Introduction

Solar energy is an important source of sustainable and environmentally friendly energy (Salah et al. 2021a). There are various ways to benefit from solar energy (Elnaggar et al. 2019). Photovoltaic (PV) is the most common method of generating electricity from solar radiation. Different factors affect the amount of received solar irradiance at the collector surface, i.e., location, specific time and day of the year, tilt angle, and the angle of incidence of the solar radiation. Among these factors, the tilt angle is the most important because the correct choice of tilt angle enables the collector to receive the maximum amount of radiation (Handoyo et al. 2013). However, it is well-known that the overall efficiency of PV-based solar-power conversion is very low, and its enhancement is an ongoing research challenge. One way to tackle this issue is to use an integrated solar-thermal collector (PVT) to harness solar radiation to produce simultaneously electrical and thermal energy. Obviously, the PVT technique would be promising in locations where, in addition to electricity, there is a considerable scope for the direct thermal energy utilization such as water heating. Accordingly, the Gaza strip of Palestine has been chosen for the present research. Gaza Strip is exposed daily to an average solar ration of 6 kWh/m2 at tilt angle of 31°. According to Palestinian households energy survey (July 2013), 62% of household in Palestinian are using solar energy for heating the water which is equivalent to 600 GWh annually (~ 100 million $) (Elnaggar et al. 2019).

In the literature, there are several studies dealing with the search for the optimal value of the tilt angle of PV systems. Hussein et al. (Hussein et al. 2004) investigate the effects of tilt angle and orientation of PV panels on the achievement of solar modules in Cairo, Egypt. Their result indicates that the maximum energy gained by PV panels occurs when the panels have tilt angle between 20 and 30° and facing the south direction. In addition, it is fine-tuned toward the west. Several studies have indicated the tilt angle substantial effect on the amount of received solar radiation (Hailu and Fung 2019; Jamil et al. 2016; Tang et al. 2009; Yunus Khan et al. 2020). Some studies suggested that the PV system tilt angle to be the same as the site latitude (Bari 2000; Benghanem 2011). In a study performed in Canada, researchers used isotropic and anisotropic diffuse sky radiation models to determine the optimum tilt angle (Hailu and Fung 2019). They recommended adapting the tilt angle value for four times a year to collect the most of solar radiation. In another study, researcher used automated solar water heating system to continuously provide hot water above a specific chosen temperature (Sadrin et al. 2009). The system works such that when the solar water heater failed to reach above the assigned temperature, the heating will be through the electric water heater. They claimed that the proposed system provides hot water using solar system 80% of the time and rest is covered by electric water heater.

In continuation of efforts for exploring green sources for power generation, Ampuno et al. (2021) studied solar parabolic thermal power generation plant model. The system is simulated using TRNSYS software and validated by MATLAB. The novelty of the work conducted by Ampuno et al. (2021) is the imitation of the entire solar collector model in terms of field and power conversion system which accomplished by enabling variation of outlet oil temperature and oil flow through decent valves. Their results showed a larger annual solar thermal energy of 2450 GJ obtained in island San Cristobal compared to 1080 GJ in Guayaquil and 1700 GJ in Manta.

The solar collectors optimum tilt angle differs at different geographical location due to longitude and latitude. All the related studies focused on areas such as Beirut (Lebanon) (Makarem et al. 2016; Sakkal et al. 1993), Surabaya (Indonesia) (Handoyo and Ichsani 2013), Cairo (Egypt) (Hussein et al. 2004), Toronto (Canada) (Hailu and Fung 2019), Malaysia (Bari 2000), Basrah (Iraq) (Saraf and Hamad 1988), Tabass (Iran) (Khorasanizadeh et al. 2014), Madinah (Saudi Arabia) (Benghanem 2011), and India (Jamil et al. 2016). Although the flat-plate solar-water heating system is used to heat water in Gaza Strip since a long time, there is a lack in studies that focus on determining the tilt angle optimal value. In previous studies, the optimal angles were determined as a function of the amount of solar radiation falling on the solar collector.

