# An Analytical Approach for Sustainable Greenhouse Heating in Lebanon: A Focus on Air Source Heat Pumps

Loubna Khaled, Rabih Dib, Bakri Abdulhay, Nazih Moubayed

► To cite this version:

Loubna Khaled, Rabih Dib, Bakri Abdulhay, Nazih Moubayed. An Analytical Approach for Sustainable Greenhouse Heating in Lebanon: A Focus on Air Source Heat Pumps. Journal of Physics: Conference Series, 2024, 2857 (1), pp.012021. 10.1088/1742-6596/2857/1/012021. hal-04748328

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Submitted on 10 Feb 2025

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# An Analytical Approach for Sustainable
Greenhouse Heating in Lebanon: A Focus on Air
Source Heat Pumps

To cite this article: Loubna Khaled et al 2024 *J. Phys.: Conf. Ser.* 2857 012021

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# An Analytical Approach for Sustainable Greenhouse Heating in Lebanon: A Focus on Air Source Heat Pumps

Loubna Khaled¹, Rabih Dib¹, Bakri Abdulhay²,³ and Nazih Moubayed¹.

¹ Laboratoire de recherche LaRGES, Faculty of Engineering, Lebanese University, Tripoli, Lebanon

² Laboratoire de recherche CERADE, Equipe GRINEEC, ESAIP La Salle – Angers – France.

³ Nantes Université, CNRS, Laboratoire de Thermique et Energie, LTeN, UMR6607, F-44000 Nantes – France.

Loubna.Khaled@st.ul.edu.lb, rabih.dib@ul.edu.lb, babdulhay@esaip.org, Nazih.Moubayed@ul.edu.lb

**Abstract.** In Lebanon, where economic challenges and Mediterranean climate dominate, protected cultivation methods, such as greenhouses, are widely used for sustainable agriculture. Tomatoes, with an annual production of around 250,000 tons in Lebanon, are the focus of this study. Tomato leaves require a temperature range of (18-25°C) for optimal growth. The present study explores the potential of air-source heat pumps as a sustainable heating method. It includes a comprehensive literature review and discusses alternative heating methods. A dynamic energy model was developed after using statistical models to plot the temperature and solar radiation profiles for the worst-case scenario for heating. This energy model sizes the heat pump to maintain 18 °C in a standard 332 m² Quonset greenhouse with thermal polyethylene covering. The model's validity was demonstrated by comparing its temperature profiles with a study conducted in West Bengal, India. The results indicate the adequate size for the studied case is 16 kW. Sensitivity analysis showed the required power for different temperature settings (12–18°C) and the effect of wind speed by analyzing the heat transfer coefficient of the cover, which doubled the power when the heat transfer coefficient increased from 4 to 10 W/m².K.

**Keywords:** Sustainable heating, Air source heat pump, Dynamic energy modelling, Leaf temperature, Sensitivity analysis, Agriculture sustainability.

## 1. Introduction

As a result of economic hardship and climate change, protected cultivation methods, such as greenhouses, have gained considerable significance in regions like Lebanon. To meet the needs of an increasing population, sector production must be increased and made more secure. Given their local consumption, tomatoes, and cucumbers have been harvested in greenhouses for several years. Therefore, the main advantages of protective cultivation are ensuring consistent crop production throughout the year and the implementation of a strategic practice of crop rotation. It is the timely rotation of different

<figure><img src="image_5.png" /></figure>
crops in the same greenhouse space. This practice is essential for several reasons. The main reason is to ensure the needed time to treat the internal environment from specific diseases and insects that affect tomatoes while not affecting cucumbers. For instance, the Tomato Yellow Leaf Curl Virus (TYLCV) predominantly targets tomatoes but does not pose a threat to cucumbers [1]. Crops require a specific range of temperatures and operating conditions to be maintained in the greenhouse to guarantee proper growth and productivity [2]. This temperature range should be set between 18 and 25°C for tomatoes and cucumbers [3], which requires heating systems in greenhouses.

In the greenhouse industry, heating costs, which exceed 70% of total expenses excluding labor [4], have increased the search for more cost-effective alternatives to burning fuel and coal. Several alternative methods for greenhouse heating have been investigated in the last decades to reduce the reliance on conventional fossil fuels and support the wave of sustainability.

