Introduction

In Ethiopia, especially in Fogera District in Amhara regional state, agricultural vegetable products like onion, potato and tomato share the biggest part of the country’s economy (Wassie. 2016). About 80–90% of the population life depends on vegetable agriculture products (ILRI 2005). Existing evidence shows that vegetable production still does not meet the need of the population, although the production of crops such as onion, tomato and potato is increased from year to year. According to Fogera Agricultural office 2017 report, about 216,788-ton of tomato was produced per year in Fogera District. From this, more than half (55%) of the products had been lost during post-harvest processes. Similarly, 3,661,312.5 ton of onion is produced per year and from this 47% would be lost during post-harvest processes and 122,862.5-ton potato is produced per year and from this 32.3% would be lost during post-harvest processes (Appendix A). The lack of appropriate preservation and storage systems caused considerable losses and reduced the vegetable supply significantly (Karim 2004).

Drying is one of the most prevailing methods of food preservation (Mustayen et al. 2014), where the moisture is removed preventing the growth of microorganisms that causes food damage (Marketing of vegetables thesis first draft). It is also a process which combined heat and mass transfer, where the surface moisture is removed first and the moisture from the interior is forced to move to the surface, which is then removed later (I. S. U. N. Drying 2006). Traditionally, the local farmers utilize open sun drying system which may be responsible for the mentioned large post-harvest loss (Solar Dryer with V-Groove Solar 2013). Therefore, utilization of technology to reduce the post-harvest loss is essential. This can be done by using solar dryer technology. This technology is unique in that the developed dryer has better turbulence effect which helps to remove the hot humidity of the drying system at each tray thereby to improve the preservation of the vegetables such as potato, tomato, and onion.

Solar dryer technology is a cost effective and feasible approached in minimizing the harvest loss and increasing the quality of the products (Soundy and Brutsch 2014, unpublished data). Using this solar vegetable drying technology is also crucial to yield high-quality marketable products which in turn can improve the economic situation of the farmers, assuring food security by minimizing vegetable product loss (Akpinar 2010).The performance of the solar dryer is significantly dependent on the weather condition. Solar dryers located in Fogera District area used solar energy to remove the moisture contained from the product. Therefore, the weather conditions have the biggest influence on the capacity of drying products that can be dried at a certain time. Then measurements of radiation components require expensive equipment that is costly to operate as well as maintain, reliable measurements are undertaken at only a limited number of stations. The solar radiation data can be used as an input variable of solar vegetable dryers. The effects of weather condition data as sources of the solar vegetable dryer before the experimental tests were recording temperature, horizontal radiation and drying humidity and summarized in Table 2 (Appendix B). Thus, data show before the experimental test that is similar to atmospheric condition. During the experimental test (at the loaded condition), the air temperature in the drying chamber, the relative humidity of drying chamber and solar radiation on solar collectors vary between 30 and 72 °C, 8–11% and 485–1165 W/m2, respectively.

Results and discussion

Result of energy analysis

As shown in Figs. 1 , 2 and 3 variations of the energy utilization ratio during the experimental test of tomato, potato and onion were calculated using Eqs. (9). The analysis was conducted depending on the drying chamber flow air temperature as a function of drying time. Moreover, as drying time decreased the energy utilization ratio slightly increased with an increase in drying air temperature. The energy utilization ratio of tomato varied between 4.8 and 19.9% on the first day at drying air temperature of 45 °C, 3.4% to 26.0%, on the second day at drying air temperature of 60 °C and 3.1% to 12.9% on the third day at drying air temperature of 65 °C as shown in Fig. 1.

Fig. 1
figure 1

Variation of energy utilization ratio in drying chamber as a function of drying time of tomato

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Fig. 2
figure 2

Variation of energy utilization ratio in drying chamber as a function of drying time of potato

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Fig. 3
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Variation of energy utilization ratio in drying chamber as a function of drying time of onion

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The energy utilization ratio of potato varied between 4.1 and 19.4% on the first day at drying air temperature of 55.9 °C, 7.4% to 45.6% on the second day at drying air temperature of 57.9 °C and 3.9 to 21.6% on the third day at drying air temperature of 55.3 °C as shown in Fig. 2.

