Experimental investigation of a vapor compression system with condenser air pre-cooling by condensate

Applied Thermal Engineering 110 (2017) 1255–1263

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Research Paper

Experimental investigation of a vapor compression system with condenser air pre-cooling by condensate Nasiru I. Ibrahim a,⇑, Abdulghani A. Al-Farayedhi b, P. Gandhidasan b a b

Center of Research Excellence in Renewable Energy (CORE-RE), Research Institute, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia Mechanical Engineering Department, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia

h i g h l i g h t s
Reasonable amount of condensate is captured from a vapor compression system.
Use of condensate for condenser air pre-cooling.
Performance of vapor compression system is improved by condenser air pre-cooling.
Electrical energy consumption of the system is reduced by condenser air pre-cooling.
The pre-cooling can be applied during peak period of high ambient temperatures.

a r t i c l e

i n f o

Article history: Received 14 June 2016 Revised 4 September 2016 Accepted 9 September 2016 Available online 10 September 2016 Keywords: Air conditioning system Experimental investigation Hot and humid climates Condensate Air pre-cooler

a b s t r a c t Air conditioning systems contribute to the largest share of energy consumption in building sector. On the other hand, the systems produce reasonable amount of condensate, especially when operating in humid climates. The aim of this study is to minimize the energy consumption and improve the performance of air conditioning systems utilizing condensate. Experimental investigation has been carried out to improve the performance of an air-cooled vapor compression system by pre-cooling air entering the condenser using condensate. A pre-cooler is incorporated on a 1.5 ton-cooling capacity split-type air conditioning system to lower the air temperature entering the condenser sensibly. Performances of the air conditioning system with and without air pre-cooling are compared and reported in this paper. The results show that pre-cooling the air by about 4 °C before entering the condenser lowers the compressor discharge pressure. The decrease in the discharge pressure resulted in the decrease in compressor power consumption by 6.1% and the cooling effect of the system is enhanced. The combined effect of the increase in the cooling effect and decrease in compressor power resulted in an increase in the coefficient of performance (COP) and second law efficiency of the system by about 21.4 and 20.5%, respectively. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Population growth and industrialization across the globe resulted in higher demand of air conditioning systems in buildings and consequently energy consumption especially in hot and humid regions. For example, air conditioning systems consume about 52% of the total electric energy in the Kingdom of Saudi Arabia (KSA) where summer seasons are normally hot and humid [1]. Recent findings indicate that about 60% of energy consumed in residential

Abbreviations: ARI, Air Conditioning and Refrigeration Institute; ACM, accumulator; BP, by-pass line; COP, coefficient of performance; Ex. V, expansion valve; FC, flow calibration line; RV, reversing valve; TXV, thermal expansion valve. ⇑ Corresponding author. E-mail address: [email protected] (N.I. Ibrahim). http://dx.doi.org/10.1016/j.applthermaleng.2016.09.042 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

sector is attributed to air conditioning in KSA [2]. Majority of air conditioning systems used in residential, commercial and industrial buildings are direct-expansion (DX) vapor compression type. Energy consumption by DX systems is the major challenge in air conditioning industry. Typical application of the DX vapor compression air conditioning system is the removal of heat from the interior of a building to the outside. This is governed by heat exchangers generally known as evaporators and condensers. Most of the DX vapor compression air conditioning systems operate with air-cooled condensers. Under extreme climate conditions, the systems suffered the problem of over-heating and hence, degradation in performance. This eventually leads to increase in the pressure ratio across the compressor, thereby increasing the power consumption. Yau and Pean [3] studied the impact of weather variation on performance of a split-type air conditioning system and

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Nomenclature Cp h _ m P Q_ T _ W

specific heat capacity of dry air (kJ/kg K) specific enthalpy (kJ/kg) mass flow rate (kg/s) pressure (kPa) rate of heat transfer (kW) temperature (°C or K) rate of work (kW)