The first is passive solar heating where greenhouses are designed to maximize the capture of solar energy during the day, reducing the need for additional heating. This method includes thermal control systems with high thermal mass like water storage, rock bed, and phase change materials (PCM) [5,6,7]. These materials absorb and slowly release heat. The main drawback of materials like PCM is the low thermal conductivity and the high cost of fabrication [8] and for the water storage is the limited available space [9].

The second method is biomass heating systems, utilizing organic materials such as woodchips [10], sawdust, or agriculture waste [11] as fuel sources. A study was done in China, using the corncob as the biomass for the heating system in the greenhouse, they calculated the annual heating cost based on the price of the ton of corncob to be around 2$/m² [12]. The main issue with this alternative is that wood biomass boilers tend to produce more particulate matter and ash emissions than other fossil fuel-based heating systems [13].

The active solar heating system is the third alternative to the conventional fuel-burning method. These systems use solar collectors to harness solar energy, which is then converted into heat for the greenhouse [14]. A study done in Morocco proved that using this technology can increase the productivity of tomatoes by around 55% in winter [15]. One disadvantage of using active solar heating systems is their reliance on sunny conditions to be effective. In regions with frequent cloud cover or during periods of extended bad weather, the solar collectors may not capture enough energy to heat the greenhouse.

Recently, heat pumps have gained attention as a sustainable alternative to conventional heating methods. This technology extracts heat from sources like outside air, geothermal energy, or waste heat from industrial processes [16,17]. The extracted heat is transferred to the location of the heating. The efficiency of the heat pump is referred to by the coefficient of performance (COP) which is the ratio of heat delivered to power needed. This coefficient is higher than 3 for air source heat pumps [18], which indicates its superior performance to boils and heaters. Heat pumps are typically categorized into two primary types based on the medium they use for heat exchange: Air Source Heat Pumps (ASHP) and Ground Source Heat Pumps (GSHP) [19]. GSHP might excel in performance [20] but due to its complexity and the availability of the ASHP in the studied area, the chosen system for this study is the ASHP. A key feature of ASHP is enabling the operation of a single system for an extended period without the need for two systems, this is because of its ability to operate in reversible mode, which permits heating in the winter and cooling in the summer.

Performing an energy balance in the greenhouse is necessary to ensure the sizing procedure. The energy balance should include all heat exchange phenomena between the inside air of the greenhouse and its surroundings. A European study conducted a simple energy balance limited by using the average values for temperature and solar radiation [21]. This limitation would not give a dynamic analysis of the heat demand variation in the greenhouse. Another study was done without considering crop transpiration, which is an important factor for calculating the heating load of a tomato greenhouse [22].

It is observed that the literature primarily focuses on European and other countries, highlighting the need for research to be conducted in Lebanon. The literature also lacks a dynamic energy model that considers almost all real-life heat exchange phenomena, like plant transpiration with
a corresponding leaf temperature model. This research will consider selecting the appropriate heat pump sizing for heating the standard Quonset greenhouse with a 332 m² area, 3m height, and thermal polyethylene cover (TPE) from MasterPAK, in Lebanon.

The process starts with computing the average daily temperature fluctuation over the year. Then, the temperature and solar radiation profiles are defined for the worst case of heating. The study encompasses a dynamic energy balance defining the various heat exchange phenomena affecting the air in the greenhouse. A model for computing the leaf temperature to greenhouse conditions is developed and validated. Finally, the results for the power needed are presented to accurately determine the proper sizing of the heat pump according to the needs of farmers or companies and the different outside wind conditions.

## 2. Methodology

### 2.1. Introduction

The heat required to maintain an adequate temperature and humidity depends on several parameters that vary throughout the day and from day to day during the year. Besides external conditions, such as outdoor temperature, humidity, solar radiation, and wind speed, the heating load needed from the heat pump must be significantly influenced by plant transpiration and its interaction with the listed parameters.

