean Channel Gap b | 2.2 mm |

Plate width W | 245 mm |

$\mathrm{Corrugation}\mathrm{pitch}\mathsf{\lambda}$ | 6.8 mm |

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**MDPI and ACS Style**

Elbarghthi, A.F.A.; Hdaib, M.Y.; Dvořák, V. Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers. *Entropy* **2022**, *24*, 1150.
https://doi.org/10.3390/e24081150

**AMA Style**

Elbarghthi AFA, Hdaib MY, Dvořák V. Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers. *Entropy*. 2022; 24(8):1150.
https://doi.org/10.3390/e24081150

**Chicago/Turabian Style**

Elbarghthi, Anas F. A., Mohammad Yousef Hdaib, and Václav Dvořák. 2022. "Heat Transfer Analysis between R744 and HFOs inside Plate Heat Exchangers" *Entropy* 24, no. 8: 1150.
https://doi.org/10.3390/e24081150