Accordingly, this study differs from previous studies by providing a comprehensive evaluation covers optimum energy gain, cost benefit, and environmental impacts from solar water heater at optimum conditions, in Palestine. To perform the calculation, two software programs are used to perform the simulation of the data which are Transient System Simulation Tool (TRNSYS) to calculate the useful solar energy obtained from the flat-plate collector and the Design-Expert software (DOE) with Response Surface Methodology (RSM) which is utilized to obtain the optimal tilt angle as mentioned in materials and methods section.Thus, this study aims to:

  1. (1)

    Determine the optimal angles for the solar systems used in Gaza, Palestine, that produce maximum value of the useful energy gain (Qu) through the solar collector. The present study pays attention for the losses through the collector from radiation such as collector, efficiency factor, and fin efficiency.

  2. (2)

    Analyze the economic benefits and potential use of the investigated solar water heater in Gaza by considering greenhouse gases emission reduction, cost benefit analysis, and payback period. This information is equally important for public, investors, and decision makers.

Materials and methods

Location of current study

Gaza strip, Palestine, is chosen for the current study. Gaza Strip lays on the east of the Mediterranean coast with latitude of 31.5° N and longitude of 34.47° E (De Meij et al. 2016; Elnaggar et al. 2017). Figure 1 shows that during May, June, July, and August, the average sun radiation reaches Gaza by month is above 200 kWh/m2.

Fig. 1
figure 1

Monthly average diffuse and global radiations for Gaza (Elnaggar et al. 2019)

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Useful gained energy using flat-plate collector

In solar water heating, the solar thermal collector (heat exchanger) is the core of the system, which converts solar energy into internal energy of the transport layer (Demirbas 2005). In this study, a flat-plate collector with gross area (Aa) equals 5 m2 was used. In order to calculate solar thermal collector efficiency (η), the Hottel-Whillier equation (Duffie and Beckman 2013) (Eq. 1) is used (Ji et al. 2014; TRNSYS16 2004).

$$\eta = \frac{{Q_{{\text{u}}} }}{{AI_{{\text{T}}} }} = \frac{{\dot{m}C_{{{\text{pf}}}} \left( {\dot{T}_{{\text{o}}} - T_{i} } \right)}}{{AI_{{\text{T}}} }}$$
(1)

where Qu (kJ) is the usable energy gain, IT (kJ/h-m2) is the global radiation incident on the titled solar collector, A (m2) is the gross area of the collector, m2 (kg/h) is the flow rate under operating conditions, Cpf (kJ/kg-K) is the specific heat of the collector fluid, and To and Ti (°C) are the inlet and outlet temperatures of the fluid into the collector. In an array of a number of Ns modules, the energy of each module is represented by the Hottel-Whillier equation (Eq. 2) (TRNSYS16 2004):

$$\dot{Q}_{{\text{u}}} = \frac{A}{{N_{{\text{s}}} }}\mathop \sum \limits_{j = 1}^{{{\text{N}}_{{\text{s}}} }} F_{{{\text{R}} \cdot j}} \left( {I_{{\text{T}}} \left( {\tau \alpha } \right) - U_{{{\text{L}} \cdot j}} \left( {T_{i \cdot j} - T_{{\text{a}}} } \right)} \right)$$
(2)

where τα is the transmittance (τ)-absorptance (α) product, UL is the overall heat loss coefficient, j is the module number, Ta (°C) is Ambient (air) temperature, and FR is the collector heat removal factor defined as in Eq. 3.

$$F_{{{\text{R}}.j}} = \frac{{N_{{\text{s}}} \dot{m}_{{\text{c}}} C_{{{\text{pc}}}} }}{{AU_{{{\text{L}},j}} }}\left( {1 - {\text{exp}}\left( { - \frac{{F^{\prime}U_{{{\text{L}},j}} A}}{{N_{{\text{s}}} \dot{m}_{{\text{c}}} C_{{{\text{pc}}}} }}} \right)} \right)$$
(3)

where F' is the fin efficiency factor and Cpc is (kJ/kg-K) is specific heat of collector. The complexity of the loss coefficient (UL,j) is due to its dependence on the collector construction and its operating conditions. An approximate value of UL,j (kJ/h-m2-K) is given in Eq. 4 (Klein 1975):

