Modeling-Based Energy Performance Assessment and Validation of Air-To-Water Heat Pump System Integrated with Multi-Span Greenhouse on Cooling Mode

The purpose of this study was to conduct a modeling-based energy performance assessment and validation of an air-to-water heat pump (AWHP) system, in the cooling mode, integrated with a multi-span greenhouse using TRNSYS software. We used the building energy simulation (BES) model to investigate the performance characteristics of the AWHP system for greenhouse cooling. We modelled the components of the AWHP system, including the fan coil unit (FCU), water storage tank, and water circulation pump integrated with the greenhouse model. The proposed model included all the components of the experimental system. We validated the proposed model by comparing the simulation results with those obtained from field experiments. We investigated the cooling energy supply to the multi-span greenhouse, greenhouse internal air temperature, heat pump (HP) output temperature, and coefficient of performance (COP). We evaluated the performance of our model by calculating the Nash–Sutcliffe efficiency (NSE) coefficient of all the validated components. Furthermore, we performed linear regression analyses (R2) to determine the relationship between the different parameters. NSE values of 0.87, 0.81, and 0.93, for the greenhouse internal air temperature, the energy supply to the greenhouse, and the HP output water temperature, respectively, validated the prediction accuracy of the model. Moreover, R2 values of 0.83 and 0.39 indicated that cooling loads are more dependent on ambient solar radiation than ambient air temperature. Furthermore, an R2 value of 0.91 showed a linear relationship between the HP’s energy consumption and ambient air temperature. The average daily COP of the HP system was 2.9. Overall, the simulation results showed acceptable correlation with the experimental results. The high NSE values validated the high predictive power of the model. The proposed validation model can be used to improve the performance of systems by optimizing the control strategies and capacities of the equipment (e.g., the HP, the FCU, and the area of the greenhouse). We have provided detailed information to enable engineers, researchers, and consultants to implement the model for their specific needs.


Introduction
Globally, fossil fuels satisfy most of our energy demands. It is projected that the total use of energy worldwide will grow by 44% from 2006 to 2030. There is a surge in energy demand owing to a growing population and industrialization [1]. This trend will not only cause scarcity in terms of fossil fuel supplies but will increase environmental pollution and CO 2 emissions [2]. In addition to other effects, the worldwide increase in oil prices is a major concern. Moreover, the expected increase in the world's population to 9.8 billion by 2050 is an area of focus in the context of achieving global sustainability [3]. Owing to climate change and consequent extreme weather conditions in both winter and summer, the growth of protected horticultural facilities is increasing globally to meet sustainability goals. According to a recent report, energy consumption in the world food chain is almost 30% of the total global energy demand, which is mostly met by fossil fuels [4]. The desired microclimate in agricultural facilities is maintained by providing cooling/heating and artificial lighting, which increases the energy consumption. The cost of energy has become one of the major factors in greenhouse farming [5]. The use of fossil fuels in greenhouse farming not only increases production costs [6] but increases environmental pollution and CO 2 emissions. The worldwide growth of environmentally controlled agriculture facilities requires innovative solutions to meet energy demands with cost-effective and sustainable energy technologies. Among the different energy-saving strategies proposed for the greenhouse sector, the use of alternative energy sources has been identified as a potential solution [7]. Several types of heat pumps (HPs) with different specifications are used globally for buildings and greenhouses [8]. Two types of HPs are used to provide heating and cooling energy: ground -and air-source HPs. Ground-source HPs are more efficient but are more expensive than air-source HPs [9].
TRNSYS is a graphical and extremely flexible software which is used to simulate the behavior of transient systems. It is used for the simulation and performance assessment of systems such as solar, geothermal, building energy, load and structure, electrical, hydronics, and storage systems as well as HPs and solar applications [10]. It is a versatile component-based simulation tool with a series of programs and addons that enable the development of simple and complex energy systems and their components [11]. It has different libraries containing numerous components for the modeling of energy systems, including a wide range of heating ventilation and air-conditioning (HVAC) components for building, industrial, residential, and commercial HVAC systems. TRNSYS is used globally, and its building model is compliant with the general technical requirements of ANSI/ASHRAE Standard 140-2001 and the European Directive on the Energy Performance of Buildings [12].
Many studies have used TRNSYS for the simulation of ground source HPs for greenhouse heating. In one study, Chargui et al. [13] evaluated a geothermal HP in the heating mode to provide heat energy to a greenhouse. In another study [14], the HP and the geometry and performance of a cooling tower system were investigated using the TRN-SYS software. The system optimization results were validated by several theoretical and experimental studies. Chargui et al. [15] simulated a dual-source HP system for heating a single house. They evaluated the temperature and energy operation in winter using different operating conditions; the results indicated that the system provided acceptable results under all operating conditions. Safa et al. conducted two studies in 2015 [16,17] to investigate the performance of air source heat pump and ground source heat pump (GSHP) systems using TRNSYS software and evaluated the cooling and heating coefficient of performance (COP) of the system. The efficiencies of different components of the system were analyzed. Mehrpooya et al. 2015 [18] designed and optimized the application of a combined solar collector and geothermal heat-pump system in greenhouse farming. The study calculated the COP of the system and evaluated technical and economic factors. Ruiz-Calvo et al. [19] optimized the design and operation of the GSHP using TRNSYS software for the heating and cooling of buildings. The model was validated against experimental data; it accurately predicted the system behavior. Jonas et al. (2017) performed TRNSYS-based modeling and the simulation of a combined solar system and HP [20]. Park et al. [21] investigated the application of a solar thermal seasonal storage system in a greenhouse. The TRNSYS software was used to analyze the dynamic performance of the system. The simulation was performed by modeling a solar thermal seasonal storage system consisting of a borehole thermal energy storage system, solar collector, storage tank, heat exchanger, boiler, pump, and controller. The results of the study satisfied the heating energy demands of the proposed system. Lamrani et at. developed a TRNSYS model and investigated the performance of an indirect hybrid solar wood dryer. The results showed that the maximum discrepancy did not exceed 10% [22]. To solve the problem of high energy consumption in winter and summer, Yang et al. [23] recently presented a study on a groundwater source HP system for a plant factory that lacked an operation strategy. The study reported a significant reduction in the energy demand of the plant factory. TRNSYS is a flexible, component-based tool for the dynamic simulation of a system; each component is called a "Type" in TRNSYS. Bordignon et al. [24] recently presented a novel type of simulation for a reversible water-to-water HP. This type of system was used to simulate different configurations of the system under different weather conditions. The study highlighted the importance of integrated simulations when evaluating complex multi-energy systems.