Similarly, the energy utilization ratio of onion varied between 5.2 and 14.5% on the first day at drying air temperature of 39 °C, 6.5% to 26.6% on the second day at drying air temperature of 41.9 °C, 11.8% to 23.5% onion on the third day at drying air temperature of 61.3 °C and 8.3% to 37.4% on the fourth day at drying air temperature of 62.2 °C as shown in Fig. 3.

Result of exergy analysis

Figures 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13 illustrate the maximum and minimum values of exergy inflow, exergy outflow, and exergy losses of the drying chamber at each tray. The rate of exergy inflow as calculated from Eqs. (11) depends on the ambient and inlet air temperature of the drying chamber. The exergy inflow of the first tray was constant since the inlet temperature drying air in the drying chamber and the ambient temperature was kept constant. The exergy inflow of tomato in the drying chamber varied between 0.188 and 1.355 kJ/kg tomato on the first day, 0.331 kJ/kg to 1.21 kJ/kg tomato on the second day and 0.28 kJ/kg to 1.981 kJ/kg tomato on the third day depending on the experimental condition of slices of tomato. The rate of exergy outflow as calculated from Eq. (12) relied on the ambient and outlet air temperature of the drying chamber. The exergy outflow of tomato in the drying chamber varied between 0.165 and 1.240 kJ/kg tomato on the first day, and 0.22 kJ/kg to 1.1134 kJ/kg tomato on the second day, and 0.221 kJ/kg to 1.960 kJ/kg tomato on the third day depending on the experimental test of tomato.

Fig. 4
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Exergy as a function of drying time (1st day) tomato

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Fig. 5
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Exergy as a function of drying time (2nd day) tomato

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Fig. 6
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Exergy as a function of time (3rd day) tomato

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Fig. 7
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Exergy as a function drying time (1st day) potato

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Fig. 8
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Exergy as a function drying time (2nd day) potato

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Fig. 9
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Exergy as a function drying time (3rd day) potato

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Fig. 10
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Exergy as a function drying time (1st day) onion

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Fig. 11
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Exergy as a function drying time (2nd day) onion

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Fig. 12
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Exergy as a function drying time (3rd day) onion

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Fig. 13
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Exergy as a function drying time (4th day) onion

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As shown in Figs. 7, 8 and 9, the exergy inflow of potato in the drying chamber varied between 0.187 and 1.987 kJ/kg potato on the first day, 0.41 kJ/kg to 1.49 kJ/kg potato on the second day, 0.35 kJ/kg to 1.511 kJ/kg potato on the third day depending on the experimental test of slices of potato. The exergy outflow of potato in the drying chamber varied between 0.181 and 1.915 kJ/kg potato on the first day, 0.303 kJ/kg to 1.470 kJ/kg potato on the second day and 0.320 kJ/kg to 1.382 kJ/kg potato on the third day depending on the experimental test of slices of potato. In addition, the exergy loss of potato in drying chamber varied between 0.06 and 0.158 kJ/kg potatoes on the first day, 0.02 kJ/kg to 0.236 kJ/kg potatoes on the second day, and 0.012 kJ/kg to 0.19 kJ/kg potatoes on the third day depending on the experimental condition of slices of potato.

Figures 10, 11, 12 and 13 illustrate that the exergy inflow of onion in the drying chamber varied between 0.277 and 1.471 kJ/kg onion on the first day, 0.231 kJ/kg to 0.562 kJ/kg onion on the second day, 0.261 kJ/kg to 1.068 kJ/kg onion on the third day and 0.22 kJ/kg to 1.416 kJ/kg on the fourth day. The exergy outflow of onion in the drying chamber varied between from 0.196 to 1.241 kJ/kg onion on the first day, 0.170 kJ/kg to 0.469 kJ/kg onion on the second day, 0.184 kJ/kg to 0.814 kJ/kg onion on the third day, and 0.172 kJ/kg to 1.283 kJ/kg on the fourth day. Besides, it depends on the experimental condition of onion. And also, the exergy loss of onion in the drying chamber varied between 0.067 kJ/kg to 0.23 kJ/kg onion on the first day, 0.001 kJ/kg to 0.170 kJ/kg onion on the second day, 0.045 kJ/kg to 0.189 kJ/kg onion on the third day, and 0.012 kJ/kg to 0.219 kJ/kg onion on the fourth day.