Choosing the right size for the heat pump is crucial to ensure optimal performance and energy efficiency. Using an undersized heat pump (HP) could have detrimental effects on both economic and environmental performance. This occurs because the system may rely more on electric resistive heating to meet the heat demand [23]. Likewise, an oversized HP can result in higher capital costs and wasted heat due to cycling on and off frequently [24]. In addition to the impact on energy efficiency, the wrong size can also affect the productivity of the plants by causing plants to stress and dry in case of excessive heating. The right size will require the identification of the worst-case scenario in heating mode which is the coldest day of the year.

### 2.2. Identification of the worst-case scenario

The significance of computing the daily average temperature of Lebanon lies in determining the worst-case scenario for the heating system, which is the day with the lowest average temperature. Given the similar climate of Cyprus and Lebanon, equation (1) can be employed for average daily temperature predictions, as this model has been tested and validated across 27 European countries [21]. Table 1 contains the values from the literature to complete the computation of the equation.

$$T_i = T_{mean} - \Delta T \cos \frac{2\pi (i - d_{t0})}{365} \quad (1)$$

$T_i$ is the daily average ambient temperature during day i in °C; $T_{mean}$ is the annual average ambient temperature in °C; $\Delta T$ is the annual ambient temperature variation in °C; i the number of the day of the year (i = 1, ..., 365); $d_{t0}$ the day of the year with the lowest temperature value. With January being the month with the lowest average temperature [25], and the 23rd of January historically recorded as the coldest day, $d_{t0}$ is considered as the 23rd of January.

<table><caption>**Table 1.** Temperature Values for Lebanon.</caption><thead><tr><td>Parameter</td><td>Value from literature</td></tr></thead><tbody><tr><td>$T_{mean}$</td><td>22.13°C [26]</td></tr><tr><td>$\Delta T$</td><td>15.19°C [25]</td></tr><tr><td>$d_{t0}$</td><td>23</td></tr></tbody></table>
## 2.3. Solar radiation and temperature profiles

The hourly global radiation is essential to compute the dynamic solar radiation transmitted to the greenhouse. The ASHRAE model is used to calculate it on the horizontal surface on a clear day [27].

It is necessary to calculate the temperature at various points throughout the day to construct a dynamic model that accurately reflects temperature fluctuations. The chosen model, presented by equations (2), (3) and (4) was selected for its simplicity and accuracy in delivering temperature readings at each hour of the day [28].

$$T_{(t)} = T_m - T_a \cos \left( \frac{\pi(t_{rise} - t)}{24 - t_{peak} + t_{rise}} \right) \quad \text{for } 0 < t \le t_{rise} \quad (2)$$

$$T_{(t)} = T_m - T_a \cos \left( \frac{\pi(t_{peak} - t)}{t_{peak} - t_{rise}} \right) \quad \text{for } t_{rise} < t \le t_{peak} \quad (3)$$

$$T_{(t)} = T_m - T_a \cos \left( \frac{\pi(24 + t_{rise} - t)}{24 - t_{peak} + t_{rise}} \right) \quad \text{for } t_{peak} < t \le 24 \quad (4)$$

Where $T_{(t)}$ is the temperature at the time t, $T_m$ is the average temperature on this day calculated by equation (1), $T_a$ is the temperature variation in Lebanon is 3.5°C, $t_{rise}$ is the sunrise hour which is 7 am in winter, and $t_{peak}$ in the hour of maximum temperature in the day which is at 1 pm.

## 2.4. Dynamic energy model of the greenhouse

### 2.4.1. Energy balance on the greenhouse

The studied architecture is the Quonset standard unit, with the geometric variables presented in Figure 1. The energy balance model considers the greenhouse as a control volume and evaluates the heat gains and losses illustrated in Figure 2. This model's main objective is to provide a comprehensive and data-driven method for managing the thermal environment of a greenhouse. It is possible to describe the basic approach of balancing gains and losses phenomena in equation (5) to maintain a stable environment for the plants within the greenhouse.