Greek symbols ; relative humidity g efficiency d uncertainty value

revealed that for every 1 °C increment in outdoor dry bulb temperature, there is about 2% reduction in both COP and total cooling capacity of the system. One of the methods of saving energy and performance improvement of DX vapor compression systems that received considerable attention by many researchers is pre-cooling air before entering condensers using evaporative coolers. Hajidavalloo [4] indicated in their experimental study that the power consumption of a window-type air conditioning system operated in hot weather conditions was reduced by 16% using evaporative cooler to precool the air stream prior to entering the condenser and the COP is improved by about 55%. Similar study involving the use of evaporative cooler to lower the air temperature of a condensing unit of split-type air conditioning system has been carried out [5]. They reported that the power consumption was reduced by up to 20% and the coefficient of performance was improved by about 50%. Delfani et al. [6] reported that the use of indirect evaporative cooler to pre-cool air entering the condenser of a conventional packaged air conditioner reduces the electrical energy consumption by 55%. Waly et al. [7] considered the following three methods of pre-cooling the condenser air: (a) the cooling pads (CP) setup, (b) the cooling mesh (CM) setup and (c) the shading setup for three split-type air-conditioning units of equal capacity during the peak summer period in Kuwait. The results showed significant drop in power consumption ranging from 8.1 to 20.5% and increase in cooling capacity by 6.4–7.8% using the CP and CM setups respectively, which in turn, resulted in an increase in the COP of the units by 36– 59%. Britto and Vasanthanathan [8] presented the results of experimental investigation on a window-type air conditioning system using evaporative cooling to pre-cool the air entering the condenser. They reported that the power consumption was decreased by about 8% while the COP increased by 14.3%. Tissot et al. [9] employed water spray evaporation upstream of condenser of a heat pump operated in cooling mode and investigated the performance improvement of the system. The results show that spray of water increases the COP of the system by 28.9% for relatively hot and dry weather conditions (relative humidity 19.7% and temperature 35 °C). Three strategies that include liquid pressure amplification (LPA), evaporative-cooled condenser (ECC) and combined LPA and ECC were applied to reduce energy consumption of air–cooled vapor compression air conditioning systems [10]. They investigated applicability, limitation and energy performance of the strategies and the results showed average energy savings of 25.3%, 18.3% and 44.2%, respectively for LPA, ECC and combined the LPA and ECC methods. Martínez et al. [11] optimized a cooling pad thickness in an evaporative cooling assisted split air-conditioner maximum COP. Condenser air pre-cooling by water mist is another means of enhancing the performance of air-cooled systems. Yang et al. [12]

Subscripts a air c condenser com compressor e exit ev evaporator g water vapor H high i inlet II second max maximum pc pre-cooler sat saturated

reported an analytical and experimental study to improve the performance of air-cooled chiller using water mist to pre-cool the air entering the condenser and the results show an increase in the COP by up to 18.6%. Application of water mist system upstream of the condenser of an air-cooled chiller with twin refrigeration circuits has been carried out numerically and experimentally [13]. The results indicate significant improvement in COP by 21.3%. It is known fact that water vapor condenses on the surface of evaporators in air conditioning systems. This occurs when the evaporator coil surface temperature is lower than the dew point temperature of the air. If the condensed water is not properly handled, it can cause leaks into the buildings and wets the ground surface leading to pathogens of different kinds. Various studies in the literature utilized condensate from air conditioning systems for domestic and irrigation purposes [14–20]. Condensate discharge from air conditioning systems can be utilized to improve the systems performance. There is limited number of studies on the use of condensate to improve the performance of air-cooled vapor compression systems. One of the related studies is the work of Sawan et al. [21], where they used condensate to precool air by evaporative cooler before entering the condenser of split-type air conditioner. The results show that the condensate would be sufficient for air pre-cooling during the month of October, resulting in 5.3% energy saving. The condensate lasted for six operating hours in a particular day in June and eight hours in August for typical weather conditions of Beirut. This resulted in a total daily reduction of consumed energy by 5% in June and 4.5% in August. A similar study was conducted to improve the performance of a window-type air conditioning system by evaporative coolingassisted cycle using condensate produced from the system [22]. Based on the above literature study, it is clear that the authors [21,22] focused on evaporative cooling using condensate to precool the air entering the condenser. In the present study, the authors considers dry cooling technique for air pre-cooling before entering the condenser of a vapor compression air conditioning system using condensate. The reason of using dry cooling instead of evaporative cooling is to avoid condensate loss while cooling the air, which is unavoidable in the case of evaporative cooling. Experimental study is carried out using a cross-flow fin-tube heat exchanger to pre-cool the air entering the condenser by condensate and the results are presented in this paper.