TRNSYS has been used in many studies for greenhouse and energy system modeling. A number of our studies have used TRNSYS for greenhouse structural modeling. Rasheed et al. [6] used the TRNSYS software to study the effect of single-span greenhouse design parameters from the perspective of energy conservation. Furthermore, they identified passive energy-saving options of single-span greenhouses by evaluating different thermal screens and their control effect on the heat energy demand of the greenhouse using the same program [25]. Two of our studies [26,27] on multi-span greenhouse energy saving options were conducted using TRNSYS software, and the proposed model was validated. In a recent study [28], we proposed and validated an air-to-water heat pump (AWHP) model using TRNSYS in the heating mode under the climatic conditions of Deagu, South Korea. Statistical analyses of the validation results encouraged us to doubt the model. Many other studies have used TRNSYS to simulate different building and energy systems. The studies mentioned above represent a small number of studies demonstrating the use of TRNSYS for different types of heat-pump modeling. Studies on the use of HPs to fulfil the cooling energy demand of greenhouses are limited. Currently, the use of air source HPs is rapidly increasing because of their low cost and ease of installation. According to the best of our knowledge and the literature reviewed and cited, the studies conducted previously on this topic were from specific point of view, and research on the use of this particular air-to-water heat pump specifically for greenhouse cooling is lacking. The cooling energy demand of the greenhouse and the performance of the AWHP could be different under different climatic conditions. Ensuring the accurate performance of the system is generally a difficult task for any designer or researcher [29]. Therefore, there is a need to develop a combined simulation model of a greenhouse with an AWHP system considering all the physical parameters of the whole system in order to evaluate the system's efficiency under specific weather conditions. In the previous section, an AWHP model was developed using the TRNSYS program, and the proposed model was validated using experimental data in the heating mode [28].
The objective of this study was to conduct a modeling-based energy performance assessment and validation of an AWHP system, in the cooling mode, integrated with a multi-span greenhouse. Furthermore, the feasibility of the use of the air-to-water heat pump to fulfil the cooling energy demand of the studied greenhouse was investigated. The modeling of the greenhouse could help to predict the total and maximum cooling energy demand, which could be used to determine the capacity of the heat pump system under local weather conditions. The ability of the model to predict the greenhouse cooling energy demand and supply energy was tested by comparing the predicted results with the results obtained experimentally. The components that were modeled included a fan coil unit (FCU), the storage tank (ST) to HP supply and the return water temperature, the ST temperature, the ST to greenhouse supply and the return temperature, the greenhouse internal air temperature, and the COP of the HP. In addition, we validated the quantitative performance and accuracy of the results statistically using the Nash-Sutcliffe efficiency (NSE) coefficient. Detailed information on each step was gathered in order to make the model convenient in terms of reuse, integration, extension, and compression. Researchers can use this model for dynamic thermal simulations in the context of specific greenhouse designs and control requirements and energy system selections and capacities according to local weather conditions and specific crop needs. This work will increase reliance on sustainable and renewable energy to ensure more stable, reliable, and resilient energy sources of greenhouse heating and cooling. Moreover, site-specific analysis under local weather conditions could help to increase the COP of the heat pump.

Description of Experimental Setup
This study was performed using an AWHP with a cooling capacity of 65 kW and a water ST with a capacity of 50 m 3 . The technical specifications of the equipment used in the AWHP are listed in Table 1. This setup was used to analyze the cooling performance of a small-sized three-span rectangular, Venlo-roofed, north-south (N-S) oriented greenhouse. The greenhouse roof was covered with horticultural glass (HG, 4 mm), a shading screen (commercial name-PH 66) was used under the roof, and the side walls were covered with polycarbonate (PC, 16 mm). Roof vents were employed for natural ventilation inside the greenhouse, with the opening and closing of the vents determined by an air temperature inside the greenhouse of 30 • C. The greenhouse was further divided into three equal parts to create different climatic conditions for different experiments; each part's dimensions were 8 m × 16.3 m × 7.6 m, with a floor area of 130.4 m 2 . HG material of 4 mm was used for the divider. Each partition in the greenhouse featured two fan coil systems with a cooling capacity of 18 kW (Table 1). The total floor area cooled was 391.6 m 2 , with a total volume of 2362.8 m 3 . The cooling setpoint on each compartment was set at 25 • C. The deployment and retraction of the shading screen were determined by an outside solar radiation intensity of >0.5 kW·m −2 . The greenhouse and the entire experimental setup were located at Kyungpook National University, Daegu, South Korea (latitude 35.53 • N, longitude 128.36 • E, elevation 48 m). Figure 1a-d show the experimental three-span greenhouse, water storage tank, AWHP, and FCU. The experiments were conducted from 1 June 2021 to 31 September 2021, during a typical summer (cooling period). m , with a total volume of 2362.8 m . The cooling setpoint on each compartment was set at 25 °C. The deployment and retraction of the shading screen were determined by an outside solar radiation intensity of >0.5 kW•m −2 . The greenhouse and the entire experimental setup were located at Kyungpook National University, Daegu, South Korea (latitude 35.53° N, longitude 128.36° E, elevation 48 m). Figure 1a-d show the experimental three-span greenhouse, water storage tank, AWHP, and FCU. The experiments were conducted from 1 June 2021 to 31 September 2021, during a typical summer (cooling period).  During the experiment, weather data inside and outside the greenhouse were recorded from 1 June to 31 September 2021 during summer period in Daegu, South Korea. The data was acquired by installing a sensor network at the site. The data was used as an input to the developed BES model of a greenhouse with an integrated AWHP. The data recorded inside the greenhouse were the air temperature and relative humidity, which were recorded using MTV Active and Ridder sensors. Figure 2 shows the mean outside air temperature and solar radiation for reference purposes. The solar radiation data were measured both inside and outside the greenhouse using a horizontally placed SR05-D2A2-TMBL, Hukseflux sensor. The wind speed and direction were measured outside the greenhouse at a height of 10 m with a Clima Sensor US, Thies Clima. Ambient pressure data were obtained from the Korean Meteorological Administration (KMA). Table 2 lists the characteristics and sensitivities of all the recorded weather variables obtained from the catalog. The data obtained from the sensors were at a 10-min interval. However, the data was interpolated to a 1-min interval to make it comparable with the simulation results.  During the experiment, weather data inside and outside the greenhouse were recorded from 01 June to 31 September 2021 during summer period in Daegu, South Korea. The data was acquired by installing a sensor network at the site. The data was used as an input to the developed BES model of a greenhouse with an integrated AWHP. The data recorded inside the greenhouse were the air temperature and relative humidity, which were recorded using MTV Active and Ridder sensors. Figure 2 shows the mean outside air temperature and solar radiation for reference purposes. The solar radiation data were measured both inside and outside the greenhouse using a horizontally placed SR05-D2A2-TMBL, Hukseflux sensor. The wind speed and direction were measured outside the greenhouse at a height of 10 m with a Clima Sensor US, Thies Clima. Ambient pressure data were obtained from the Korean Meteorological Administration (KMA). Table 2 lists the characteristics and sensitivities of all the recorded weather variables obtained from the catalog. The data obtained from the sensors were at a 10-min interval. However, the data was interpolated to a 1-min interval to make it comparable with the simulation results.   The actual experimental setup consisted of three AWHPs; however, in this study, only one AWHP was in operation, as it met the energy demand of the FCU. Other HPs were installed at the site for the future extension of the greenhouse. The water ST stored cold water from the AWHP and supplied it to the greenhouse when cooling to the setpoint internal air temperature. We monitored the water flow rate and temperature at various locations, namely the ST to HP supply and the return temperature and flow rate and the ST to greenhouse supply and the return temperature and flow rate ( Figure 3). We acquired water temperature data using a HortiMax Omni Transducer, Ridder sensor. The FS-WLH 40 and FLSTRONIC sensors ( Table 2) were used to measure the water flow rate. The cooling energy supply from the AWHP to the water storage tank and from the water ST to the greenhouse was calculated using Equation (1).