<figure><img src="image_6.png" /><figcaption>Figure 1. Quonset structure of greenhouse with A=8m, B=41.5m, and H=3m.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 2. Energy balance on the greenhouse.</figcaption></figure>

$$Q_{solar} + Q_{heating} = Q_{conv1} + Q_{conv2} + Q_{vent} + Q_{plants} \quad (5)$$

$Q_{solar}$ is the solar heat gain (equation (6)), $Q_{heating}$ is the mechanical heat from the heat pump or heating load, $Q_{conv1}$ is the convection loss with outside air (equation (7)), $Q_{conv2}$ is the convection loss with the ground (equation (8)), $Q_{vent}$ is the loss due to ventilation (equation (9)), and $Q_{plants}$ is the loss due to plants transpiration (equation (10)).
$$Q_{solar} = \tau_{cover}SA_g \qquad (6)$$

$\tau_{cover}$ is the transmittance of the thermal polyethylene cover (TPE), $S$ is the solar radiation, and $A_g$ area of the ground (332 m²).

$$Q_{conv1} = U_c A_c (T_{required} - T_i) \qquad (7)$$

$U_c$ is the heat transfer coefficient of the cover (TPE), $A_c = \frac{\pi}{2}(A \times B) + \frac{\pi}{4}A^2$ is the surface area of the cover, $T_{required}$ is the temperature inside the greenhouse (18°C), and $T_i$ is the ambient temperature calculated in equations (2), (3) and (4).

$$Q_{conv2} = U_g A_g (T_{required} - T_{surface}) \qquad (8)$$

$U_g$ is the heat transfer coefficient of the ground which depends on the depth, $T_{surface}$ is the temperature of the ground's surface.

To calculate the temperature of the surface of the ground, an energy balance must be applied to the ground where the heat obtained by the ground should be equal to the heat dissipated, in the mean of this case study, the heat convection between the inside air of the greenhouse and the surface of the ground must be equal to the conduction between the surface of the ground where $x=0$ and a certain thickness that has a known temperature. The expression in the steady state condition of the conduction thermal energy in the ground is presented in equation (8-a).

$$-\frac{k}{l} \times A_g \times \frac{\partial T}{\partial x_{x=0}} = \frac{k}{l} A_g (T_{x=0} - T_{x=l}) \qquad (8-a)$$

$k$ is the soil thermal conductivity, $l$ is the thickness of the ground (depth) which will be considered as 0.5 m for this study, $T_{x=0}$ is the temperature of the ground's surface ($T_{surface}$), and $T_{x=l}$ is the temperature of the ground at the desired thickness $l$.

A study done in Greece examined the correlation between air and ground temperature for different depth values to find the ground temperature [29]. It could be used for the studied case because this correlation is valid for a temperature range between 5 and 25 °C which is the case for Lebanon in Winter. At 0.5 m depth, the correlation is described in the equation (8-b).

$$T_{ground} = -0.0116 \times T_{air}^2 + 1.4289 \times T_{air} - 0.3515, R^2 = 0.9892 \qquad (8-b)$$

$T_{ground}$ is the temperature of the ground at 0.5 m depth ($T_{x=l}$) and $T_{air}$ is the temperature of ambient air computed in equations (2), (3), and (4).

$$Q_{vent} = NH\rho C_p (T_{required} - T_i) \qquad (9)$$

$N$ is the ventilation rate, $H$ is the height of the greenhouse, $\rho$ is the density of air, and $C_p$ is the specific heat capacity at constant pressure of air.

$$Q_{plants} = \frac{\lambda \rho \in I_{LA}}{P_{atm}} \left( \frac{e(T_L)^* - e_o}{r_s + r_a} \right) \qquad (10)$$

$\lambda$ is the latent heat of vaporization, $I_{LA}$ is the leaf index area (leaf area per unit ground area), $\epsilon$ is the ratio of molecular weight of water vapor to dry air (0.622), $P_{atm}$ is the atmospheric pressure, $e(T_L)^*$ is the saturated water vapor pressure at leaf temperature $T_L$ (modelled in the next section), expressed in equation (10-a) [30], $e_o$ is the actual water vapor pressure at the required temperature $T_{required}$ and relative humidity RH, $r_s$ the stomatal resistance defined in equation (10-b) [31], and $r_a$ is the aerodynamic resistance presented in equation (10-c) [32].

$$e^*(T) = \exp(25.317 - \frac{5144}{T + 273.15}) \qquad (10-a)$$
$$r_s = 200\left(1 + \frac{1}{\exp(0.05(S - 50))}\right) \qquad (10-b)$$

$$r_a = 305 \left( \frac{\sqrt{LA}}{U_i} \right)^{0.5} \qquad (10-c)$$

$\overline{LA}$ is the average area of the leaf, and $U_i$ is the internal air speed.