2. Experimental set-up The experimental set-up consists of a base air conditioning system, climate chamber, insulated condensate storage tank and air pre-cooler as shown in Fig. 1. The base air conditioning system is a 1.5 ton-capacity split-type air conditioner with technical

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Fig. 1. Schematic of the experimental set-up.

specifications given in Table 1. The basic components of the conventional vapor compression system are shown in Fig. 2. The climate chamber is used to simultaneously generate and control the air temperature and relative humidity before entering the evaporator. It consists of a water pump, an air blower, air heater, water heater, and humidifying pads. The air heater is located at the inlet of the climate chamber to control the desired air temperature. Three humidifying pads, each of 10 cm thickness are fixed after the heater. A 100-L humidifier water tank is connected to a pump which sprays the water on the pads. The desired humidity of the air is obtained by regulating the flow rate of the water. In order to compensate for the decrease of air temperature due to water spray, a water heater is installed inside the water tank to warm up the water. The air and water heaters are connected to separate temperature controllers. The temperature controllers are digital-switch setting type, model: T4L-B3RK4C. Condensate dripping from the evaporator is collected into the storage tank before the commence-

Table 1 Specifications of the base air conditioning system. Parameter

Value

Cooling capacity at 27 °C DB/19 °C WB and 35 °C DB outdoor Power input Current input Energy efficiency rating (EER) R-22 charge Compressor type – Rotary Expansion device – TXV Evaporator face area Volume flow rate of air at evaporator side Condenser face area Volume flow rate of air at condenser side

4.747 kW 2.075 kW 9.7 A 7.81 1.3 kg – – 0.259 m2 0.135 m3/s 0.548 m2 0.73 m3/s

ment of the experiment. The storage tank is connected to a pump which circulates the condensate through the pre-cooler. The pre-cooler is a finned-tube cross flow heat exchanger consisting of copper tube and aluminum fins, shown in Fig. 3. The two ends of the pre-cooler tube are connected to the pipe where condensate is circulating. Air and condensate temperatures at the inlet and exit of the pre-cooler are measured using thermocouples as also shown in Fig. 4. Positions of the thermocouple are indicated in the figure by five square dots between the condenser and the pre-cooler and other five at the opposite side of the pre-cooler. 3. Methodology Experiments are conducted in Dhahran, Saudi Arabia during high ambient temperatures (40–46 °C). Condensate was collected from the air conditioning system and stored in the insulated storage tank before the start of the experiment. The first experiment is conducted without operating the pre-cooler (baseline) while the second with the pre-cooler under the same conditions for comparison. The experimental conditions, which are based on ARI standard rating conditions for a forced-circulation air cooling coil [23] are given in Table 2. Experimental data are recorded at every minute interval. Temperatures of air, refrigerant and that of the condensate circulating through the pre-cooler are measured using type-T thermocouples at points i, e, 1–4 in Fig. 2 and various locations shown in Figs. 3 or 4. Air velocity across the front face of evaporator is measured using a hydro-thermo anemometer of accuracy ±2%. Mass flow rate of air is obtained from the measured velocity. The refrigerant suction and discharge pressures are measured using pressure transducers PX309 series, Omega each of accuracy 0.25%. The compressor power consumption is measured by the use of current transmitter; model number PM – H721LC with accuracy ±2%.

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Air out

3 Condenser

2

Expansion valve

4

Air in

i

Fan

Evaporator

Ambient air in

Ambient air in

1

Compressor

Fan Conditioned air out

e

Condensate tray

Fig. 2. Basic components of conventional vapor compression system.

Fig. 3. Photograph of the condenser and pre-cooler during the construction of experimental rig.

Relative humidity of the air is measured using relative humidity transmitters capable of measuring from 3 to 95%. The accuracy of the humidity transmitter is ±2.5% for the range of 20–80% relative humidity and ±3.1% below 20% and above 80% relative humidity.

The mass flow rate of condensate circulating through the precooler is measured using special type flow transmitters of accuracy ±2% full scale. The transmitter displays the measured flow rate digitally and transmits the flow signal to a computer. All the sensors

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Fig. 4. 3-D sketch of condenser-pre-cooler arrangement showing positions of the thermocouples.

Table 2 Experimental conditions.

Table 4 Uncertainty values of experimental results for system with pre-cooler.