where Q is the cooling capacity of the AWHP (kW),ṁ is the mass flow of water (kg·s −1 ), cp is the specific heat capacity of water (kW·kg −1 · • C −1 ), and ∆T is the temperature difference between the supply and return temperatures ( • C). The COP of the HP was calculated using Equation (2): where P HP is the power usage of the AWHP (kW).  The actual experimental setup consisted of three AWHPs; however, in this study, only one AWHP was in operation, as it met the energy demand of the FCU. Other HPs were installed at the site for the future extension of the greenhouse. The water ST stored cold water from the AWHP and supplied it to the greenhouse when cooling to the setpoint internal air temperature. We monitored the water flow rate and temperature at various locations, namely the ST to HP supply and the return temperature and flow rate and the ST to greenhouse supply and the return temperature and flow rate ( Figure 3). We acquired water temperature data using a HortiMax Omni Transducer, Ridder sensor. The FS-WLH 40 and FLSTRONIC sensors ( Table 2) were used to measure the water flow rate. The cooling energy supply from the AWHP to the water storage tank and from the water ST to the greenhouse was calculated using Equation (1).
where Q is the cooling capacity of the AWHP (kW), ṁ is the mass flow of water (kg•s −1 ), cp is the specific heat capacity of water (kW•kg −1 •°C −1 ), and ΔT is the temperature difference between the supply and return temperatures (°C). The COP of the HP was calculated using Equation (2): where PHP is the power usage of the AWHP (kW).

Modeling and Simulation
The modeling was divided into two steps. In the first step, we developed a multi-span greenhouse model and a HP model including other components, an FCU, a water ST, and pumps. Figure 4 shows the simulation studio (the main interface of the TRNSYS program) connecting all the components of the greenhouse model. The modeling of the greenhouse considered all the physical aspects and control settings of the experimental greenhouse (Section 2.1), including its design, covering, and screen materials and its thermal screen, ventilation, day/night and seasonal internal temperature controls, while simultaneously considering different thermal phenomena, i.e., the three-dimensional shortwave and longwave radiative exchange, airflow exchanges, and the ground and convective heat transfer coefficients.

Modeling and Simulation
The modeling was divided into two steps. In the first step, we developed a multispan greenhouse model and a HP model including other components, an FCU, a water ST, and pumps. Figure 4 shows the simulation studio (the main interface of the TRNSYS program) connecting all the components of the greenhouse model. The modeling of the greenhouse considered all the physical aspects and control settings of the experimental greenhouse (Section 2.1), including its design, covering, and screen materials and its thermal screen, ventilation, day/night and seasonal internal temperature controls, while simultaneously considering different thermal phenomena, i.e., the three-dimensional shortwave and longwave radiative exchange, airflow exchanges, and the ground and convective heat transfer coefficients. Each component has a special name in TYRNSYS called a "Type." The components used in the BES modeling of the multi-span greenhouse ( Figure 4) and their descriptions are as follows: The greenhouse description is passed to the component using a ".idf" file prepared via the 3D modeling of the greenhouse using Transys3d (an add-on of Google SketchUpTM) program and imported into TRNSBuild (a building interface of the TRNSYS program, TYPE 56). The greenhouse covering and screen material properties were input into the Lawrence Berkeley National Laboratory Windows 7.7 program, creating the DOE-2 file of the materials, which was readable by TRNSBuild. Table 3 shows the physical, thermal, radiometric, and air permeability properties of the covering and screen materials, while Table 4 shows the steel (greenhouse structure pipes) and ground properties used in the simulation. The covering material properties were chosen from a previous study [30].
Meanwhile, the shading screen properties were experimentally measured, the thermal conductivity was measured using a thermal conductivity meter, the radiometric properties were measured using the energy balance method, and the air flow was measured with a laboratory-designed air suction device. The details of these measuring procedures were presented in a recent study [31]. TRNSBuild managed the thermal model of the building, and to account for natural ventilation into the greenhouse, TRNSYFLOW was used. TRNSFLOW (a ventilation module of the TRNSYS program) coupled the airflow network with the thermal model to simulate the effect of the natural ventilation that is handled in "TYPE 56." This component was used to simulate the thermal behavior of the greenhouse with natural ventilation. All heat transfer calculations were performed in this component. The thermal conductivity of the materials was used to calculate the thermal conduction of Each component has a special name in TYRNSYS called a "Type." The components used in the BES modeling of the multi-span greenhouse ( Figure 4) and their descriptions are as follows: The greenhouse description is passed to the component using a ".idf" file prepared via the 3D modeling of the greenhouse using Transys3d (an add-on of Google SketchUpTM) program and imported into TRNSBuild (a building interface of the TRNSYS program, TYPE 56). The greenhouse covering and screen material properties were input into the Lawrence Berkeley National Laboratory Windows 7.7 program, creating the DOE-2 file of the materials, which was readable by TRNSBuild. Table 3 shows the physical, thermal, radiometric, and air permeability properties of the covering and screen materials, while Table 4 shows the steel (greenhouse structure pipes) and ground properties used in the simulation. The covering material properties were chosen from a previous study [30].