### 2.4.2. Energy balance of the leaf

It is essential to model the leaf's temperature to complete the transpiration model's computation. Referring to the second edition of the book “An Introduction to Environmental Biophysics” [33], The leaf temperature is determined by doing an energy budget on the leaf as illustrated in Figure 3.

<figure><img src="image_8.png" /><figcaption>Figure 3. Energy budget on the leaf.</figcaption></figure>

The energy balance equation on the leaf, neglecting heat storage and metabolic heat production, is presented in equation (11) with the different heat transfer phenomena affecting the leaf temperature.

$$R_{abs} = R_{emitted} + H + L \qquad (11)$$

$R_{abs}$ is the absorbed radiation by the leaf, $R_{emitted}$ is the emitted radiation by the leaf (equation (12)), $H$ is the sensible heat loss which is the convective heat transfer between the leaf and the ambient air (equation (13)), and $L$ is the latent heat (equation (14)).

The absorbed radiation $R_{abs}$ depends on the absorptivity of the studied crop, which is tomatoes. A study was done to determine the amount of solar radiation absorbed by the leaf after the transmission from several cover materials [34]. One of the studied materials is thermal polyethylene (TPE) which is commonly used and available in Lebanon. The measured value of the flux absorbed by the tomato leaf is about 80% of the solar radiation transmitted by the cover material.

$$R_{emitted} = \varepsilon_s \sigma T_L^4 \approx \varepsilon_s \sigma T_a^4 + 4\varepsilon_s \sigma T_a^3 (T_L - T_a) \qquad (12)$$

$\varepsilon_s$ is the emissivity of the leaf, $\sigma$ is the Stefan-Boltzmann constant, $T_L$ is the leaf temperature, and $T_a$ is the temperature around the leaf which is the $T_{required}$ in the greenhouse, 18°C. Note that a binomial expansion was performed on the equation.

$$H = G_A C_p (T_L - T_a) \qquad (13)$$

$G_A$ is the leaf boundary layer conductance representing the heat transfer coefficient of convection on leaf surfaces [35].
$$L = \lambda g_v \frac{e(T_L)^* - e(T_a)}{P_{atm}} \qquad (14)$$

$g_v$ is the vapor conductance of the leaf, which is the average surface and boundary conductance of the leaf, The term $e(T_L)^* - e(T_a)$ can be approximated by the Penman transformation in equation (14-a).

$$e(T_L)^* - e(T_a) = e(T_L)^* - e(T_a) + e(T_a)^* - e(T_a)^* \approx \delta(T_a)(T_L - T_a) + D(T_a) \qquad (14-a)$$

$\delta(T)$ is the slope of the saturation water vapor pressure curve [33] defined in equation (14-b), and $D(T_a)$ pressure deficit. The equation of latent heat can be developed as in equation (14-c).

$$\delta(T) = \frac{17.502 * 240.97 * e^*(T)}{(240.97 + T)^2} \qquad (14-b)$$

$$L = \lambda g_v \frac{\delta(T_a)(T_L - T_a) + D(T_a)}{P_{atm}} \qquad (14-c)$$

The final model for predicting the leaf temperature according to ambient conditions is expressed in equation (15).

$$T_L = T_a + \frac{R_{abs} - \varepsilon_s \sigma T_a^4 - \lambda g_v \frac{D(T_a)}{P_{atm}}}{4\varepsilon_s \sigma T_a^3 + G_A C_p \rho + \lambda g_v \frac{\delta(T_a)}{P_{atm}}} \qquad (15)$$

### 2.4.3. Heating load and power requirement

The heating load or the thermal requirements of the modelled greenhouse for heating ($Q_{heating}$) during a given day can be determined using equation (16). This equation must be applied to the coldest day of the year to specify the maximum heating needed to keep the greenhouse at 18°C in winter for optimum growth. This quantity will translate to the required heat from the heat pump.

$$Q_{heating} = \max(Q_{vent} + Q_{plants} + Q_{conv2} + Q_{conv1} - Q_{solar}, 0) \qquad (16)$$

The needed power by the heat pump for delivering the heating demands in the coldest scenario of the year is presented in equation (17).

$$Power = \frac{Q_{heating}}{COP} \qquad (17)$$

COP is the coefficient of performance for the heat pump, which is currently set at 3.5, will be the focus of this study. This value was determined through a specific simulation that will be discussed in future research.