Figures 14, 15 and 16 show the variation of the exergy output, exergy solar radiation input and exergy efficiency, exergy utilization efficiency and exergy system efficiency in the drying chamber and flat plate solar collector as a function of drying time. The exergy efficiency for each component was calculated by using Eq. (14). It is dependent on the exergy inflow, outflow and loss of exergy in the drying chamber. As shown in Figs. 14, 15 and 16, the exergy efficiency of tomato in the drying chamber varied from 53.35 to 95.60% on the first day, 59.10% to 93.3% on the second day and 61.78% to 98.93% on the third day. It is dependent on the experimental condition of slices of tomato. The rate of exergy output was calculated using Eq. (17) and it is dependent on the ambient and outlet air temperature of the drying chamber. The exergy output of tomato in the drying chamber was found to be 80.20 W to 311.8 W on the first day, 80.9 W to 208.3 W on the second day, and 112.3 W to 182.6 W on the third day. The exergy solar radiation input was calculated by using Eq. (18) and it is dependent on the ambient temperature and the sky temperature, collector area. The exergy solar radiation of tomato varied between 166.3 w to 324.74 W on the first day, 177.44 W to 390 W on the second day and 171.4 W to 387.10 W on the third day depending on the experimental test of tomato. The exergy utilization efficiency was calculated by using Eqs. (16) and it is dependent on the exergy solar radiation input and exergy output. The exergy utilization efficiency of tomato varied between from 43.2 to 95.9% on the first day, 38.7% to 89.1% on the second and 52.9% to 88.7% on the third day depending on the experimental test of tomato. The exergy system (net) efficiency was calculated by using Eq. (15). It was dependent on the exergy utilization efficiency and exergy efficiency. The exergy system (net) efficiency varied between 30.2 and 86.8% tomato on first day, 26.9% to 71.2% tomato on second day and 37.3% to 80.8% tomato on the third day depending on the experimental test of tomato.

Fig. 14
figure 14

Variation of efficiency as a function of drying time and exergy in the drying chamber (1st day) tomato

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Fig. 15
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Variation of efficiency as a function of drying time and exergy in the drying chamber (2nd day) tomato

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Fig. 16
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Variation of efficiency as a function of drying time and exergy in the drying chamber (3rd day) tomato

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Figures 17 and 18 illustrate the exergy efficiency of potato in the drying chamber varied from 54.17% to 96.68% on the first day, 51.1% to 98.64% on the second day and 59.1% to 97.5% on the third day depending on the experimental condition of slices of potato. The rate of exergy output was calculated using Eq. (17). It was dependent on the ambient temperature and outlet air temperature of the drying chamber. Figures 17, 18 and 19 show that the exergy output of potato in the drying chamber varied between 165.5 and 211.7 W on the first day, 122.5 W to 298.6 W on the second day, and 70.71 W to 299.3 W on the third day. The exergy solar radiation input was calculated by using Eq. (18) based on the ambient temperature, the sky temperature and the collector area. Figures 17, 18 and 19 show that the exergy solar radiation input of potato varied between 201.87 and 324.55 W on the first day, 197.9 W to 335.2 W on the second day and 129.5 W to 386.50 W on the third day depending on the experimental test of potato. The exergy utilization efficiency was calculated by using Eq. (16) and it was dependent on the exergy solar radiation input and exergy output. The exergy utilization efficiency of potato varied between 61.6 and 85.6% on the first day, 54.7% to 92.3% on the second day and 53.4% to 92.5% on the third day depending on the experimental condition of potato. The exergy system (net) efficiency was calculated by using Eq. (15) and it was dependent on the exergy utilization efficiency and exergy efficiency. Figures 17, 18 and 19 show that the exergy system (net) efficiency varied between 37.9 and 76.96% on the first day, 27.9% to 91.0% on the second day and 32.3% to 87.5% on the third day depending on the experimental condition of potato.

Fig. 17
figure 17

Variation of efficiency as a function of drying time and exergy in the drying chamber (1st day) potato

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Fig. 18
figure 18

Variation of efficiency as a function of drying time and exergy in the drying chamber (2nd day) potato

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Fig. 19
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Variation of efficiency as a function of drying time and exergy in the drying chamber (3rd day) potato

