Experimental Performance Analysis of R410A Heat Pump System in Northeastern US Winter Climates

Heat pumps (HP) can be a good alternative to heating and cooling technologies for residential, industrial, and commercial applications. It has been an economical and environmentally friendly way to recover heat from different sources and so it can provide the most impactful solutions to the greenhouse effects and global warming. Over the past three decades, a lot of research has been done to improve the performance and energy efficiency of heat pump systems [1].

In the northeastern US region, e.g., in New York City, gas furnace-based heating systems are used mostly for space heating and hot water applications. Approximately 60% of US homes use natural gas for space and water heating, cooking, and drying clothes [2]. Space heating accounts for 42% of energy consumption in the residential sector [2] and 75% of greenhouse gas (GHG) emissions [3] in the United States. Recently, New York City has passed a law known as local law 97 to decarbonize the city by 80% by 2050 [3]. Among different initiatives, one of the most prominent ones is the electrification of the buildings' heating and cooling systems by replacing the natural gas and oil-based heating systems with HPs. Using HPs can significantly reduce natural gas consumption in the northeastern United States, which will strengthen the decarbonization efforts. However, the usage of hydrofluorocarbon (HFC) based refrigerants in heat pump technology is now a major concern as they have high global warming potential (GWP).

The performance of ASHP degrades significantly as the outdoor temperature becomes extremely low [4–6]. Due to the high discharge pressure and temperature ratio, ASHP usually provides very low heating capacity and efficiency at extremely low outdoor temperatures [4]. Modern ASHP can provide improved performance in cold climates through multistaging or oversized compressors [5]. ASHP faces the degradation of performance due to the frost forming on the surface of the outdoor coil when the surrounding temperature is 19–41 °F and the relative humidity is higher than 65% [6]. The frost stored on the surface decreases the heat transfer rate and the air flowrate which results in an unexpected shutdown of the heat pump [7]. Besides these performance-related challenges, there are some other challenges regarding the environmental impact of the refrigerants used in heat pumps. HFC-based refrigerants usually have high GWP, so alternate refrigerants with low GWPs must be found. However, there are several concerns while searching for low GWP refrigerants such as heating (cooling) capacity, energy efficiency, compressor discharge temperature and pressure, flammability, and toxicity [8].

Bertsch and Groll [5] studied the performance of two-stage air source heat pumps for residential heating and cooling in northern US climates. They compared the performance of single-stage and two-stage air source heat pumps in terms of COP, and heating capacity with outdoor temperature as low as −30 °C and supply temperatures of up to 50 °C in space and water heating modes. An improved heat pump cycle was developed using a scroll compressor economizer and the performances were tested comprehensively [9]. It was found that the improved heat pump cycle could provide a sufficiently high heating capacity, cooling capacity, and COP with a relatively low discharge temperature at very low outdoor temperatures. Safa et al. [10] investigated the performance of two-stage variable capacity air source heat pumps and found that variable speed ASHP provides higher coefficients of performance compared to other available options. Wang et al. [11] proposed a new performance index named “loss coefficient in nominal output heating capacity” of ASHP to provide a comprehensive evaluation of the performance of ASHP with frosting-defrosting operation. Liu et al. [12] analyzed the performance of a multifunctional heat pump system using four different combinations of heat sources such as air source only, water source only, air source–water source in parallel, and air source–water source in series. They found that heat source combinations have a great impact on the heating capacity and COP of the system, and they revealed that the ASHP (air source-only combination) has the lowest COP and heating capacity in all conditions. Safa et al. [13] compared the performance of variable capacity ASHP and horizontal ground loop ground source heat pump (GSHP) based on heating capacity, power consumption, and COP. They found that the heating performance of GSHP is better than that of ASHP in cold climates. Jia et al. [14] studied the performance of ASHP using a gravity-driven radiator as the indoor heating terminal and found that the energy efficiency of the system increased significantly. Dhillon et al. [15] studied the performance of heat pump systems using a load-based testing methodology. They tested a variable speed residential heat pump system at different building loads for heating and cooling seasons and found that the system can match the capacity with the building loads from part-load capacity to full capacity with the help of variable speed operation.