$$U_{{{\text{L}},j}} = \frac{3.6}{{\frac{{N_{{\text{G}}} }}{{\frac{C}{{T_{{{\text{P}}.j}} }}\left[ {\frac{{\left( {T_{{{\text{avg}}}} - T_{{\text{a}}} } \right)}}{{N_{{\text{G}}} + F}}} \right]^{.33} + \frac{1}{{h_{{\text{w}}} }}}}}} + \frac{{3.6 \sigma \left( {\left( {T_{{{\text{avg}}}}^{2} - T_{{\text{a}}}^{2} } \right)\left( {T_{{{\text{avg}}}} - T_{{\text{a}}} } \right)} \right)}}{{\frac{1}{{\varepsilon p + .05 N_{{\text{G}}} \left( {1 - \varepsilon p} \right)}} + \frac{{2N_{{\text{G}}} + f - 1}}{\varepsilon g} - N_{{\text{G}}} }}$$
(4)

where NG is number of glass cover, Tavg is average collector fluid temperature, Convection coefficient of wind hw = 5.7 + 3.8 W (W/m2-K), W (m/s) is mean wind velocity, f = (l − 0.04 hw + 0.0005 hw2) (l + 0.091 NG) and c = 365.9 (l − 0.00883 β + 0.0001298 β2) where β is tilt angle. The value of τα is defined in Eq. 5.

$$\tau \alpha = \frac{{I_{{{\text{bT}}}} \left( {\tau \alpha } \right)_{{\text{b}}} + Id\frac{{\left( {1 + \cos \beta } \right)}}{2}\left( {\tau \alpha } \right)_{{\text{s}}} + \rho I\frac{{\left( {1 - \cos \beta } \right)}}{2}\left( {\tau \alpha } \right)_{{\text{g}}} }}{{I_{{\text{T}}} }}$$
(5)

where IbT is beam radiation incident on the solar collector, Id is diffuse horizontal radiation, I is global horizontal radiation, (τα)s, (τα)b, and (τα)g are product for sky diffuse radiation, for beam radiation depending on the incidence angle θ, and for ground reflected radiation, respectively. Their values are found using function routine. The outlet temperature (To,j) of one module and the inlet to the next module (Ti,j) are given as:

$${\text{T}}_{{{\text{o}},{\text{j}}}} = \frac{{AF_{{{\text{R}},j}} \left( {I_{{\text{T}}} \left( {\tau \alpha } \right) - U_{{{\text{L}},j}} \left( {T_{i.j} - T_{{\text{a}}} } \right)} \right)}}{{N_{{\text{s}}} \dot{m}_{{\text{c}}} C_{{{\text{pc}}}} }} + T_{i}$$
(6)

When collector flow equals zero, the value of the collector stagnation temperature (Tp) is given in Eq. 7.

$${\text{T}}_{{\text{P}}} = \frac{{I_{{\text{T}}} \left( {\tau \alpha } \right)}}{{U_{{\text{L}}} }} + T_{{\text{a}}}$$
(7)

For the definitions of all variables in Eqs. (1–7), please see Nomenclature table.

Solar thermal collector tilt angle

Figure 2 displays the parameters that affect the quantity of yearly solar radiation that hits the solar collector, i.e., the sun site in the sky. When the solar panel is horizontally placed (at β = 0), the incidence angle (θ) will equal the sun zenith angle (θz) which varies between 0 and 90°. At normal incidence, that is, the solar radiation strikes the surface of the solar panel at θz = 0, and solar panel will receive maximum amount of radiation. The tilt angle is an important parameter for acquiring the utmost solar radiation by solar panel which mainly relies on the location of the sun that varies daily, monthly, and yearly. To obtain maximum solar radiation, researchers try to optimize the values of tilt and incidence angle of solar collectors. For example, researchers work to minimize incidence angle of beam radiation by tracking the sun (Handoyo and Ichsani 2013; Yadav and Chandel 2013).