Meanwhile, the shading screen properties were experimentally measured, the thermal conductivity was measured using a thermal conductivity meter, the radiometric properties were measured using the energy balance method, and the air flow was measured with a laboratory-designed air suction device. The details of these measuring procedures were presented in a recent study [31]. TRNSBuild managed the thermal model of the building, and to account for natural ventilation into the greenhouse, TRNSYFLOW was used. TRNSFLOW (a ventilation module of the TRNSYS program) coupled the airflow network with the thermal model to simulate the effect of the natural ventilation that is handled in "TYPE 56." This component was used to simulate the thermal behavior of the greenhouse with natural ventilation. All heat transfer calculations were performed in this component. The thermal conductivity of the materials was used to calculate the thermal  (3) and (4) are the governing equations for calculating the convective and radiative heat transfers for the greenhouse surfaces.
where Q Conv is the convective heat transfer (kJ·h −1 ·m −2 ·k −1 ), h conv is the convective heat transfer coefficient (kJ·h −1 ·m −2 ·k −1 ), T o is the outside surface temperature ( • C), T i is the inside surface temperature ( • C), Q r is the radiative heat flux to the surface (kJ·h −1 ·m −2 ·k −1 ), σ is the Stephen-Boltzmann constant (W·m −2 ·k −1 ), ε 0 is the long-wave emissivity (-), and T sky is the sky temperature ( • C). The airflow caused by natural ventilation inside the greenhouse was estimated using TRNFLOW in TRNSBuild. There are different options for creating an airflow network in TRNFLOW, for example, through large openings, creaks, fans, and straight ducts. We used a large opening window as it was the option that was best suited to the context of a greenhouse. Equation (5) provides the equation to calculate the airflow for a large opening window:ṁ whereṁ is the air mass flow rate (kg·h −1 ), 1−>2 is the flow direction from one air node to another (-), C d is the discharge coefficient (-), H is the total height of the window (m), ρ(z) is the air density (kg·m −3 ) at height z, z is the height of the opening (m), α is the angle of the window opening ( o ), W is the width of the rectangular opening (m), f(z) is the pressure difference at height z (pa).
In the simulation studio, the weather data processors (Type 9) were linked to Type 56 to simulate the effect of an ambient environment using the user-provided weather data file (the field-measured weather data from 1 June to 31 September 2021). Type 33 (a psychrometric chart) was used to calculate the dew-point temperature using the dry bulk temperature and humidity ratio. Type 165 (a controller) was used to control the natural ventilation of the multi-span greenhouse, i.e., the opening and closing of the roof. Type 65 (a result plotter) was used to plot and compare results. Type 25 (a printer) was used to obtain the results for the user-provided external files. An equation editor was used to introduce different user-defined equations. Type 518 (monthly forcing functions) is a scheduler that was used to input screen opening and closing schedules, which change monthly. Type 16 (a solar radiation processor) was used to calculate the total, beam, reflected, and diffuse radiation on all the tilted greenhouse surfaces. Solar radiation data are typically estimated for a horizontal surface. This component interpolates the data related to the position of the sun to estimate the beam, reflected, and diffuse radiation on horizontal and tilted surfaces when only the total horizontal solar radiation is input. The solar radiation processor estimates the diffuse radiation fraction on the horizontal surface as a function of the clearness index, solar altitude angle, relative humidity, and ambient temperature. Equation (6) expresses the relationship [32]: The horizontal beam radiation is calculated by the difference between the total radiation and the diffuse component provided by Equation (7).
where I is the total radiation of the horizontal surface (kJ·h −1 ·m −2 ), I d is the diffuse radiation of the horizontal surface (kJ·h −1 ·m −2 ), kt is the clearness index, α s is the solar altitude angle ( o ), T amb is the ambient temperature ( • C), and rh is relative humidity (%). The model calculates the total radiation on a tilted surface using Equation (8) by estimating and adding the beam, diffuse, and reflected radiation on the tilted surface (Equation (9)). I T = I bT + I gT + I dT (8) where I T is the total radiation on the tilted surface (kJ·h −1 ·m −2 ), I bT is the beam radiation of the tilted surface (kJ·h −1 ·m −2 ), I gT is the ground-reflected radiation on the tilted surface (kJ·h −1 ·m −2 ), I dT is the diffuse radiation of the tilted surface (kJ·h −1 ·m −2 ), θ is the incident angle of the beam radiation ( o ), θ z is the solar zenith angle ( o ), β is the slope of the surface( o ), and ρ g is the reflectance of the ground (-). Type 69 (the sky temperature) was used to calculate the sky temperature using the ambient temperature, dew point temperature, beam, and diffuse radiation on a horizontal surface. These parameters were further used by Type 56 to estimate the longwave radiation exchange from external surfaces. The mathematical reference for this component is shown in Equation (10): where T sky is the sky temperature ( • C), T amb is the ambient temperature ( • C), ε 0 is the emittance of the clear sky (−), C cover is the cloudiness factor of the sky. The cloudiness factor of the sky is calculated internally as a ratio of diffuse to global radiation, where 0 indicates a clear sky and 1 indicates a fully cloud-covered sky. Figure 5 shows a simulation studio picture of the AWHP system and the connections between components. Type 941, from the TRNSYS Tess library, was used to model the AWHP. This model works on the principle of the water stream rejecting energy in the cooling mode and absorbing energy in the heating mode. The model is based on userdefined performance data files containing catalog data for the water capacity and power for cooling/heating. The cooling performance data file (Table A1) and the data sheet provided by the manufacturer of the HP in the cooling mode are listed in Table A2 of Appendix A. The model uses the water temperature, flow rate, relative humidity, and entering air temperature at the inlet as inputs to calculate the water temperature at the outlet. The component reads the temperatures of the water and air entering the system and interpolates these with the cooling/heating performance data. The HP is controlled using an on/off signal. The capacity and power are used as functions for the entering water temperature. Equation (11) provides the mathematical reference for the calculation.