Bilgen and Takahashi [16] performed the exergy analysis of commercial wall-mounted room air conditioners and found that exergy efficiency decreases with the increase of heating load. Sun et al. [17] studied the exergy loss of multifunctional heat pump systems with domestic hot water (DHW) mode and compared the results with the conventional heat pump systems. They compared the exergy efficiency of the system with the variation of DHW supply temperature and found that multifunctional heat pump systems show higher exergy loss during space heating with DHW supply mode compared to conventional heat pump systems. Yildiz and Güngör [18] studied the energy and exergy of heat pumps for space heating of a building based on different building components such as powerplant, storage, and distribution. They compared the energy and exergy efficiencies of liquid natural gas (LNG) condensing boiler, LNG conventional boiler, and ASHP system and found that the ASHP system has the highest energy efficiency, but lowest exergy efficiency compared to those of boiler systems. However, the authors didn’t investigate the exergy loss at different component levels of the heat pump systems. Kabul et al. [19] performed an exergy analysis of the vapor compression refrigeration cycle with R600A as refrigerant using matlab software and found that the condenser & evaporator temperatures have significant effects on energetic and exergetic performances of heat pump systems. Shilliday et al. [20] performed exergy and energy analysis of R744, R290, and R404A refrigerants using simulation software and found that R744 has the lowest COPs in cold climates compared to those of R290 and R404A. The authors also reported that the compressor has the highest exergy loss in the R290 and R404A systems while the expansion valve and gas cooler can be the worst components in the R744 system in terms of exergy losses. Yumrutaş et al. [21] developed a computational model to investigate the effects of evaporating and condensing temperature on exergy loss and second law efficiency of a vapor compression refrigeration cycle. The authors found that evaporating and condensing temperatures strongly influence the exergy losses in both the evaporator and condenser, as well as the COP and the second law efficiency of the cycle. However, the exergy losses in the compressor and expansion valve are barely influenced by evaporating and condensing temperatures.

Under local law 97 of New York City, all the natural gas and fossil-fuel-based heating systems will be replaced by heat pumps where ASHP can play a vital role due to easy installation and cost efficiency. In this study, the performance of the ASHP system has been tested under extreme winter conditions in New York City. Outdoor winter conditions similar to January 2022 in New York City have been simulated inside the laboratory to test a commercially available 1.5-ton ASHP system. Figure 1 shows the temperature variations in New York City during the month of January 2022. The temperature data were collected from the New York City weather history file located at LaGuardia Airport station [22]. From the literature survey, it has been found that no research has been done on the experimental performance analysis of ASHP using R410A as a refrigerant. Most of the previous research on exergy analysis is focused on the ground source and solar-assisted heat pump systems whereas comprehensive exergy analysis of air source heat pump systems has not been done yet, specifically with R410A refrigerant. Moreover, most of the exergy analysis of heat pump systems has been done by simulation software and no experimental energy and exergy analyses have been noted yet in the literature on the ASHP system with R410A refrigerant. So, in this study, a comprehensive performance analysis of the ASHP system with R410A refrigerant has been done using extensive experimental data analysis. First and second law analysis have been performed and an exergy analysis has been done at different component levels of the heat pump system. The performance analysis of this ASHP system has been done based on the outdoor winter conditions of New York City in January 2022 to verify the feasibility of deploying ASHP systems in Northeastern US winter climates. A Blackbox model of the heat pump has also been developed using manufacturer-provided data and the model has been compared with the experimental performance of the heat pump.

A dedicated laboratory setup was built to test the performance of ASHP inside the laboratory. Temperature and humidity inside the laboratory were controlled with precision to ensure the high accuracy of testing data. The testing room contains an outdoor environment simulator, a heat pump indoor and outdoor unit, a window AC unit, and a dehumidifier. It is a 25 ft. × 23 ft. concrete room located in the basement of a seven-story building. The temperature and humidity inside the laboratory were controlled using the window AC unit and dehumidifier to provide a steady-state indoor environment for all the tests.