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Figures 20, 21, 22 and 23 show that the exergy efficiency of onion in the drying chamber varied between 53.06 and 87.44% on the first day and 45.45% to 96.64% on the second day, 45.84% to 96.64% on the third day and 56.6% to 98.65% on the fourth day depending on the experimental condition of onion. The rate of exergy output was calculated using Eqs. (17), and it was dependent on the ambient and outlet air temperature of the drying chamber. Figures 20, 21, 22 and 23 show that the exergy output of onion in the drying chamber varied between 156.9 and 310.3 W on the first day, 96.64 W to 133.4 W on the second day, and 126.2 W to 861.5 W on the third day and 119.0 W to 226.08 W on the fourth day depending on the experimental test of onion. The exergy solar radiation input was calculated by using Eqs. (18), based on the ambient temperature, the sky temperature, and the collector area. Figures 20, 21, 22 and 23 show that the exergy solar radiation input of onion varied between 221.5 and 310.3 W on the first day, 179.2 W to 301.8 W on the second day and 171.1 W to 1084.6 W On the third day and 188.2 W to 307.7 W on the fourth day depending on the experimental condition of potato. Figures 20, 21, 22 and 23 show the exergy utilization efficiency calculated by using Eq. (16). It was dependent on the exergy solar radiation input and exergy output. The exergy utilization efficiency of onion varied between from 66.3 to 92.9% on the first day, 50.6% to 90.09% on the second day, 56.0% to 80.1% on the third day and 58.5% to 89% on the fourth day depending on the experimental condition of onion. The exergy system (net) efficiency was calculated by using Eq. (2). It is dependent on the exergy utilization efficiency and exergy efficiency. Figures 20, 21, 22 and 23 show that the exergy system (net) efficiency varied between 35.2 and 80.1% on the first day, 31.8% to 83.8% on the second day and 32.6% to 73.1% on the third day and 40.3% to 76.6% onion the fourth day depending on the experimental condition of onion.

Fig. 20
figure 20

Variation of efficiency as a function of drying time and exergy in the drying chamber (1st day) onion

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Fig. 21
figure 21

Variation of efficiency as a function of drying time and exergy in the drying chamber (2nd day) onion

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Fig. 22
figure 22

Variation of efficiency as a function of drying time and exergy in the drying chamber (3rd day) onion

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Fig. 23
figure 23

Variation of efficiency as a function of drying time and exergy in the drying chamber (4th day) onion

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Conclusion

The performance of solar vegetable dryer was analyzed experimentally. The solar vegetable dryer was analyzed based on the 1st and 2nd laws of thermodynamic analysis, viz. energy and exergy analysis. In this study, tomato, potato and onion was used as to dry in the solar dryer. The air temperature required to dry the tomato is from 34.5 to 72.3 °C, for potato is from 37.5 to 66.9 °C and onion is from 36.3 to 63.4 °C. The exergy inflow in drying chamber was found to be 0.188 kJ/kg to 1.981 kJ/kg for tomato, 0.187 kJ/kg to 1.987 kJ/kg for potato, and 0.22 kJ/kg to 1.471 kJ/kg for onion. The exergy outflow in drying chamber was found to be 0.165 kJ/kg to 1.96 kJ/kg for tomato, 0.181 kJ/kg to 1.92 kJ/kg for potato and 0.17 kJ/kg to 1.283 kJ/kg for onion. The average energy utilization ratio in the drying chamber was found to be 3.1 to 26% for tomato, 3.9 to 45.6% for potato and 5.2 to 37.4% for onion. Regarding the drying period, tomato takes 33 h, potato takes 27 h and onion takes 44 h for onion during experimental test. The dried relative humidity ranges from 10.01% to 11%, for tomato, 8.22% to 10.32% for potato and 9.7% to 11.18% for onion. The energy utilization ratio in the drying chamber was found to be 3.1% to 26%, for tomato, 3.9% to 45.6% for potato and 5.2% to 37.4% for onion.

Method/experimental

Experimental set-up

The detailed information on the experimental system and instrumental set-up is given below (Bhardwaj et al. 2017). The collector part and the drying part have an area of 1 × 2 m2 and 1 × 1.07 m2, respectively. The schematic diagram of this dryer is shown in Fig. 24.

Fig. 24
figure 24

Experimental setup of solar dryer

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Thermocouples were used to measure ambient temperature and the drying air temperature inside the dryer chamber. The range of operational temperature is 20 °C to 150 °C.