T water, out = T water, in + · q wateṙ m water Cp water (11) where T water, out is the temperature of the HP's water output ( • C), T water, in is the temperature of the HP's water inlet ( • C), · q water is the energy drawn by the water (kJ·h −1 ),ṁ water is the water flowrate (kg·h −1 ), and Cp water is the specific heat of the water (kJ·kg −1 ·k −1 ). AWHP. This model works on the principle of the water stream rejecting energy in the cooling mode and absorbing energy in the heating mode. The model is based on userdefined performance data files containing catalog data for the water capacity and power for cooling/heating. The cooling performance data file (Table A1) and the data sheet provided by the manufacturer of the HP in the cooling mode are listed in Table A2 of Appendix A. The model uses the water temperature, flow rate, relative humidity, and entering air temperature at the inlet as inputs to calculate the water temperature at the outlet. The component reads the temperatures of the water and air entering the system and interpolates these with the cooling/heating performance data. The HP is controlled using an on/off signal. The capacity and power are used as functions for the entering water temperature. Equation (11) provides the mathematical reference for the calculation.
where T , is the temperature of the HP's water output (°C), T , is the temperature of the HP's water inlet (°C), q is the energy drawn by the water (kJ·h −1 ), ṁ is the water flowrate (kg·h −1 ), and Cp is the specific heat of the water (kJ·kg −1 ·k −1 ).  Table 1 lists the rated heating capacity and power consumption of the HP. Type 4 (a water ST) was used to model a stratified tank with variable inlet positions. Type 114 (a circulation pump) delivers water to the HP at a constant speed. From the ST to the greenhouse, cold water was provided using a Type 3 (a variable speed circulation pump) with a Type 22 proportional integral (PI) derivative controller to control the mass flow rate with feedback control. Type 108 (thermostat), a five-stage thermostat with an on/off control function, was used to control the circulation pump and FCU using the greenhouse's internal temperature setpoint. Type 709 (a pipe) is used to deliver water from the ST to the greenhouse. Energy loss from the pipes is considered in the model. Type 928 (a fan coil unit) was used to simulate the FCU to exchange the cooling energy inside the greenhouse. This model uses the stream of the air passing across the fan and the coil containing either hot or cold water. The model relies on the energy exchange between the air stream and water in the coil. It uses the water temperature, water flow rate, and return air temperature as inputs and outputs the water temperature and flowrate after energy exchange,  Table 1 lists the rated heating capacity and power consumption of the HP. Type 4 (a water ST) was used to model a stratified tank with variable inlet positions. Type 114 (a circulation pump) delivers water to the HP at a constant speed. From the ST to the greenhouse, cold water was provided using a Type 3 (a variable speed circulation pump) with a Type 22 proportional integral (PI) derivative controller to control the mass flow rate with feedback control. Type 108 (thermostat), a five-stage thermostat with an on/off control function, was used to control the circulation pump and FCU using the greenhouse's internal temperature setpoint. Type 709 (a pipe) is used to deliver water from the ST to the greenhouse. Energy loss from the pipes is considered in the model. Type 928 (a fan coil unit) was used to simulate the FCU to exchange the cooling energy inside the greenhouse. This model uses the stream of the air passing across the fan and the coil containing either hot or cold water. The model relies on the energy exchange between the air stream and water in the coil. It uses the water temperature, water flow rate, and return air temperature as inputs and outputs the water temperature and flowrate after energy exchange, outlet air temperature, and cooling/heating transfer to air. If the coil water temperature is less than the temperature of the air exiting the fan, the system will operate in the cooling mode and vice versa in the heating mode. This type uses many equations to calculate the functions detailed in the manual, and the governing equations are used to obtain the desired output. The water flow rate was the same as the inlet flow rate, and the water outlet temperature was calculated using Equation (12): T water, out = T water, in + T water, in + T air, fan Cp water (12) where T air, fan is the temperature of air entering the fan ( • C).
The output of the model is the fan heat loss to the surroundings; therefore, the enthalpy of the air exiting the fan is computed using Equation (13) where h air,fan is the enthalpy of the exiting air (kJ·kg −1 ), h air, mix is the enthalpy of the air mixing (kJ·kg −1 ), q air, fan is the energy drawn by the fan, which is the output of the model, indicating the fan energy loss to the surrounding (kJ·h −1 ),ṁ air, fan is the mass flowrate of air leaving the fan and is equal to the mass flowrate of air entering the fan (kg·h −1 )

Statistical Analysis of BES Model
Statistical analyses were performed to predict the performance of the BES model using the NSE coefficient and to compare the experimentally measured data with the BES model's output. This coefficient quantitatively describes the accuracy of the model results, indicating how well the plot of the observed versus simulated data fits the 1:1. Its value ranges from −∞ to 1, and the closer the values are to 1, then the better the predictive power of the model. The NSE is mathematically expressed using Equation (3). The performance rating for NSE values is NSE > 0.9 = very good, 0.8-0.9 = good, 0.65-0.80 = acceptable, and <0.6 = unsatisfactory [33]. The mathematical description is shown in Equation (14): where T exp i is the experimental value, T sim i is the simulated value, T mean i is the mean of the experimental values, and n is the total number of observations.