An outdoor environment simulator was built inside the laboratory to simulate the extreme winter environment similar to New York City in January 2022. The simulator is a hydronic loop that is built using copper tubes, a refrigerator, an in-line centrifugal pump, and two fin-tube heat exchangers. One end of the hydronic loop is connected to a fin-tube heat exchanger which is located inside a refrigerator and the other end is connected to another fin-tube heat exchanger which is attached parallel to the outdoor unit of a heat pump. The hydronic loop runs through the refrigerator–heat exchanger system to another heat exchanger–heat pump outdoor unit system and carries cold water from the refrigerator to the heat exchanger to provide a cold environment for the heat pump outdoor unit. A centrifugal pump was used to drive the cold water through the circulation loop. Since the refrigerator–heat exchanger system cools down the water flowing through the hydronic loop to generate extreme outdoor conditions for the heat pump outdoor unit, the hydronic loop requires it to function below the freezing point temperature of water which is a challenging task. To avoid the freezing of water and subsequent hazards, glycol was mixed with water and the resultant mixture was able to provide the lowest temperature around 16 °F which was good enough to test the ASHP system. The fin-tube heat exchanger–heat pump outdoor unit system was put inside an insulated box to control the temperature inside the box by preventing heat transfer to the surrounding air. The temperature inside the insulated box represents the simulated outdoor temperature of winter climates. A dehumidifier was placed inside the box to control the humidity. During the testing of a heat pump in heating mode, a window AC unit was used to dump the generated heat out of the laboratory to keep a nearly constant indoor temperature inside the laboratory for all the tests. A single zone high-efficiency wall mount heat pump and different sensors such as thermocouples, pressure transducers, flowmeter, anemometer, hygrometer, and power meter were installed to perform testing and measure the necessary testing parameters. Heat pump and sensor specifications are given in Tables 1 and 2 respectively.

NI LabVIEW 2021 software was used along with the Daxus DXS-100 data acquisition module to build the data logging and monitoring system. This data acquisition system was able to monitor the system and record the real-time data of the system’s performance. A simple schematic of the experimental setup and the actual experimental setup has been shown in Figs. 2 and 3.

Temperature, pressure, refrigerant mass flowrate, and input power were measured to calculate the heat pump performance indexes such as heating capacity, coefficient of performance, second law efficiency, compressor efficiency, exergy analysis, and energy efficiency ratio. All those performance characteristics were calculated using the following equations extracted from the literature [23–25]. The procedure to estimate the enthalpy at the evaporator exit has been shown in the  Appendix.

The working principle of the ASHP system is based on the vapor compression refrigeration cycle; therefore, a basic schematic diagram and T-S diagram of the vapor compression refrigeration cycle have been shown in Figs. 4 and 5. Exergy losses at four different components of the ASHP such as compressor, condenser, expansion valve, and evaporator have been calculated to determine the total exergy destruction of the system at different outdoor temperatures. The following equations extracted from the literature have been used to perform the exergy analysis of different components of the ASHP system [23–25]. Figures 4 and 5 have been used to identify different states in these equations. Numerical subscripts have been used to indicate the thermodynamic properties at different states.

Compressor exergy analysis:

Condenser exergy analysis:

Expansion valve exergy analysis:

Evaporator exergy analysis:

Total exergy analysis:

All the experiments were performed at nearly constant room temperature and relative humidity. All the tests were performed at steady-state conditions and each result represented in this study comes from an average of at least 10 min of steady-state operation. The indoor relative humidity and room temperature were controlled to the extent possible with 40% and 63 °F for all the tests. Testing and Data Analysis were performed complying with ASHRAE Standard 206-2013, “Method of Testing for Rating of Multipurpose Heat Pumps for Residential Space Conditioning and Water Heating.”

The variation of heating capacity, power input, COP, compressor efficiency, and energy efficiency ratio were measured at different outdoor temperatures ranging from 16 °F to 50 °F based on Fig. 1. Table 3 represents the results of the heat pump performance testing at different outdoor temperatures.

From Fig. 6(a), we can see that heating capacity decreases with the increase of outdoor temperature for variable capacity ASHP. Similar results have been found in the literature [10]. During lower outdoor temperatures the compressor reaches its maximum capacity and consumes much larger power compared to that of higher temperatures. Since the pump has a variable speed compressor, it adjusts the compressor speed based on the outdoor temperature and the indoor heating output requirements. The indoor temperature and humidity were maintained to be nearly constant for all the tests, so the only variable was the outdoor temperature which regulates the part-load capacity of the heat pump. Moreover, discharge pressure decreases with the increase of outdoor temperature which decreases the refrigerant flowrate. As a result, heating capacity drops with an increase in outdoor temperature. The heating demand of the conditioning space decreases with the increase of outdoor temperature which may also push the variable speed heat pump system to produce the lower heating output [10]. The heat pump that has been used in this study has a maximum heating capacity of 22,340 Btu/h (according to manufacturer's data) at an indoor temperature of 70 °F and outdoor temperature of 17 °F. In our experiment, we found the maximum heating capacity of 21,296 Btu/h at an indoor temperature of 63.17 °F DBT and an outdoor temperature of 16 °F DBT. So, the experimental performance of the heat pump is consistent with the manufacturer's data.