Parameter

Values

System with pre-cooler

Evaporator entering air temperature Evaporator entering air relative humidity Volumetric flow rate of air at the evaporator Ambient air temperature Initial condensate temperature at the pre-cooler inlet Mass flow rate of condensate through the pre-cooler Volume of condensate in the tank at the beginning of air pre-cooling

27–29 °C 40–43% 0.135 m3/s 40–46 °C 25 °C 0.18 kg/s 0.9 m3

Description

are connected to a data acquisition (DAQ) system from National Instruments (model PXle -1062Q), which records the various measurements in a data file. 3.1. Uncertainty analysis The temperatures, pressures, relative humidity, compressor current and flow rate of air are measured using the aforementioned instruments with their respective sensitivities. Uncertainties of

Average value

Total uncertainty value

Total uncertainty (%)

Measured parameters Evaporator inlet air temperature, °C Evaporator exit air temperature, °C Evaporator inlet air relative humidity Evaporator exit air relative humidity Pre-cooler inlet air temperature, °C Pre-cooler exit air temperature, °C Suction temperature, °C Discharge temperature, °C Compressor electric current, A Suction pressure, kPa Discharge pressure, kPa Air velocity, m/s

27.4 9.40 0.40 0.93 42.8 38.6 2.90 65.8 9.10 321 1779 1.91

±0.23 ±0.22 ±0.012 ±0.024 ±0.27 ±0.34 ±0.23 ±0.34 ±0.20 ±2.14 ±10.6 ±0.11

±0.84 ±2.34 ±3.00 ±2.58 ±0.63 ±0.88 ±7.93 ±0.52 ±2.19 ±0.67 ±0.59 ±5.76

Calculated parameters Cooling effect, kW Compressor power, kW Coefficient of performance COP Second law efficiency

4.07 2.00 2.04 0.18

±0.26 ±0.04 ±0.13 ±0.013

±6.39 ±2.00 ±6.37 ±7.22

Table 3 Uncertainty values of experimental results for base system. Base system Average value

Total uncertainty value

Total uncertainty (%)

Measured parameters Evaporator inlet air temperature, °C Evaporator exit air temperature, °C Evaporator inlet air relative humidity Evaporator exit air relative humidity Condenser inlet air temperature, °C Compressor electric current, A Suction pressure, kPa Discharge pressure, kPa Suction temperature, °C Discharge temperature, °C Air velocity, m/s

28.70 9.40 0.32 0.92 43.1 9.70 328.7 1979.9 2.90 70.6 1.91

±0.22 ±0.22 ±0.01 ±0.024 ±0.27 ±0.204 ±2.23 ±7.18 ±0.23 ±0.27 ±0.11

±0.77 ±2.34 ±3.13 ±2.61 ±0.62 ±2.10 ±0.68 ±0.36 ±7.93 ±0.38 ±5.76

Calculated parameters Cooling effect, kW Compressor power, kW Coefficient of performance, COP Second law efficiency

3.57 2.13 1.68 0.15

±0.25 ±0.045 ±0.12 ±0.011

±7.00 ±2.11 ±7.14 ±7.33

Description

calculated parameters such as cooling effect, COP, and second law efficiency are determined on the basis of the uncertainties in the measured parameters following the procedure given in [24]. The uncertainty values of the experimental data for the base system and the system with pre-cooler are calculated using the above procedure with details given in Appendix A and are summarized in Tables 3 and 4, respectively.

4. Analysis of the experimental data The following assumptions are made for the analysis of the experimental data:
Pressure drop across the condenser and evaporator are neglected which are usually about 7% and 5% [5].
Saturated states at the evaporator and condenser outlets are assumed.
Heat gains and heat losses on the refrigerant lines are neglected.

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The cooling effect of the air conditioning system is calculated using the measured parameters on the air side of the evaporator as:

_ a;ev ðha;ev ;i  ha;ev ;e Þ Q_ ev ¼ m

ð1Þ

where the enthalpies of the air are obtained from the measured drybulb temperature and relative humidity at the inlet and exit points _ a;ev is calculated from the of the evaporator. The mass flow rate m measured air velocity across the evaporator taking the density of air as a function of the inlet temperature and relative humidity of the air. The first law performance of refrigeration cycle is defined as the COP and is expressed as the cooling effect produced per unit work input.

_ com COP ¼ Q_ ev =W

ð2Þ

The second law efficiency of the system is defined as:

gII ¼

COP COPmax

ð3Þ

where

COP max ¼

TL TH  TL

ð4Þ

and T L is the low temperature taken as the mean air temperature during heat exchange through the evaporator, defined as [25]:

TL ¼

T a;ev ;i  T a;ev ;e lnðT a;ev ;i =T a;ev ;e Þ

Table 5 Hourly rate of condensate yield of a typical day in August, Dhahran climate. Time (h)

Temperature (°C)

Humidity (%)

Condensate (kg/h)