## 3. Leaf temperature model validation

In this section, results for the leaf temperature model defined in equation (14), are compared with those of a study conducted in West Bengal, India, focusing on the temperature profiles within the greenhouse, particularly the leaf temperature [36]. After assigning the present model with region-specific variables and plotting the data for temperature and solar radiation, we compare calculated parameters from the model to the findings of the referenced study, as illustrated in Figure 4.
<figure><img src="image_9.png" /><figcaption>**Figure 4.** Comparison between (a) the study results in West Bengal, India [36], and (b) the results of equations (2), (3), (4), and (14) for the greenhouse and leaf temperature profiles in the same area.</figcaption></figure>

It can be observed that the shape of the temperature profiles is very similar between the two studies. Early in the morning, the leaf temperature is slightly lower than the greenhouse's air temperature in both models. Then between 7 am and 10 am, the temperatures are the same. At noon when the temperature inside the greenhouse is 27°C, the leaf temperature is less than the air temperature by 2°C in the study so 25°C, but in our model, the difference is 1°C with the value of 26°C. In the rest of the day, both temperatures decrease with the same pace in the 2 studies. The small difference, which does not exceed the 5% margin, between the study's findings and our model might be due to the 75% relative humidity parameter in our model. Overall, our model aligns with the study's findings, proving its relative accuracy in the simulation.
**4. Results and discussion**

Figure 5 presents the results of the predictive model employed in equation (1), plotting the variation of the average daily temperature in Lebanon throughout the year. It can be identified that the 23rd of January presents the most unfavourable circumstances, with an average temperature of 7.13°C. the ambient temperature and solar radiation profiles for this day are illustrated in Figure 6, providing insight into the day's fluctuating conditions. This is done to ensure proper heating and the importance of adjusting the dimensions of the heat pump to suit this day's conditions.

<figure><img src="image_10.png" /><figcaption>**Figure 5.** Average daily temperature variation over the year in Lebanon.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 6.** Conditions for the 23rd of January: (a) temperature and (b) solar radiation profiles.</figcaption></figure>

Table 2 contains the necessary variables for this analysis. As a perspective, sensitivity studies will include some variables to assess their impact on the system's performance. Figure 7 shows the power demand of the heat pump, which correlates with the appropriate size needed. It can be noticed that, at midday, the solar radiation surpasses the greenhouse's losses, eliminating the need for heat pump intervention. Based on these findings, it is recommended that a heat pump with a capacity of around 16 kW be installed to maintain the ideal temperature of 18 °C for optimal tomato growth in the standard Quonset unit of 332 m² while accounting for a safety margin.
<table><caption>**Table 2.** Variables to complete the model.</caption><thead><tr><th>Variable</th><th>Value</th><th>Variable</th><th>Value</th><th>Variable</th><th>Value</th></tr></thead><tbody><tr><td>Transmittance of the cover <i>τ</i><sub>cover</sub></td><td>0.91</td><td>Ground thickness <i>l</i></td><td>0.5 m</td><td>Emissivity of leaf <i>ε</i><sub>s</sub></td><td>0.98[38]</td></tr><tr><td>Surface area of the cover <i>A</i><sub>c</sub></td><td>571 m<sup>2</sup></td><td>Thermal conductivity of soil <i>k</i></td><td>1.9 W/m.K [37]</td><td>Ventilation rate <i>N</i></td><td>2/hr</td></tr><tr><td>Heat transfer coefficient of cover <i>U</i><sub>c</sub></td><td>4 W/m<sup>2</sup>.K</td><td>Heat transfer coefficient of ground <i>U</i><sub>g</sub></td><td>4.26 W/m<sup>2</sup>.K</td><td>Leaf index area <i>I</i><sub>LA</sub></td><td>3.5</td></tr><tr><td>Internal air speed <i>U</i><sub>i</sub></td><td>0.1 m/s</td><td>Average leaf area <i>LA</i></td><td>300 cm<sup>2</sup></td><td>Latent heat of vaporization <i>λ</i></td><td>2.45 MJ/Kg</td></tr><tr><td>Boundary layer conductance <i>G</i><sub>A</sub></td><td>1.5 cm/s [35]</td><td>Vapor conductance <i>g</i><sub>v</sub></td><td>0.3 mol/m<sup>2</sup>.s</td><td>Relative humidity <i>RH</i></td><td>75%</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>**Figure 7.** Power needed to maintain the greenhouse at 18°C on the 23rd of January.</figcaption></figure>