Figure 6(b) shows that the power consumption of ASHP decreases with the increase of outdoor temperature. Similar results have been found in the literature [10]. As the outdoor temperature goes up, the compressor turns to run at part-load conditions with comparatively lower speeds which decreases the input power requirements. Moreover, refrigerant evaporating temperature in the outdoor unit increases with the increase in outdoor temperature which causes the refrigerant to absorb more heat from the outdoor environment and release it to the indoor environment. As a result, the compressor consumes less power to meet the heating demand inside the conditioning space. It was found that power consumption decreases by almost 72% when the outdoor temperature increases from 16 °F to 50 °F. The decrease in power consumption has a significant impact on the exergy efficiency of the system which has been discussed later in this study. Moreover, the decreasing input power to the compressor significantly decreases the discharge pressure and temperature of the compressor which influences the heating capacity, coefficient of performance, and the overall performance of the system.

Figures 7(a) and 7(b) show that the COP and Energy Efficiency Ratio (EER) increase with the increase in outdoor temperature. The increasing outdoor temperature increases the evaporator temperature but decreases the condenser temperature which enables the system to absorb more heat from the outside environment and provide the necessary heating output to conditioning space with the utilization of much lower input power to the compressor. As a result, the COP increases along with a higher EER. The COP is calculated using an energy balance approach which is basically the first law of thermodynamics. COP merely gives insight into the performance of a heat pump system because it does not count the exergy loss in the system. The second law of thermodynamics deals with the exergy of the system which identifies the scope of improvement of efficiency of the thermal system in terms of thermodynamic perspectives. In this study, it was found that the COP varies between 2.53 and 3.81 and EER varies between 8.64 and 13.01 with the change of the outdoor temperature between 16 °F and 50 °F. According to the manufacturer-provided data, the rated EER of this heat pump is 12.58, so the experimental EER is very consistent with the manufacturer's data.

From Fig. 8, we can see that the isentropic efficiency of the compressor tends to increase with the increase in outdoor temperature. The lowest compressor efficiency was found to be 69.2% corresponding to the outdoor temperature at 16 °F while the highest compressor efficiency was 90.6% at the outdoor temperature of 50 °F. With the increase in outdoor temperature, the isentropic efficiency of a variable speed compressor tends to increase. With the increase of outdoor temperatures, the loss to the surroundings decreases resulting in less difference between isentropic and actual compressor work. As a result, the isentropic efficiency increases with the increase of outdoor temperature.

The second law of thermodynamics emphasizes the quality of energy and the degradation of the quality of energy during a thermodynamic process or a cycle. The second law analysis includes the irreversibility of a thermodynamic process and the loss of exergy (available energy) throughout the process. So, the second law analysis identifies the room for improvement of the efficiency of a thermodynamic process or component. Table 4 shows the experimental performance data from the second law analysis of the ASHP system.

From Fig. 9, we can see that the condenser temperature decreases with the increase in outdoor temperature. Since the compressor provides lower discharge pressure and temperatures at higher outdoor temperatures, these result in lower condenser temperatures as well. Condenser temperature along with the room temperature is important parameter for the second law efficiency of the system. When condenser temperature decreases, the COP of the reversible cycle decreases which results in an increase in second law efficiency as we can see in Fig. 10(a). So, the higher outdoor temperature decreases the condenser temperature which reduces the irreversibility of the system thus resulting in a higher second law efficiency as shown in Fig. 10(b). There are several factors that influence the second law efficiency of any system such as component temperature, surrounding temperature, refrigerant properties, and system structure.