1:00 AM 2:00 AM 3:00 AM 4:00 AM 5:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 AM 11:00 AM Noon 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 7:00 PM 8:00 PM 9:00 PM 10:00 PM 11:00 PM 12:00 AM

35 34 34 33 32 31 31 33 35 36 38 39 39 40 41 39 38 37 35 34 34 34 33 33

59 59 59 63 66 70 70 66 63 63 56 50 50 45 26 37 37 56 71 75 75 75 79 80

3.5 3.5 3.5 2.8 3.2 3.2 3.2 3.2 3.5 3.5 3.7 3.3 3.3 3.3 1.5 2.4 2.4 3.5 4.2 5.1 5.1 5.1 3.9 3.9

Yield (kg/day)

83.7

ð5Þ

The ambient air temperature, which is the temperature of the air entering the condenser, T a;c;i is considered as the high temperature T H for base system analysis while air temperature at the exit of the pre-cooler, T a;pc;e is considered as T H for the system with air precooling. A code is written in Engineering Equation Solver (EES) [26] to determine the properties of the fluids (air, water and R-22) such as enthalpy from the experimental data and performance parameters such as COP and second law efficiency.

Air/condensate temperature (oC)

1260

55

45

35

25 Air temperature before pre-cooler 15

Air temperature after pre-cooler Pre-cooler inlet condensate temperature

5. Results and discussion 5

Before discussing the performance of the air conditioning system with and without air pre-cooling, it is important to present part of the results of condensate collected from the system. Hourly rates of condensate yields on a typical day of August in Dhahran from the base air conditioning system are given in Table 5. The condensate was collected and measured at each hour during the day. It can be observed that the condensate yield increases during the evening until the early morning hours when the humidity is high. The maximum hourly condensate yield is observed at night between 8:00 and 10:00 pm with a value of 5.1 kg. Variations of air and condensate temperatures across the precooler with time are shown in Fig. 5. The difference in pre-cooler inlet and outlet air temperatures represent the amount of air pre-cooling achieved. It is observed that the air temperature difference across the pre-cooler decreases with increase in condensate inlet temperature as expected. The increase in the condensate temperature is due to the continuous recirculation of the condensate from the tank through the pre-cooler. It is noted that the condensate temperature is effective for air pre-cooling until about five and half hours when the air temperatures at the pre-cooler inlet and exit became equal. Once both temperatures became equal, no more cooling can be achieved. At this point, the condensate tank must be drained and refilled with fresh condensate or water from other source.

0

50

100

150

200

250

300

350

Time (Min) Fig. 5. Temperatures variation across pre-cooler.

Pre-cooling the condenser inlet air shows a positive effect on the compressor discharge pressure. Comparison of compressor discharge pressure between the base system and the system with precooler is shown in Fig. 6 and a significant decrease in the discharge pressure is observed. By lowering the discharge pressure, the life expectancy of the compressor can be improved. The decrease in the discharge pressure as a result of air pre-cooling leads to the decrease in the discharge temperature as shown in Fig. 7. The advantage of lower discharge pressure and temperature due to decrease in condenser air temperature is the decrease in compressor power consumption as depicted in Fig. 8. The percentage decrease in the compressor power is about 10% at the beginning of the pre-cooling operation and then gradually decreases as a result of the rise in condensate temperature with time. The average percentage decrease in compressor power consumption after about 3.5 h of operation is 6.7% and 6.1% after the entire experimental period. The cooling effect is increased by about 30% at the beginning of air pre-cooling as shown in Fig. 9. The reduction in power con-

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2300

actual flow rate of water used is 10.8 L/min while the nominal flow rate of the pump is 35 L/min. Hence the pump does not represent the actual electric power that could be required for the used flow rate and therefore not included. Fig. 11 shows the comparison of second law efficiency between the base system and the system with pre-cooler. The efficiency is improved by about 20.5% on average. The results indicate that pre-cooling the condenser inlet air by condensate or water reduces the energy consumption of vapor

1900 1700 1500 1300

6

Base system

1100

System with pre-cooler 0

50

100

150

200

250

300

5 350

Time (Min) Fig. 6. Compressor discharge pressure comparison.

Discharge temperature (oC)

90

4 3 2 1

80

0

70

Base system System with pre-cooler 0

50

100

150

200

250

300

350

Time (Min) 60

Fig. 9. Evaporator cooling effect comparisons.

50 3

Base system

40

System with pre-cooler 30

0

50

100

150

200

250

300

350

Time (Min) Fig. 7. Compressor discharge temperature comparisons.

