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).
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).
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.