Fig. 2
figure 2

Solar collector tilt angle (β) and the surface incidence angle (θ)

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Modeling using TRNSYS

TRNSYS program to obtain the monthly maximum Qu of the solar collector at different angles of inclination and incidence. The months of October, January, April, and July were selected to represent the seasons of Autumn, Winter, Spring, and Summer, respectively. The proposed solar-water-heating system model was analyzed using TRNSYS program, that is, a trustworthy tool used for solar energy applications. The designed model comprised three main parts: a storage tank, a flat-plate collector, and a pump. The TRNSYS model has the following components in its library (Fig. 3):

  • Weather Data reading and processing (Type 109-TMY2)

  • Flat-plate collector (Type 73) with total surface area of 5 m2

  • Storage tank (Type 4)

  • Pump (Type 3b)

  • Differential Controller w_Hysteresis (Type 2b)

  • Plotter (Type 26)

  • output\Printer (Type 25c)

Fig. 3
figure 3

TRNSYS model of solar water heating system (Extracted from TRNSYS software)

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Experimental layout and statistical analysis

The statistical analysis using DOE software is done using RSM which known for optimizing functioning parameters (Baş and Boyacı 2007; Elnaggar et al. 2013). RSM evaluates the dependence of the useful energy gain (Qu) on the incidence and tilt angles. Moreover, it has been used to obtain the optimal values of the operating variables. The software DOE is used to determine the optimal value for the angle of inclination. Each independent variable (the angle of incidence (A) and the angle of inclination (B) were changed to three levels: low (− 1), medium (0), and high (+ 1), as shown in Fig. 4. The levels of the independent variables depend on the results of the first simulations.

Fig. 4
figure 4

Level of functional variables

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Benefit analysis of SWH

Figure 5 shows a simple model developed particularly for the financial evaluation of solar water heating system. The model includes the key inputs for calculating the potential benefits of solar water heating system in Gaza, and employing this information to assess the cost, benefits, and the return of investment of SWH in Gaza. Table 1 presents the specification of SWH and energy benefits.

Fig. 5
figure 5

Key information for modeling the cost–benefit, and payback period of a solar water heating system in Gaza

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Table 1 Specification of SWH and energy benefit
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Pollutant emissions based on different energy sources

Table 2 exhibits the emission factors (indicators) of the individual energy sources as well as the measurement of the energy source in the electricity production mix in Palestine 2018. The emissions of air impurities resulted from the combustion of fossil fuels such as coal, oil, and natural gas for electricity generation depend primarily on the type of energy source used. It was reported that different sources contain different quantities of emissions or their mixtures (Saidur et al. 2007).

Table 2 Air emission factors based on various energy sources. Data sources: (Jing et al. 2015)
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The benefit was evaluated by considering the solar radiation in Palestine and energy harvesting by the proposed solar water heating system that comprises cost reduction and saving via replacing fossil fuels by renewal low-cost solar energy and emissions reduction.

Cost savings from replacing non renewable energy sources

Expenditure saving from replacing energy sources was projected based on the quantity of energy supplied and the associated costs. In this study, the energy replaced is electricity, and the unit price equals 0.17 $/kWh. The expenditure saved by replacing energy was computed using Eqs. 8 (Jing et al. 2015):

$${\text{CBE}} = {\text{BE}} \times P$$
(8)

where BE = total energy cut, kWh; CBE = cost savings from switching energy source, $; P = unit price of switched energy, $/kWh.

Cost savings from pollution reduction

The cost that can be saved by reducing gas emissions can be estimated by the reduction in the amount of air pollutants emitted after the use of the solar boiler and the associated cost of treating these contaminants. Jing et al. (2015) highlighted that the expenses for treating 1000 kg of CO2, NOx and SOx is approx. $ 20, $ 674.5, and $ 656.5, respectively. The cost conserving by gas emission reductions was assessed by Eq. 9–10:

$${\text{BP}}_{{\text{p,f}}} = {\text{BE}} \times {\text{EF}}_{{\text{p,f}}} \times {\text{PE}}_{{\text{f}}}$$
(9)
$${\text{CBP}}_{{\text{f}}} = \mathop \sum \limits_{{\text{p}}} \left( {{\text{BP}}_{{\text{p,f}}} \times {\text{TE}}_{{\text{p}}} } \right)$$
(10)

where EFp,f = emission factor of pollutant p by energy source f, kg/kWh; PEf = percentage of energy source f in the energy mix; BPp,f = quantity of emissions p that are decreasing (e.g., CO2, NOx and SOx) if solar. water heater avoids using electricity produced by energy source f, kg; CBPf = avoided cost of treating greenhouse gas and air pollutant emissions if SWH avoids using electricity from combustible fuels f, $; TEp = unit price of treating pollutant p, $/kg. The two values EFp,f and PEp are given in Table 1.