2.3 2.2

Compressor power (kW)

Cooling effect (kW)

900

Coefficient of performance, COP

Discharge pressure (kPa)

2100

2.1

2.5 2 1.5 1 0.5

Base system System with pre-cooler

0

2

0

50

100

150

200

250

300

350

Time (Min)

1.9

Fig. 10. COP comparisons.

1.8 1.7

0.25 Base system

1.6 1.5

0

50

100

150

200

250

300

350

Time (Min) Fig. 8. Compressor power comparisons.

sumption and the corresponding increase in the cooling effect resulted in significant increase in COP of about 40% at the beginning of the air pre-cooling as depicted in Fig. 10. The average percentage increase in COP during the entire experimental period is 21.4% when the air entering the condenser is pre-cooled. It is to be noted that the water pump requires an electric input power that needs to be included in the COP calculation. However, the pump used in this study has not yet been optimized, it is oversized. The

Second law efficiency,

II

System with pre-cooler

0.2

0.15

0.1

Base system

0.05

System with pre-cooler 0 0

50

100

150

200

250

Time (Min) Fig. 11. Second law efficiency comparisons.

300

350

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compression system as well as improving its performance and therefore, the technique can be applied during the peak period of high ambient temperatures.

The compressor power consumption is obtained from the measured current with voltage source of 220 V. In this case, the compressor power is a function of current only and the uncertainty in the power is given by,

6. Conclusions Performance evaluation of a vapor compression air conditioning system utilizing condensate to pre-cool the air entering the condenser is presented in this paper. It is found that the compressor power consumption is decreased by 6.1% on average as a result of the decrease in discharge pressure when the air temperature entering the condenser is lowered by circulating the condensate through a pre-cooler. The coefficient of performance (COP) is increased by 21.4% and the second law efficiency by 20.5%, on average. The temperature of the circulating condensate was effective for air pre-cooling until about 5.5 h when the air temperatures at the pre-cooler inlet and exit became equal. This is a clear indication that the pre-cooling technique can be used to improve the system performance, particularly for large capacity cooling systems which produces reasonable amount of condensate. The technical advantage of the decrease in the discharge pressure in addition to lower compressor power consumption is the tendency of the compressor to have better life expectancy due to reduced thermal stresses on the compressor parts.

_ com @W dI @I

dW_ com ¼

! ðA:6Þ

Uncertainties in COP and COPmax are calculated, respectively, as,

dCOP

" 2  2 #1=2 @COP @COP ¼ dQ_ þ d _ com W_ com @W @ Q_ ev ev

ðA:7Þ

" 2  2 #1=2 @COP max @COP max dT L þ dT H @T L @T H

dCOPmax ¼

" where dT L ¼

@T L dT @T a;ev ;i a;ev ;i

2

 þ

@T L dT @T a;ev ;e a;ev ;e

ðA:8Þ 2 #1=2 ðA:9Þ

The second law efficiency uncertainty is determined by,

" dgII ¼

@ gII dCOP @COP

2

 þ

@ gII dCOPmax @COP max

2 #1=2 ðA:10Þ

Acknowledgements The authors would like to acknowledge King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia for the financial support through the project DRP-5-11 and King Fahd University of Petroleum and Minerals Dhahran, Saudi Arabia for the facilities. We appreciate the technical support provided by Mr. Mohammad Karam Adham and Mr. Sarfaraz Ahmed Furquan. Appendix A The cooling effect of the system Q_ ev is a function of air mass flow rate and enthalpy difference across the evaporator and the uncertainty in the cooling effect is determined by,

2

dQ_ ev

@ Q_ ev ¼4 d _ a m_ a @m

!2

@ Q_ ev þ dh @ha;ev ;i a;ev ;i

!2

@ Q_ ev þ dh @ha;ev ;e a;ev ;e

!2 31=2 5 ðA:1Þ

where the enthalpy of the air is a function of temperature and humidity and is given as,

h ¼ Cp T þ

0:622;Pg ð2501:3 þ 1:86TÞ P  ;P g

ðA:2Þ

where Cp is the specific heat capacity of dry air with a value 1.01 kJ/ kg K. From Eq. (A.2),

@h 1:1569;Pg ¼ Cp þ @T P  ;Pg

ðA:3Þ

@h 0:622Pg ð2501:3 þ 1:86TÞP ¼ 2 @; ðP  ;Pg Þ

ðA:4Þ

and therefore,

" dh ¼

@h dT @T

2

 2 #1=2 @h d; þ @;

ðA:5Þ

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