Results and Discussion
The proposed AWHP system integrated with the multi-span greenhouse BES model was validated by comparing the computed supply cooling energy, internal air temperature of the greenhouse, HP output temperature, and ST temperature with those obtained experimentally under the same physical and operating conditions. Validation analyses were conducted during the summer (1 June to 31 September 2021) in Deagu, South Korea. Figure 6 shows the results for the greenhouse internal temperature under three different conditions: first, with natural ventilation and a shading screen, second, without natural ventilation (fully closed greenhouse), and third, using a reference temperature setpoint for cooling. The results show that the inside temperature of the greenhouse is greater than the reference temperature setpoint value during this period; therefore, cooling is required to control the inside temperature of the greenhouse. Moreover, the results revealed that from mid-Jul to mid-August, both daytime and nighttime cooling is required because of the high greenhouse temperature. The cooling energy demand of the greenhouse was determined using the proposed greenhouse model (Figure 4) at 25 • C (cooling setpoint at 25 • C). We determined the monthly maximum value of the cooling energy demand for the same period. Figure 7 shows the monthly cooling energy demand using the recorded ambient weather data (detailed in Section 2.1). To evaluate the performance of the heating system, it is important to determine the maximum monthly cooling energy demand of the greenhouse. The results showed that at the end of July, for the 391.2 m 2 of greenhouse, a maximum cooling energy of 168.6 kW and 0.43 kW·m −2 (Table 5) is required when the outside solar radiation level is as high as 1.01 kW·m −2 . The maximum values obtained determine the capacity of the HP system. Moreover, from mid-Jul to mid-August, both day-and nighttime cooling are required to meet the required temperature conditions inside the greenhouse. The heating pump system has to operate continuously (24 h) to meet the energy requirement.  (Table 5) is required when the outside solar radiation level is as high as 1.01 kW·m −2 . The maximum values obtained determine the capacity of the HP system. Moreover, from mid-Jul to mid-August, both day-and nighttime cooling are required to meet the required temperature conditions inside the greenhouse. The heating pump system has to operate continuously (24 h) to meet the energy requirement.     Figure 9a-d, confirmed the accuracy of the simulation model in predicting that the cooling energy supply was sufficient for Jun, Jul, August, and September, respectively. The results show that the maximum cooling energy provided to the greenhouse was 0.23 kW·m −2 , as the maximum cooling capacity of the two FCUs in each compartment were 36 kW, which was 0.27 kW·m −2 per unit area of greenhouse. The HP and water ST capacities were much higher, and could fulfil the cooling energy demand of the greenhouse, but the  (Table 5) is required when the outside solar radiation level is as high as 1.01 kW·m −2 . The maximum values obtained determine the capacity of the HP system. Moreover, from mid-Jul to mid-August, both day-and nighttime cooling are required to meet the required temperature conditions inside the greenhouse. The heating pump system has to operate continuously (24 h) to meet the energy requirement.     Figure 9a-d, confirmed the accuracy of the simulation model in predicting that the cooling energy supply was sufficient for Jun, Jul, August, and September, respectively. The results show that the maximum cooling energy provided to the greenhouse was 0.23 kW·m −2 , as the maximum cooling capacity of the two FCUs in each compartment were 36 kW, which was 0.27 kW·m −2 per unit area of greenhouse. The HP and water ST capacities were much higher, and could fulfil the cooling energy demand of the greenhouse, but the   Figure 8a-d presents the results for the cooling energy supply from the ST to the greenhouse with the ambient solar radiation for the analyzed months, i.e., June, July, August, and September, respectively. The results reveal a consistent correlation between the experimental and simulation results. The NSE values of 0.87, 0.87, 0.85, and 0.86, presented in Figure 9a-d, confirmed the accuracy of the simulation model in predicting that the cooling energy supply was sufficient for June, July, August, and September, respectively. The results show that the maximum cooling energy provided to the greenhouse was 0.23 kW·m −2 , as the maximum cooling capacity of the two FCUs in each compartment were 36 kW, which was 0.27 kW·m −2 per unit area of greenhouse. The HP and water ST capacities were much higher, and could fulfil the cooling energy demand of the greenhouse, but the installed FCU had a lower capacity. Both the HP and FCU capacities, wherein the maximum cooling capacities are 65 kW and 36 kW, respectively, are shown in Figure 10, confirming the above statement.  Figure 10, confirming the above statement.     Figure 10, confirming the above statement.    Figure 11 shows the greenhouse internal temperatures obtained via the simulation as well as experimentally, with the ambient temperature for the period 1 Jun to 23 September 2021. The experimental data from 23-28 July, 2021 and the last week of Sep were missing; hence, the results for up until 23 September 2021 are presented. The simulated greenhouse internal temperature results correlated consistently with the experimentally measured temperatures. The NSE values shown in Figure 12 for each month were 0.81, 0.67, 0.82, and 0.76, respectively. The results are acceptable for all months except Jul. The value in Jul (0.67) was slightly lower because some experimental data were missed by the sensors. The overall performance analysis results show that the proposed BES model is sufficiently accurate when predicting the internal air temperature of a multi-span greenhouse. The monthly maximum temperature in the greenhouse using the supplied energy shown in Figure 8 was 33 °C, whereas the greenhouse cooling setpoint was 25 °C. Therefore, the FCU capacity must be increased to obtain the desired temperature inside the greenhouse.   Figure 11 shows the greenhouse internal temperatures obtained via the simulation as well as experimentally, with the ambient temperature for the period 1 June to 23 September 2021. The experimental data from 23-28 July 2021 and the last week of September were missing; hence, the results for up until 23 September 2021 are presented. The simulated greenhouse internal temperature results correlated consistently with the experimentally measured temperatures. The NSE values shown in Figure 12 for each month were 0.81, 0.67, 0.82, and 0.76, respectively. The results are acceptable for all months except July. The value in July (0.67) was slightly lower because some experimental data were missed by the sensors. The overall performance analysis results show that the proposed BES model is sufficiently accurate when predicting the internal air temperature of a multi-span greenhouse. The monthly maximum temperature in the greenhouse using the supplied energy shown in Figure 8 was 33 • C, whereas the greenhouse cooling setpoint was 25 • C. Therefore, the FCU capacity must be increased to obtain the desired temperature inside the greenhouse.  Figure 11 shows the greenhouse internal temperatures obtained via the simulation as well as experimentally, with the ambient temperature for the period 1 Jun to 23 September 2021. The experimental data from 23-28 July, 2021 and the last week of Sep were missing; hence, the results for up until 23 September 2021 are presented. The simulated greenhouse internal temperature results correlated consistently with the experimentally measured temperatures. The NSE values shown in Figure 12 for each month were 0.81, 0.67, 0.82, and 0.76, respectively. The results are acceptable for all months except Jul. The value in Jul (0.67) was slightly lower because some experimental data were missed by the sensors. The overall performance analysis results show that the proposed BES model is sufficiently accurate when predicting the internal air temperature of a multi-span greenhouse. The monthly maximum temperature in the greenhouse using the supplied energy shown in Figure 8 was 33 °C, whereas the greenhouse cooling setpoint was 25 °C. Therefore, the FCU capacity must be increased to obtain the desired temperature inside the greenhouse.   