Experimental procedure

The daily drying rate was estimated by measuring the weight loss of the product after each day of drying. The relative humidity and solar radiation data were obtained from meteorological and measuring data. All results obtained from the experiments were used to perform the energy and exergy analyses of the solar vegetable drying process. Fresh vegetable products were used in the experiments and the moisture content was recorded as 91% for tomato, 73% for potato and 81% for onion. The drying experiments were carried out at drying air temperature of 35 °C for tomato, 55 °C for potato, and 70 °C for onion and the drying air velocity was 0.5 m/s for tomato, 1.5 m/s for potato and 2 m/s for onion. The final moisture content of samples was calculated based on weight samples of the vegetables and the final drying moisture content was determined as 9%, for tomato, 12%, for potato and 13% for onion based on weight analysis. During the experiments, ambient temperature inlet and outlet temperatures of drying air in the chamber were recorded. To measure drying air temperature, thermocouple and digital thermometer with manually controlled eight (8) channels at the inlet and outlet of the drying chamber during an experimental test was used (Borah et al. 2015). The velocity of air in the drying chamber varied from 0 to 2.5 m/s which was measured from the anemometer.

Steps of drying vegetable

See Fig. 25.

Fig. 25
figure 25

Shows the flowchart of drying vegetable steps

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Theoretical analysis

Analysis of solar energy

Energy analysis

The theoretical and derivation of the formulas have been based on first and second laws of thermodynamics principle to determine energy, exergy and utilization ratio of the vegetable drying system (Amjad et al. 2016). These parameters were determined at the inlet, outlet and intermediate section of the drying system based on the empirical formula and measured data on the system (i.e., solar radiation, atmospheric air temperature, drying temperature, outlet temperature, and relative humidity). The air conditioning process throughout the drying of vegetables includes the processes of heating, cooling, and humidification (Akpinar 2010). The air conditioning processes can be modeled as steady-flow processes that were analyzed by applying the steady-flow conservation of mass (for both dry air and moisture) and conservation of energy principle (El-sebaii and Shalaby 2012). General equation of mass conservation of drying air is (Minaei et al. 2014):

$$\sum {\dot{m}_{ai} } = \sum {\dot{m}_{ao} } .$$
(1)

General equation of mass conservation of moisture.

$$ \begin{aligned}& \sum \left( {\dot{m}_{{wi}} + \dot{m}_{{mp}} } \right) = \sum \dot{m}_{{wo}} ~\\ &\quad\;or\;\sum \left( {\dot{m}_{{ai}} w_{i} + \dot{m}_{{mp}} } \right) = \sum \dot{m}_{{ai}} w_{o}\end{aligned} $$
(2)

General equation of energy conservation.

$$\dot{Q} - \dot{W} = \sum \dot{m}_{o} \left( {h_{o} + \frac{{v_{o}^{2} }}{2}} \right) - \sum \dot{m}_{i} \left( {h_{i} + \frac{{v_{i}^{2} }}{2}} \right).$$
(3)

The changes in kinetic energy of fan were taken into consideration while the potential and kinetic energy in other parts of the process was neglected (Sami et al. 2011). During the energy and exergy analyses of the vegetables drying process, the following equations were generally used to compute the relative humidity and enthalpy of drying air (Arepally et al. 2017):

The relative humidity:

$$\phi = \frac{wp}{{\left( {0.622 + w} \right)p_{\text{sat@T}} }},$$
(4)

where w is the specific humidity, p atmospheric pressure, \(p_{\text{sat@T}}\) the saturated vapor pressure of drying air.

The enthalpy of drying air:

$$ h = C_{pda} T + wh_{\text{sat@T}} , $$
(5)

where \(C_{pda}\) the specific heat of drying air, T is drying air temperature, and \(h_{\text{sat@T}}\) is the enthalpy of saturated vapor.

Determination of fan outlet conditions

$$h_{fo} = \left[ {\left( {\dot{w}_{f} - \frac{{v^{2}_{fo} }}{2 \times 1000}} \right)\left( {\frac{1}{{\dot{m}_{da} }}} \right)} \right] + h_{fi} ,$$
(6)

where \(h_{fi}\) characterizes the enthalpy of drying air at the inlet of the fan, \(h_{fo}\) the enthalpy at the outlet of the fan vfo the drying air velocity at the outlet of the fan, \(\dot{w}_{f}\) fan energy and \(\dot{m}_{da}\) mass flow of drying air (R. Development. 2016). Considering the values of dry-bulb temperature and enthalpy from Eq. (4), the specific and relative humidity of drying air at the fan were determined by using the psychrometric chart (I. S. U. N. Drying 2006).