Study to analyze the total cost of a solar water heating system

Because the economical profit of solar water heating system was valued every year, the necessary capital and operational costs were correspondingly anticipated per year for the payback analysis afterward. Table 3 presents the cost of solar water collectors in Gaza which was adopted in this study to estimate the potential saving once replaced the electric water heater.

Table 3 Cost of solar water Panel in Gaza
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Payback period analysis

The reimbursement duration is the period needed after using solar water heater to regain its financial investment. The payback period was calculated by looking into and comparing both annual cost and benefit over certain duration. In this study, the annual cost for each working year was assessed taking into consideration the capital and operatorial cost. Concerning the economic profit, it was evaluated mainly based on the energy cost saved per year.

Results and discussion

Flat-plate collector useful gained energy

The assumed values of the flat-plate collector parameters (Fig. 6) are applied into the TRNSYS program such as the solar collector area is 5 m2, collector fin efficiency factor of 88% and number of covers of 1.

Fig. 6
figure 6

Values of flat-plate collector parameters used to run TRNSYS software

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Based on these parameters, TRNSYS program has been running, and each time the values of the functional parameters (A and B) are changed to get the Qu by 5 m2 area of flat-plate solar collector and data were recorded.

The months January, April, July, and October were selected to exemplify the seasons of the year Winter, Spring, Summer, and Autumn, respectively. The lowest useful energy was recorded in January, while the maximum useful energy was recorded in July. It is noted also from Fig. 7 that both angles have a noteworthy effect on harvesting the useful gained energy. In July, it is noticed that the value of Qu increases with the decrease in the tilt and incidence angles, as the maximum value Qu reaches 588.08 kWh at tilt angle and incidence angle of 20° and 0°, respectively, whereas in January, the value of Qu increases with the increase in the tilt angle on condition of decrease in incidence angle as the highest value of Qu in January equals 223.20 kWh at the tilt angle of 50° and the angle incidence angle of 0°. In April, the highest value of Qu is 480.88 kWh at the tilt angle of 20° and the angle incidence angle of 0°. In October, the highest value of Qu equals 485.49 kWh at the tilt angle of 35° and 0° incidence angle. In general, the smaller the incidence angle leads to increase useful energy in all months of the year, while the tilt angle varies in each month to obtain the largest useful energy. Therefore, to solve this entanglement and overlap, the authors used the DOE software tool with (RSM) to achieve the optimal tilt angles for each season of the year.

Fig. 7
figure 7

Monthly average Qu (kWh) at various vales of incidence and tilt angles

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Analysis of variance (ANOVA)

Table 4 shows the analysis of variance of the regression parameters of the predictive quadratic response surface paradigm. As can be seen from Table 4, the F value of the model for Qu of 32.77 means that the model is significant. For January, the P-value for the model is equal to 0.0001(˂0.05) which shows the significance of the presented model terms. In the present case, the terms A, B, AB, A2 and B2 are the significant terms of model. Similarly, the models for Qu calculations are repeated for April (Table 5), July (Table 6), and October (Table 7). As shown in Tables 5, 6 and 7, the P-values are also less than 0.05 which confirms that terms of model A, B, AB, A2, and B2 are also a significant term of the presented model. On the other hand, the P-values for the month of July are greater than 0.1, which mean that the model terms such as B2 are not significant. Therefore, B2 was excluded to obtain a better model for July.

Table 4 Winter ANOVA quadratic model
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Table 5 Spring ANOVA quadratic model
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Table 6 Summer ANOVA quadratic model
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Table 7 Autumn ANOVA quadratic model
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In order to foresee the average monthly useful energy gain, the response surface model is created which has been considered feasible. The final regression models for each winter, fall, spring, and summer are mathematically presented in the second-order polynomial in Eqs. (11, 12, 13, and 14), respectively.

$${\text{Q}}_{{\text{u}}} = 186.9469 + 0.588048A + 1.69084B - 0.00833AB - 0.01227A^{2} - 0.02024B^{2}$$
(11)
$${\text{Q}}_{{\text{u}}} = 455.0281 - 0.10478A + 2.39287B + 0.013603AB - 0.02111A^{2} - 0.04853B^{2}$$
(12)
$${\text{Q}}_{{\text{u}}} = 610.4899 + 0.904408A - 0.93539B - 0.00911AB - 0.02588B^{2}$$
(13)
$${\text{Q}}_{{\text{u}}} = 369.162 - 0.00164A + 1.48526B - 0.0078411AB - 0.01757A^{2} - 0.02992B^{2}$$
(14)

where Qu is useful energy gained by collector in kWh unit, A is incidence angle in degree unit and B is tilt angle in degree unit. The equations are expressed in terms of actual factors to see the direct relations between different factors and the useful gained energy and to forecast the response for specified altitudes of each factor.