The sensitivity analysis results on the required temperature and the heat transfer coefficient of the cover are presented in Figure 8. The first section is the variation in the heat pump's power to maintain the range of operating temperatures suggested by some companies, spanning between 12 and 18°C. 12°C is the smallest temperature to maintain an acceptable crop growth with some losses in productivity. Comparing the results for different temperatures, it is evident that the required size for maintaining a temperature of 12°C is smaller than that of 18°C. The final decision depends on the company's objectives and the financial investment they are willing to make. Selecting the size for 12°C will decrease the cost of the heat pump, but on the other hand, it will result in losses in productivity, taste, and the size of the cultivated crops.

The second part of the sensitivity analysis is the heat transfer coefficient of the greenhouse cover, which is highly dependent on wind speed outside the greenhouse. The study investigates the Uc range of [4-10] with a step of 2 W/m².K. The figure shows the significant difference between 4 and 10 W/m².K to be roughly double. However, the studied coefficient typically remains under 6, even in the worst-case scenario in Lebanon.
<figure><img src="image_13.png" /><figcaption>**Figure 8.** Results for the sensitivity analysis: (a) the power needed for different T\_required, and (b) the power needed for different Uc on Day 23.</figcaption></figure>

The finding of this study underlines the importance of using heat pumps as a sustainable heating method in agriculture. For instance, the 16-kW needed for the studied system will be equivalent to using 56 kW of heat (16\*3.5). Using conventional techniques like heaters and boilers to deliver this amount would lead to a high cost and environmental impact. The air source heat pump technology, known for its versatility in reversible mode, provides both winter heating and summer cooling, making it an excellent choice for year-round climate control in greenhouses. This feature helps decrease the carbon footprint and reduce the system's operational cost, leading to more sustainable agricultural practices. Optimizing the performance of this system can be done by using renewable energies to power the heat pump or incorporating a heat recovery system in case of using diesel engines. Multi-objective optimization can enhance the system's efficiency and ensure optimal performance by evaluating the importance of the various parameters listed in Table 2 in the sizing procedure.

**5. Conclusion**

This study considers the importance of incorporating sustainable heating methods for tomato greenhouses in countries experiencing economic difficulties and environmental challenges, such as Lebanon. The research examines alternative heating techniques for burning fuel and creates a dynamic energy model to highlight the potential of air-source heat pumps. The model was validated with a study done in India to increase its reliability. Results suggest that heat pumps offer a feasible option for greenhouse heating while reducing costs and environmental impact in the case of using renewable energy sources or even incorporating heat recovery mechanisms for the used engine. A 16-kW capacity heat pump is needed to maintain the Quonset greenhouse of 332 m² of unit area, 3 m of height, and a TPE cover, at 18°C on the coldest day of the year. The sensitivity studies show the significance of variables such as the required temperature and heat transfer coefficient of the cover on the heat pump's power. Further work will consider using a reversible heat pump for heating and cooling instead. Along with additional sensitivity studies and comparisons between common architectures, exploring the various operating strategies to optimize the system's performance and advancements in the agricultural and food security fields will be a major goal for further studies.

**Acknowledgments**

We sincerely thank Prof Salem Hayyar (Department of Agriculture, Lebanese University) for assisting with case selection. Special thanks go to the CEO and COO of the company Robinson, Lebanon for their support.
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