Exergy loss at different component levels of R410A ASHP has been shown in Fig. 11. The maximum exergy loss occurs in the compressor followed by the condenser, expansion valve, and evaporator. So, the compressor has the highest irreversibility compared to the other components. Similar results have been found in the literature using other refrigerants [19,23]. The condenser releases heat to the indoor environment, while the evaporator absorbs heat from the outdoor environment. So, the evaporator is actually gaining exergy which makes the exergy losses for the evaporator negative in Table 4. Exergy loss or irreversibility basically depends on the difference between the surface temperature of any component and the surrounding temperature. The higher the temperature difference the higher the exergy loss and irreversibility. Moreover, condensing and evaporating temperature regulates the exergy loss and irreversibility of condenser and evaporator which ultimately influences the total exergy loss of the system [19]. Figure 11 also shows that exergy loss is higher in the condenser compared to that in the evaporator. This can be explained by the temperature difference with surroundings being higher in the condenser compared to that in the evaporator, so heat transfer in the condenser occurs at a much larger temperature difference compared to that in the evaporator. Since heat transfer is higher in the condenser compared to that of the evaporator, exergy loss is also higher in the condenser compared to that in the evaporator.

Figures 12(a) and 12(b) show the variation of exergy loss of R410A ASHP with the change of condenser and evaporator temperature, respectively. It was found that total exergy destruction of the system increases with the increase in condenser temperature, but it tends to decrease with the increase in evaporator temperature. Similar results have been found in the literature for other refrigerants [23]. This happens because the increasing condenser temperature increases the temperature difference between the refrigerant in the condenser and the ambience which results in a higher heat transfer rate from the refrigerant to the ambience and hence increases the exergy loss of the condenser. On the other hand, increasing the evaporator temperature results in a lower temperature difference between the refrigerant inside the evaporator and the ambience which lowers the heat transfer rate from ambient to the refrigerant and eventually lowers the exergy loss of the evaporator.

Figure 13(a) shows the variation of compressor exergy loss with the change in outdoor temperature. Exergy loss and the irreversibility of the compressor decrease with the increase in outdoor temperature. Input power to the compressor decreases significantly with the increase in outdoor temperature and the entropy generation also decreases due to the decrease in temperature difference. As a result, the exergy loss decreases across the compressor with the increasing outdoor temperature. Since the compressor is responsible for most of the exergy loss in the system, it is easily understandable from Fig. 13(b) that the total exergy loss of the system will also decrease with the increase in outdoor temperature.

A Blackbox model for the COP of the air source heat pump system was developed using the performance data provided by the manufacturer and the model was compared with experimental COPs. In the Blackbox model, four different compressor efficiencies such as 50%, 64%, 70%, and 90% were assumed to compute COPs. For each level of compressor efficiency, COPs were calculated at different outdoor temperatures such as 20 °F, 25 °F, 32 °F, 41 °F, 47 °F, and 53 °F. The outdoor temperature levels were selected based on the data available from the manufacturer. It was assumed that refrigerant pressure remains constant at the inlet and outlet of the condenser for each level of compressor efficiency. It was also assumed that the condenser outlet temperature remains constant at all levels of compressor efficiency for all the outdoor temperatures. The flowchart in Fig. 14 shows the algorithm that has been used to run the Blackbox model.

Here, $Q˙$ represents the heat transfer rate, ε is the effectiveness, $V˙$ is the volumetric flowrate of air, ρ and C_p are the density and specific heat of air, P is the pressure, s is the entropy, and $W˙c$ is the power consumption rate to the compressor. Numerical subscripts have been used to indicate the thermodynamic properties at different states as illustrated in Figs. 4 and 5.

The Blackbox model was plotted in Fig. 15 along with the experimental data to compare with it. The uncertainty analysis of the experimental COPs was performed, and the detailed procedure has been shown in the  Appendix. From the figure it was found that the Blackbox model could estimate the range of COPs at different outdoor temperatures and the experimental COPs were closer to the lower limits of the Blackbox model. From experimental data analysis, it was found that the compressor works at different efficiency levels at different outdoor temperatures to provide the necessary heating output based on the heating loads. The machine provides lower COP at higher compressor efficiency at lower outdoor temperatures compared to those of the Blackbox model. So, the rate of change of COP with outdoor temperature is lower in variable compressor efficiency than that of constant compressor efficiency.

During the experiments, pressure does not remain constant at the condenser inlet and outlet at different outdoor temperatures and the condenser outlet temperature does not remain constant as well. As a result, the experimental COPs differ from those of the Blackbox model. However, the Blackbox model gives us a good estimate of the performance of the heat pump by providing a range of COPs at different outdoor temperatures, and we can see from Fig. 16 that the experimental COPs are always within that range at each outdoor temperature, and they do not go beyond those limits.