Useful energy gained by the collector dependence on tilt and incidence angle

Equations 11, 12, 13, and 14 are numerically analyzed to envisage the effect of the operating variables which are the incidence and the tilt angles on the average monthly Qu. The three-dimensional figures (Figs. 8, 9, 10 and 11) are the products of the DOE software tool with RSM, and they show the influence of the tilt angle (B) and incidence angle (A) on the useful energy gain (Qu). Results clearly shown that a considerable effect on harvesting the useful energy gained from solar collector by the tilt and incidence angles.

Fig. 8
figure 8

Winter Qu as a function of tilt and incidence angles

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Fig. 9
figure 9

Spring Qu as a function of tilt and incidence angles

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Fig. 10
figure 10

Summer Qu as a function of tilt and incidence angles

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Fig. 11
figure 11

Autumn Qu as a function of tilt angle and incidence angles

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The useful energy from the solar collector in January is shown in Fig. 8. The figure clarifies the effect of tilt and incidence angles on the useful energy from the solar collector in January that mainly representing the winter season. It is noticed from Fig. 8 that the useful energy increases when the angle of incidence ranges from 0° to 12°, after which the descent begins. In addition, the highest possible obtained energy during winter season reaches about 223.52 kWh for the tilt angle ranging between 32 and 50°.

Figure 9 displays the useful energy gained by solar collector as a function of tilt and incidence angles in April, which represents spring season. It is noticed from Fig. 9 that the useful energy increases when the incidence angle is less than 14°. For angles greater than 14°, the useful energy gained decreases. Meanwhile, during the spring season, it is found that the highest possible obtained energy reaches an about of 484.6 kWh at the tilt angle ranging between 0 and 32°.

July (which represents the summer season in this study) is one of the months with the highest useful energy of the year. This is because the sun is in the sky the most hours per day in July, reaching more than 13 h in Gaza. Moreover, the ambient temperature reaches 32 degrees, and the sky is clear and cloudless. As shown in Fig. 10, the useful energy obtained increases when the inclination and incidence angles decrease, since the maximum value of Qu reaches 596.56 kWh when the inclination angle is 20°, and the incidence angle is less than 12°

Figure 11 shows the useful energy gained by solar collector as a function of tilt and incidence angles in October, which represents autumn season. Figure 11 shows that the maximum useful energy gained at the incidence angle of 12° and the tilt angle of 32° reaches 386.51 kWh.

Optimization

For achieving the optimal tilt angle of the solar collector, DOE software with RSM, which is useful and dedicated tool, was used. To get accurate and realistic optimal tilt angle, the tilt angle is related to the incidence angle, and the optimum angles at which the maximum useful energy were adopted. Figure 12 shows the tilt angles for the four seasons, respectively, and the maximum useful energy obtained. It is also noticeable from Fig. 12 that the optimum incidence angle is relatively stable during the seasons of the year, which are small values ranging from 10 to 12°.

Fig. 12
figure 12

Collector gained useful energy with the optimum incidence seasonal tilt and incidence angles

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Figure 12 displays that the values of the incidence angle is stable and small around 10–12° throughout the seasons to obtain the maximum useful energy. However, optimal tilt angles varies with seasons. It is found that in the summer season represented by the month of July in which it has a high temperature, the optimal tilt angle is small around 20°, whereas during the winter season represented by January where the temperature going low, the optimal tilt angle is relatively high around 39.57°.

A study compared the solar collector optimized tilt angle for Gaza city in Palestine with the same results for Madinah city in Saudi Arabia which is presented as shown in Fig. 13 (Benghanem 2011). The results had revealed that the tilt angle is homogeneous in both cities in all months. Furthermore, it is noted that the tilt angle for Gaza is slightly larger than the tilt angle for the city of Madinah. This is because the ambient temperature in Madinah city is higher than in Gaza city.