Determination of the outlet conditions of the tray

The inlet conditions of the drying chamber were determined depending on the inlet temperatures and specific humidity of drying air (Bolaji and Olalusi 2008). The inlet conditions of the tray were assumed as equal to the inlet conditions of the drying chamber (Celma and Cuadros 2009). Meanwhile, it was considered that the mass flow rate of drying air was equally passed throughout the tray (Kalaiarasi et al. 2016). Thus, the inlet conditions of the tray can be written:

$$ \begin{aligned}&w_{\text{di}} = w_{\text{tri}} ,T_{\text{dci}} = T_{\text{tri}} , \\ &\phi_{\text{dci}} = \phi_{\text{tri}} , h_{\text{dci}} = h_{\text{tri}} \; {\text{and}} \;\dot{m}_{da} = \dot{m}_{\text{datri}} .\end{aligned} $$

Using Eqs. (1) and (2), the equation of the specific humidity at the outlet of the tray was derived:

$$w_{\text{tro}} = w_{\text{tri}} + \frac{{\dot{m}_{\text{vegetable}} }}{{\dot{m}_{da} }},$$
(7)

where \(w_{\text{tri}}\) is the specific humidity at the inlet of the tray, \(\dot{m}_{\text{vegetable}}\) the mass flow rate of the moisture removed from the vegetable (product). The relative humidity and enthalpy of drying air at the outlet of the tray were, respectively, estimated using Eqs. (4 and 5) (Singh and Kumar 2012). During the humidification process at the tray, the heat transfer can be calculated using the following equations:

$$\dot{Q}_{tr} = \dot{m}_{da} \left( {h_{\text{tri@T}} - h_{\text{tro@T}} } \right),$$
(8)

where \(h_{\text{tri@T}}\), \(h_{\text{tro@T}}\) are the enthalpies at the inlet and outlet of the tray.

During the experiments, ambient temperature and the relative humidity, inlet and outlet temperature of drying air in the dryer chamber were recorded as shown in Fig. 7 (Arepally et al. 2017) (Fig. 26).

Fig. 26
figure 26

Schematic illustration of the tray

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The inlet conditions of the tray were assumed as equal to the inlet conditions of the dry drying chamber (George 2007). In addition, the outlet conditions of trays were assumed as equal to the outlet conditions of the drying chamber (Darvishi et al. 2018). Solar dryer energy analysis based on the first law of thermodynamics never reflects the quality of energy destruction (Bennamoun 2012). During the solar drying process, the energy utilization ratio of the drying chamber is estimated using the following equation (Minaei et al. 2014; Akpinar et al. 2006):

$$EUR = \frac{{\dot{m}_{ia} \left( {h_{ia} - h_{oa} } \right)}}{{\dot{m}_{ia} C\left( {T_{ia} - T_{aai} } \right)}} = \frac{{cp_{i} T_{dci} - cp_{0} T_{dco} }}{{cp_{i} T_{dci} - cp_{o} T_{a} }},$$
(9)

where \(\dot{m}_{ia}\) is the mass flow rate of the dry air (kg/s), \(h_{oa }\) is absolute humidity of the air leaving the drying chamber (%), \(h_{ia}\) is the absolute humidity of the air entering the drying chamber (%), c = specific heat of air (J/kg/°C), and EUR, the energy utilization ratio.

Exergy analysis

Exergy is the maximum amount of work that can be produced by the system or flow of mater or energy reach equilibrium with a reference environment. Energy and exergy analyses of the drying process should be performed to determine the energy interaction and thermodynamics behavior of drying air throughout a drying chamber (Fudholi et al. 2014a). Exergy analysis allows for effective energy resource use because the analysis enables the determination of locations and magnitudes of the losses (Fudholi et al. 2014b).

Exergy analysis is based on the second of law of thermodynamics therefore, the general form of the exergy equation that is applicable to steady-flow systems may be expressed as (Niksiar and Rahimi 2009; Oztop et al. 2013) (Fig. 27):

$${\text{Ex}} = \dot{m} cp\left[ {\left( {T - T_{a} } \right) - T_{a} { \ln }\frac{T}{{T_{a} }}} \right],$$
(10)

where \({\text{Ex}}\) is the exergy, \(\dot{m}\) the mass flow rate (kg/s), and \(T_{a}\) the ambient temperature (°C).