Figure 13 depicts a comparison of the model and field results regarding the monthly cooling load vs. the monthly ambient solar radiation and air temperature. These comparisons were made to determine the relationship between the cooling load with ambient solar radiation and the air temperature by following the approach proposed by Safa et al. [34,35]. The results of linear regression analysis revealed that the cooling load is more dependent on ambient solar radiation than the ambient temperature, as, according to linear regression analysis (R 2 ) of the solar radiation, a value of 0.83 correlates well compering with 0.39, a R 2 value of the ambient air temperature. In addition, Figure 13a,b shows that the simulated R 2 values of 0.83 and 0.39 are more accurate than the equivalent experimental values, 0.79 and 0.35, for both analyses, respectively. After the successful validation of the cooling energy supply and greenhouse internal temperature, experiments were conducted concerning the HP output water temperature. Figure 14a shows a comparison of the between the experimental and simulated results for  Figure 13 depicts a comparison of the model and field results regarding the monthly cooling load vs. the monthly ambient solar radiation and air temperature. These comparisons were made to determine the relationship between the cooling load with ambient solar radiation and the air temperature by following the approach proposed by Safa et al. [34,35]. The results of linear regression analysis revealed that the cooling load is more dependent on ambient solar radiation than the ambient temperature, as, according to linear regression analysis (R 2 ) of the solar radiation, a value of 0.83 correlates well compering with 0.39, a R 2 value of the ambient air temperature. In addition, Figure 13a Figure 13 depicts a comparison of the model and field results regarding the monthly cooling load vs. the monthly ambient solar radiation and air temperature. These comparisons were made to determine the relationship between the cooling load with ambient solar radiation and the air temperature by following the approach proposed by Safa et al. [34,35]. The results of linear regression analysis revealed that the cooling load is more dependent on ambient solar radiation than the ambient temperature, as, according to linear regression analysis (R 2 ) of the solar radiation, a value of 0.83 correlates well compering with 0.39, a R 2 value of the ambient air temperature. In addition, Figure 13a,b shows that the simulated R 2 values of 0.83 and 0.39 are more accurate than the equivalent experimental values, 0.79 and 0.35, for both analyses, respectively. After the successful validation of the cooling energy supply and greenhouse internal temperature, experiments were conducted concerning the HP output water temperature. Figure 14a shows a comparison of the between the experimental and simulated results for After the successful validation of the cooling energy supply and greenhouse internal temperature, experiments were conducted concerning the HP output water temperature. Figure 14a shows a comparison of the between the experimental and simulated results for June 2021 concerning the outlet water temperature of the HP. The normal operation of the HP in the cooling mode was repeated daily; therefore, only one month of analysis results are presented here. The results show that the HP produces water with temperatures between 12 and 7 • C. Figure 14b shows a good 1:1 fit line between the experimental and simulation results and an NSE value of 0.93, indicating an acceptable prediction by the HP model. tween 12 and 7 °C. Figure 14b shows a good 1:1 fit line between the experimental and simulation results and an NSE value of 0.93, indicating an acceptable prediction by the HP model. Figure 15 shows the daily average COPs values between the experimental and model results. The analysis was carried out for the period 1 Jul to 31 August 2021. The average seasonal value of the COP over the complete analysis period was 2.9. The maximum COP deviation between the experimental and simulated results was 0.8. The simulated value was smooth over the analysis time, while a few outliers were observed in the experimentally calculated values owing to the sensitivity of the water sensor to the sudden change in the water temperature. The overall validation results indicate that the results are within the manufacturer's data range.  We further calculated the electric consumption of the HP over every hour of its operation. Figure 16a presents the electric consumption of the HP in the cooling mode with an ambient temperature for two days. The results are presented for the period when the HP was operated for 24 h. A short time period was selected, as the HP function did not change throughout the analysis period. The results showed that at peak operating conditions, the maximum power consumption of the HP was approximately 22 KW during the day, when maximum cooling was required, and 10 kW at night, when less cooling was required. The electricity consumption showed a linear trend with the ambient air temperature. In Figure 16b, which depicts the linear relationship between both the parameters of the HP, an R 2 value of 0.90 confirmed the trend.  Figure 15 shows the daily average COPs values between the experimental and model results. The analysis was carried out for the period 1 July to 31 August 2021. The average seasonal value of the COP over the complete analysis period was 2.9. The maximum COP deviation between the experimental and simulated results was 0.8. The simulated value was smooth over the analysis time, while a few outliers were observed in the experimentally calculated values owing to the sensitivity of the water sensor to the sudden change in the water temperature. The overall validation results indicate that the results are within the manufacturer's data range. Jun, 2021 concerning the outlet water temperature of the HP. The normal operation of the HP in the cooling mode was repeated daily; therefore, only one month of analysis results are presented here. The results show that the HP produces water with temperatures between 12 and 7 °C. Figure 14b shows a good 1:1 fit line between the experimental and simulation results and an NSE value of 0.93, indicating an acceptable prediction by the HP model. Figure 15 shows the daily average COPs values between the experimental and model results. The analysis was carried out for the period 1 Jul to 31 August 2021. The average seasonal value of the COP over the complete analysis period was 2.9. The maximum COP deviation between the experimental and simulated results was 0.8. The simulated value was smooth over the analysis time, while a few outliers were observed in the experimentally calculated values owing to the sensitivity of the water sensor to the sudden change in the water temperature. The overall validation results indicate that the results are within the manufacturer's data range.  We further calculated the electric consumption of the HP over every hour of its operation. Figure 16a presents the electric consumption of the HP in the cooling mode with an ambient temperature for two days. The results are presented for the period when the HP was operated for 24 h. A short time period was selected, as the HP function did not change throughout the analysis period. The results showed that at peak operating conditions, the maximum power consumption of the HP was approximately 22 KW during the day, when maximum cooling was required, and 10 kW at night, when less cooling was required. The electricity consumption showed a linear trend with the ambient air temperature. In Figure 16b, which depicts the linear relationship between both the parameters of the HP, an R 2 value of 0.90 confirmed the trend. We further calculated the electric consumption of the HP over every hour of its operation. Figure 16a presents the electric consumption of the HP in the cooling mode with an ambient temperature for two days. The results are presented for the period when the HP was operated for 24 h. A short time period was selected, as the HP function did not change throughout the analysis period. The results showed that at peak operating conditions, the maximum power consumption of the HP was approximately 22 KW during the day, when maximum cooling was required, and 10 kW at night, when less cooling was required. The electricity consumption showed a linear trend with the ambient air temperature. In Figure 16b, which depicts the linear relationship between both the parameters of the HP, an R 2 value of 0.90 confirmed the trend.  Figure 17 shows the simulation model output for the temperature of the water supply and its return to the ST from the greenhouse and HP. The results are shown for the period 1-10 August 2021. A longer duration was not required as the operation is repetitive. The results indicate that the difference between the greenhouse supply and return temperatures was 6 °C, with a maximum flow rate of 4500 Lhr −1 , while the HP supply and return temperatures were less than 2 °C, and the flow rate of water was 42,000 Lhr −1 . The results show that the proposed model can simulate the entire system and estimate the energy supply.