Fig. 13
figure 13

Comparison between the values of optimal tilt angles between Gaza, Palestine and Madinah, Saudi Arabia

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The daily average Qu at the optimal tilt angle for January, April, July, and October is presented Table 8. It clearly noticed from the shown data that utmost useful energy is produced during July where its value can reach 21.83 kWh in the day. It also can be found from Table 8 that during the month of January, the harvested amount of useful energy is minimal.

Table 8 Daily average Qu by flat-plate collector (5 m2) at optimum tilt angle
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Table 8 also reveals that the value of Qu in the first day of January is the smallest and equals 1.544 kWh. This can be explained because the first day of January was rainy or cloudy, and the sun did not rise except for very limited periods. At the optimum tilt angle, the total of the daily Qu by the collector for January, April, July, and October is 812,498 kJ (225.69 kWh), 1,733,604 kJ (481.56 kWh), 2,157,837 kJ (599.40 kWh), and 1,390,281 kJ (386.19 kWh), as shown in bold in Table 8 and Fig. 14.

Fig. 14
figure 14

Average monthly Qu by the collector at optimum tilt angle for each season

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Figure 15 displays the daily distribution of useful energy obtained from a flat-plate collector (5 m2) at an optimal tilt angle for January, April, July, and October. Figure 15 is a graphical representation of the values presented in Table 6. It was observed that the useful energy of April exceeded that of July on the 29th day, which could be due to the difference in climate on that day in these two months.

Fig. 15
figure 15

Daily distribution of useful energy earned by flat-plate collector (5 m2) at optimum tilt angle for January, April, July, and October

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The monthly average Qu for each optimal tilt angle for all of the year is demonstrated as shown in Table 9. It clearly noticed from the obtained data that utmost useful energy in all of the year was produced at the optimal tilt angle of 32.2° where its value can reach 18,168,728 kJ/yr (5046.87 kWh/yr). The minimum value of the yearly useful energy was 17,857,296 kJ (4960.36 kWh) at the optimal tilt angle of 39.57°. The maximum values of the monthly average Qu for each optimal tilt angle in kWh is shown in bold in Table 9.

Table 9 Monthly average useful energy gained by flat-plate collector (5 m2) for each optimum tilt angle
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Figure 16 shows the yearly useful energy gained by the collector for each optimum tilt angle where its value can reach 17,888,685 kJ, 18,129,492 kJ, 18,168,728 kJ, and 17,857,296 kJ at the optimum tilt angles of 20.15°, 26.72°, 32.2°, and 39.57°, respectively.

Fig. 16
figure 16

Yearly useful energy gained by the collector for each optimum tilt angle in kJ

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Benefit analysis of solar water heating system

The revenue of employing a solar water heating system was evaluated depending on the total quantity of energy that produced by SWH including profit by swapping energy sources and pollution reduction. It was found that each solar panel (5 m2) has the capability to provide electricity to 12 capitals (heating water) continuously in Gaza and thus replace the dependency on the current non-renewable, non-reliable, and costly sources. Table 3 lists the solar panel cost and specification.

Cost saving by replacing energy source

In Gaza, nearly all of the building appliances consume electricity generated from non-renewable imported fossil fuels for operation (Salah et al. 2021b). By utilization of solar energy, reduction in energy cost, emission can be achieved. Cost saving by changing energy source was estimated by Pan et al. (2012), depending on the quantity of energy generated and its expenses once swap electricity with solar energy.

As given in Table 9, the useful energy of 5046.87 kWh/yr can be produced at the optimal tilt angle of 32.2°. It also can provide hot water to 12 persons. Consequently, a conventional solar water heater can avoid spending around $857.87 of energy fee per year, which is equal to $71.5 each month. This is a potential cost-effective benefit to the community, especially for low-income households, as it can reduce the financial inconvenience caused by electricity bills.

Cost saving through air emissions reduction.