Fig. 27
figure 27

Exergy balance (Niksiar and Rahimi 2009)

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For the exergy inflow to the drying chamber

$${\text{Ex}}_{\text{dci}} = \dot{m} cp\left[ {\left( {T_{\text{dci}} - T_{a} } \right) - T_{a} { \ln }\frac{{T_{\text{dci}} }}{{T_{a} }}} \right],$$
(11)

where \(T_{\text{dci}}\) is the inflow temperature of the drying chamber.

For the exergy outflow from the drying chamber:

$${\text{Ex}}_{\text{dco}} = \dot{m} {\text{cp}}\left[ {\left( {T_{\text{dco}} - T_{a} } \right) - T_{a} { \ln }\frac{{T_{\text{dco}} }}{{T_{a} }}} \right].$$
(12)

Exergy loss during solar drying is determined by

$${\text{Ex}}_{\text{loss}} {\text{ = Ex}}_{\text{dci}} - {\text{Ex}}_{\text{dco}} .$$
(13)

Exergy efficiency can be defined as the ratio of (No Title. 2004) energy use (investment) in product drying to the exergy of the drying air supplied to the system (No Title. 2004). However, this efficiency can also be defined as the ratio of exergy outflow to exergy inflow in the drying chamber. The exergy efficiencies of the drying chamber can be determined based on this definition (Zohri et al. 2018). Therefore, the general form of exergy efficiency is expressed as follows (Fudholi et al. 2014a):

$$\eta_{{{\text{Ex}} . {\text{do}}}} = \frac{{{\text{Ex}}_{\text{dco}} }}{{{\text{Ex}}_{\text{dci}} }} = 1 - \frac{{{\text{Ex}}_{\text{loss}} }}{{{\text{Ex}}_{\text{dci}} }}.$$
(14)

Given a greenhouse tunnel-type solar dryer system with a chimney that uses solar radiation energy, the given system efficiency is (Bolaji and Olalusi 2008):

$$\eta_{{{\text{Ex}} . {\text{net}}}} = \eta_{{{\text{Ex}} . {\text{da}}}} \times \eta_{{{\text{ex}} . {\text{solar}}}} .$$
(15)

For a greenhouse solar dryer system, the exergy utilization efficiency (\(\eta_{{{\text{ex}} . {\text{solar}}}}\)) required to raise internal air temperature is determined as follows (Prommas et al. 2010):

$$\eta_{{{\text{Ex}} . {\text{solar}}}} = \frac{{{\text{Ex}}_{\text{out}} }}{{{\text{Ex}}_{\text{rad}} }},$$
(16)

where the exergy output (\({\text{Ex}}_{\text{out}}\)) and the exergy of solar radiation input (\({\text{Ex}}_{\text{rad}}\)) to the dryer was calculated as follows:

$${\text{Ex}}_{\text{out}} = \left( {1 - \frac{{T_{a} }}{{T_{at} }}} \right)\left[ {\frac{{\dot{m}c\left( {T_{at} - T_{a} } \right)}}{\Delta t}} \right],$$
(17)

where \(T_{at}\) is the air temperature in the dryer (°C) and \(T_{a}\) is the ambient temperature (°C).

$${\text{Ex}}_{\text{rad}} = {\text{SXA}}\left[ {1 - \frac{4}{3}\left( {\frac{{T_{a} }}{{T_{s} }}} \right) + \frac{1}{3}\left( {\frac{{T_{a} }}{{T_{s} }}} \right)^{4} } \right],$$
(18)

where Ts is the sky temperature.

The exergy efficiency of a system or process is maximized when exergy loss (\({\text{Ex}}_{\text{loss}}\)) is minimized.

Experimental analysis of solar vegetable dryer

Solar collectors as heat exchangers transfer the absorbed solar radiation to air passing next to the absorber plate (Akpinar 2010). Thus, hot air is obtained from these collectors and they are used in space heating, agricultural product drying, greenhouse heating and preheating in ventilation systems (Tripathy and Kumar 2009).

Solar air collector is a simple device for air heating by utilizing solar energy for many applications, which require low-to-moderate temperature below 60 °C such as drying and space heating (Arepally et al. 2017; Bennamoun 2012).

The flowchart of the drying process during the experiment is shown in Fig. 28.

Fig. 28
figure 28

Flowchart of the solar drying process

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