A comprehensive experimental performance of the ASHP system using R410A refrigerant has been studied in this article. Some concluding remarks of this study can be summarized as follows:

1. With the increase in outdoor temperature, the Heating capacity decreases while COP increases for variable capacity ASHP system, and the power consumption decreases. COP increases from 2.53 to 3.81 when the outdoor temperature increases from 16 °F to 50 °F.

2. The isentropic efficiency of the compressor decreases slowly with the increase of outdoor temperature. Isentropic efficiency varies between 90.6% and 69.2% with the outdoor temperature variation between 50 °F and 16 °F.

3. The second law efficiency of the ASHP system increases significantly with the increase of outdoor temperature. This happens due to the decrease in condenser temperature with higher outdoor temperature. The second law efficiency varied between 25.64% and 81.10%.

4. The compressor has the highest exergy loss among all the components of the ASHP system while the evaporator has the lowest exergy loss. Total exergy loss of the system increases with the increase of condenser temperature but decreases with the increase in evaporator temperature. Compressor exergy loss decreases with the increase in outdoor temperature.

5. Condenser and evaporator temperatures have significant effects on the performance of the ASHP system.

6. The experimental COPs are consistent with the estimated COPs in the Blackbox model.

From this study, it can be concluded that the air source heat pump systems can be an alternative to the natural gas-based heating system in residential buildings in New York City. Performance optimization of the ASHP system depends on the structural optimization of the heat exchangers such as condenser and evaporator and on the optimization of the operation strategy of the system under different outdoor conditions in cold climates [26]. Thus, future studies of this research will be aimed to extend the work to develop optimal control strategies for cold climate conditions for multifamily ASHPs and to the design, development, and performance optimization of ASHP systems using low GWP refrigerant such as $CO2$ (R744). This new $CO2$ system will be a high-pressure system working in transcritical states on dual modes for both heating and cooling for typical Northeastern US climate conditions.

The authors would like to acknowledge the U.S. Department of Energy for sponsoring the project under grant no. W911SR-14-2-0001 RPP-2008. Partial funding for the effort was also provided by the US National Science Foundation under the Industry-University Cooperative Research Center Program Grant No. EEC 2113874.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$h$ =

Enthalpy at any state

$s$ =

Entropy at any state

$h1,r$ =

Refrigerant enthalpy at compressor inlet

$h2,r$ =

Refrigerant enthalpy at compressor outlet

$h2s$ =

Isentropic enthalpy at the compressor outlet

$h3,r$ =

Refrigerant enthalpy at the condenser outlet

$h4,r$ =

Refrigerant enthalpy at evaporator inlet

$Itotal$ =

Total exergy loss or irreversibility

$Icomp$ =

Compressor exergy loss or irreversibility

$Icond$ =

Condenser exergy loss or irreversibility

$Ievap$ =

Evaporator exergy loss or irreversibility

$Iexp$ =

Expansion valve exergy loss/irreversibility

$Qh$ =

Heating capacity

$T0$ =

Ambient temperature of any component

$Tc$ =

Condenser temperature

$Te$ =

Evaporator temperature

$Toutdoor$ =

Outdoor temperature

$Troom$ =

Room temperature

$Wc,in$ =

Compressor power input

$m˙r$ =

Refrigerant flowrate

COP =

Coefficient of performance

$COPrev$ =

COP for reversible cycle

DBT =

Dry bulb temperature

EER =

Energy efficiency ratio

$ηcomp,isen$ =

Compressor isentropic efficiency

$ηII$ =

Second law efficiency

$ψ$ =

Specific exergy in any state

For a measured variable x, the range over which the possible values of mean value might be at some probability level P is estimated by Eq. (A1) based on the sample data. A general variable R is defined by Eq. (A2) and the error propagation through R is calculated using Eq. (A4) where the best estimate of the mean value $R′$ is defined by Eq. (A3). The sample mean and uncertainty of R are defined by Eqs. (A5) and (A6), respectively. $aR$ reflects the individual contributions of the individual uncertainties as they are propagated through the result and $θi$ is the sensitivity index which indicates the change of each independent variable on R.

$h2$ is the enthalpy at the compressor exit, $Wc$ is the power consumption of the compressor, and $mr$ is the refrigerant mass flowrate. Table 5 provides the enthalpy $h1$ at different outdoor temperatures.