Since the solar water heater does not consume electrical energy for its daily operation, substituting electricity generated from fossil fuels with solar one will result in indirect reduction in the GHGs emissions (Jing et al. 2015; Salah et al. 2021a). Total expenses reduction due to the decrease in air pollutants emissions when consuming solar heater system and the expenses of treating those air impurities was assessed by Eq. 2 and Eq. 3. Table 2 introduces the emission factors of electricity production in Palestine and the share of each energy source in electricity production mix in 2018. As exemplified in Table 2, the emission factor for CO2 from the main energy sources is considerably more than other impurities; this means that electricity generation generally releases more carbon dioxide than other pollutants. Hence, the use of solar energy has the highest CO2 emission reduction followed by SO2 and NOx. Taking into consideration the approximate fee for treating 1 metric ton of CO2, NOx, and SO2 as $20, $674.5, and $656.5, the expenses prevented due to the reduce in GHGs emissions are given in Table 10. As given in Table 10, each solar unit can help to avoid electricity power produced from fossil fuels can save $11.33 of treating cost per year.

Table 10 Pollutant emissions reduction in Gaza per year per solar unit
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Cost analysis and payback period

The investment cost commonly consists of initial installation cost, operational cost including energy consumption, and maintenance expense. Solar water heating systems do not incur energy costs; therefore, the total investment cost is composed of the initial cost of the solar system installation and the maintenance cost (Ali et al. 2009). To ensure high productivity of SWH, solar heating systems need to be maintained once a year. Thus, it is important to determine the entire servicing and repairing cost for each year of operation. Figure 17 compares the cumulative costs of SWH versus EWH for 15 years. Solar water heaters which can be operated effectively for a longer duration have a lower annual cost than those operated for a shorter operating year. As longer operating interval means that the investment cost can be obtain back over longer period of time, it is crucial to ensure that the solar heating system can operate for as long as possible, or it will not be cost effective. In this research, the payback period of the investment for a SWH in Gaza was performed and reported. The economic benefits can recoup the relatively high initial investment cost for solar water heating system, through savings in electrical energy expenditures. Environmental benefit is not measured as a cost to the solar water heating system, as it is the funds reimbursed by the industry or government for treating those impurities discharged throughout electricity production. Normally, the payback period of the investment can be checked by comparing the costs and benefits of solar water heating systems. To calculate the payback period of the investment, the curves of annual cost and annual profit were constructed. The payback period of the investment corresponds to the working year in which the curves of annual cost and annual profit intersect. As shown in Fig. 17, the yearly cost of the solar water heater reduced considerably with the year of operation at the same time as the annual benefit increases with the year of operation; and the payback period is the year of operation in which the curves of year where the annual cost and annual benefit intersect. The estimated time for return of investment in a solar water heating system was 3.4 years.

Fig. 17
figure 17

Annual cost analysis for SWH versus EWH in Gaza

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Conclusion

The energy sector in Palestine is highly dependent on imports from other countries to meet the scarcity of energy supply, which mainly derived from fossil fuels. One possible alternative to reduce the use of fossil fuels utilization and ecological challenges is to use solar water heating systems instead of electric water heaters.

The effect of the title angle and incidence angle on the useful gained energy by PVT is studied and simulated for four seasons. Two programs are used to perform the simulations. The useful solar energy obtained by the flat-plate collector was calculated using TRNSYS program, while RSM was applied to optimize the tilt angle. In the study, the dependent variable is the useful energy, and the independent variables are the title and incidence angles. The study result indicates that both tilt and incidence angles are important factor that affect the maximum value of gained useful energy. It is also shown that optimal tilt angle changes its value according to the seasons and/or the months of the year. It is also found that incidence angle is hardly changes with seasons with small value that varies between 10 and 12° to obtain maximum gained useful energy. Though this occurs for small period of time, energy is gained during the rest of the day. But this work is concerned on maximum energy. The found maximum average useful values gained energy by PVT are 225.69 kWh, 481.56 kWh, 599.40 kWh, 386.19 kWh at optimal title angles values are 39.57°, 26.72°, 20.15°, and 32.2° for Winter, Spring, Summer, and Autumn, correspondingly. Also, the result exposes that the utilization of a standard solar water system can save up to $857.87 of energy cost per year. The payback on the investment in a solar water heating system in Gaza is 3.4 years. The results confirmed that replacing of electrical water heating system by solar water heating system is promising and in line with the United Nations Sustainable Development Goals as it can contribute to energy security, economic growth, and sustainable environment.