Considering the outcomes of this study, the proposed model has the potential to evaluate AWHP systems along with water storage tanks integrated with multi-span greenhouses. This work promotes and advances the development of work towards the use of renewable energy sources in greenhouse farming and maximizes the related economic benefit by increasing the profitability of greenhouse farming. In a future study, we will apply the model under different weather conditions to establish a feasible way of increasing the COP to achieve sustainability in greenhouse farming.

Conclusions
In this study, an experimentally validated BES model of an AWHP and a water ST was proposed to satisfy the cooling energy requirements of a three-span greenhouse. The  Figure 17 shows the simulation model output for the temperature of the water supply and its return to the ST from the greenhouse and HP. The results are shown for the period 1-10 August 2021. A longer duration was not required as the operation is repetitive. The results indicate that the difference between the greenhouse supply and return temperatures was 6 • C, with a maximum flow rate of 4500 Lhr −1 , while the HP supply and return temperatures were less than 2 • C, and the flow rate of water was 42,000 Lhr −1 . The results show that the proposed model can simulate the entire system and estimate the energy supply.  Figure 17 shows the simulation model output for the temperature of the water supply and its return to the ST from the greenhouse and HP. The results are shown for the period 1-10 August 2021. A longer duration was not required as the operation is repetitive. The results indicate that the difference between the greenhouse supply and return temperatures was 6 °C, with a maximum flow rate of 4500 Lhr −1 , while the HP supply and return temperatures were less than 2 °C, and the flow rate of water was 42,000 Lhr −1 . The results show that the proposed model can simulate the entire system and estimate the energy supply.
Considering the outcomes of this study, the proposed model has the potential to evaluate AWHP systems along with water storage tanks integrated with multi-span greenhouses. This work promotes and advances the development of work towards the use of renewable energy sources in greenhouse farming and maximizes the related economic benefit by increasing the profitability of greenhouse farming. In a future study, we will apply the model under different weather conditions to establish a feasible way of increasing the COP to achieve sustainability in greenhouse farming.

Conclusions
In this study, an experimentally validated BES model of an AWHP and a water ST was proposed to satisfy the cooling energy requirements of a three-span greenhouse. The Considering the outcomes of this study, the proposed model has the potential to evaluate AWHP systems along with water storage tanks integrated with multi-span greenhouses. This work promotes and advances the development of work towards the use of renewable energy sources in greenhouse farming and maximizes the related economic benefit by increasing the profitability of greenhouse farming. In a future study, we will apply the model under different weather conditions to establish a feasible way of increasing the COP to achieve sustainability in greenhouse farming.

Conclusions
In this study, an experimentally validated BES model of an AWHP and a water ST was proposed to satisfy the cooling energy requirements of a three-span greenhouse. The proposed model was validated by comparing its computational results with the experimen-tal results. Furthermore, the performance of the BES model was confirmed using the NSE coefficient. The results of this study are detailed below.

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The validation results for the cooling energy supplied to the greenhouse showed NES values of 0.87, 0.87, 0.85, and 0.86, for June, July, August, and September, respectively.

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The validation results for the air temperature inside the greenhouse showed NES values of 0.81, 0.67, 0.82, and 0.76, for June, July, August, and September, respectively. • The observed R 2 values of the experimental and simulated cooling loads compared with solar radiation were 0.83 and 79, respectively. • The observed R 2 values of the experimental and simulated cooling loads compared with the outside air temperature were 0.39 and 35, respectively. • The R 2 results demonstrate that the cooling load is more dependent on solar radiation rather than the outside air temperature. Moreover, the R 2 value of the simulated data was more accurate than that of the experimental data, which could be due to a prediction error relating to the water temperature and flowrate sensors and the high predictive power of the simulation model.

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The results concerning the power of the HP and FCU revealed that the HP has the potential to supply more energy. To utilize the HP's energy fully, the number of FCUs or the capacity of the FCU should be increased.

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The results for the daily average COP value of the HP during the extreme hot months of July and August showed a good correlation, with an overall average COP of 2.9. • A data sheet used to calculate the cooling capacity is provided for the HP model (PSET-C60W-MIDEA). In addition, data file for the cooling performance of the AWHP, which is a necessary input to the simulation model, is also provided.
Overall, the simulation results correlate well with the experimental results. The high NSE values reveal the high predictive power of the model. The proposed model can be used for optimizing the control strategies and capacities of the equipment (e.g., the HP, FCU, and area of the greenhouse) so that the overall system can be improved. Detailed information on each step has been provided to enable engineers, researchers, and consultants to adapt the model for their specific needs. The prediction of the maximum cooling energy demand under local weather conditions will help individuals to decide on the capacities of the system's components, including the heat pump, fan coil units, water storage tank, and circulation pump. Moreover, the AWHP simulation model can aid in the search for a feasible way to increase the COP.  Pressure difference at height z (pa) 1−>2 Flow direction from one air node to another (-) I Total radiation of horizontal surface (kJ·h −1 ·m −2 ) I d Diffuse radiation of horizontal surface (kJ·h −1 ·m −2 ) kt Clearness index (-) T amb Ambient temperature ( • C) rh Relative humidity (%) I T Total radiation on tilted surface (kJ·h −1 ·m −2 ) I bT Beam radiation on tilted surface (kJ·h −1 ·m −2 ) I gT Ground reflected radiation on tilted surface (kJ·h −1 ·m −2 ) I dT Diffuse radiation on tilted surface (kJ·h −1 ·m −2 ) T sky Sky temperature ( • C) C cover Cloudiness factor of sky (-) T water, out Temperature of HP water output ( • C) T water, in Temperature of HP water input ( • C) · q water Energy drawn by water (kJ·h −1 ) m water Water flowrate (kg·h −1 ) m 12 Air mass flow rate from one zone to another (kg·h −1 ) T air, fan Enthalpy of exiting air (kJ·kg −1 ) h air, mix Enthalpy of air mixing (kJ·kg −1 ) q air, fan Energy drawn by fan (kJ·h −1 ) m air, fan Mass flowrate of air leaving the fan (kg·h −1 ) Greek Symbols σ Stephen-Boltzmann constant (W·m −2 ·k −1 ) ε Long-wave emissivity (-) ρ (z) Air Table A1 lists the cooling performance data file used as an input to the simulation. The data sheet provided by the manufacturer, including the testing conditions of the HP (in the cooling mode) is listed in Table A2.