# Regulation of Temperature on Multitrays in an Indirect Solar Dryer (ISD) with Energy Storage and Three Airflow Modes

Authors: G. B. Tchaya; E. Tchoffo Houdji; J. H Tchami; C. Kapseu; M. Kamta
Journal: Journal of Engineering
 (2021)

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## Abstract

This work presents the regulation of temperature in an indirect multitrays solar dryer with oriented flux under the irradiance fluctuation. The temperature regulator using a negative temperature coefficient (NTC) as a sensor and fans is designed, and a similar device is also used to measure humidity through a sensor. Inlet and outlet dryer temperature and temperature on the three trays have been recorded with the regulation system according to different airflow modes. Irradiance and humidity have also been recorded. The model of outlet temperature with energy storage was given by using heat transfer equations. The results have shown that in the linking airflow mode, the average temperature on the three trays is 51.3 ± 1.5a°C, 52.18 ± 1.4a°C, and 51.9 ± 1.2a°C, respectively, with 52°C as setpoint temperature and NTC fixed on tray number 2. With temperature sensor in the same tray and 51°C as setpoint temperature, the average temperatures on the three trays are 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C, respectively, in mixed mode, whereas in crossing airflow mode, the temperature gradient does not allow regulation on all trays. The regulation is possible when the temperature in the dryer chamber exceeds the set point temperature by more than 5%. The proportional type corrector is suitable for the temperature controller in indirect solar dryers. When the energy source is unstable, humidity which is a variable parameter is used to mark the end of drying instead of time.


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## Body

## 1. Introduction

Generally, regulation helps to stabilize unstable systems, increase accuracy, productivity, and control production quality, and improve the flexibility of the production chain. Particularly, in agro-food, it improves hygiene (less staff) and limits the effects of final product variability [1–3].Regulation is well-known and mastered in industrial because the energy source is stable. Generally, the control chain is curly. The difference of temperature between the order temperature and the desired temperature is determined [4]. This is not the case for equipment power by renewable energy sources such as the solar or wind energy system because of their intermittent nature.The solar drying equipment for agricultural products has been improved with the introduction of new equipment as the integration of heat storage systems such as biomass [5–7], sensible heat energy [8, 9], thermochemical reactions or phase change materials [10–12], and the regulation obtained with hybrid sources [13–15]. However, the sizing and design rules of this process are still insufficient so that these structures meet farmers' expectations [16, 17]. Though different solar dryer designs are now available in Africa for both direct and indirect drying chamber designs [3, 18], research studies to seek new design are still going. Simo-tagne et al. [19], for example, recently proposed a new indirect solar dryer with collector consisting of conical and parabolic solar concentrator. They found that the parabolic concentrator had comparatively poor drying kinetics when compared with conical concentrators, while coaxial design outperformed the noncoaxial design for drying kinetics. Modelling and numerical simulations solar dryers are one of the promise means on the way to seek the best solar dryer for different products to dry [8, 20–22].In general, food products are dried at a fix temperature between 45°C and 60°C [23–26]. This temperature range is obtained without difficulty when the energy source is electric (in the case of equipment in industrial sectors); but, this becomes difficult with solar-thermal source because of their dependence on weather and climate conditions.If the drying temperature and humidity ranges are known using the control of the drying parameters of food products, the dried products will be in good quality [27–29]. Smart sensors using the fuzzy logic-based control system are increasingly used to master the drying parameters (temperature and humidity in particular) [30, 31], but for populations of rural areas, this type of control system would make the dryer more expensive. So, the classical control theory with low-cost temperature and humidity sensors are used to build the regulation control system for indirect solar dryers to reduce their costs [3]. This approach is used in this work to control the temperature and humidity in an indirect multitrays solar dryer with oriented flux.


## 2. Materials and Methods

### 2.1. Measuring Equipment

Data acquisition is done by an acquisition station (ALMEMO 2690–8). It allows storing the drying parameters with the appropriate sensors every five minutes. The measurements of the parameters were made using sensors of temperature (NiCr-Ni thermocouple), humidity (FHAD 46), and irradiance (Lux Probe Head FLA 603), all connected to the ALMEMO.


### 2.2. Synoptic of Indirect Solar Dryer

Figure1 shows the model of the dryer used for the experiments. It consists of three compartments (solar collector, drying chamber with three trays, and chimney). However, the chamber gives the possibility of drying in three different ways based on the air circulation mode. Thus, we can distinguish the crossing, licking, and mixed mode.Figure 1
Indirect solar dryer with airflow oriented (ISDAO) [32].The first experimentation was carried out to characterize the equipment without regulation. It consists of measuring temperature at inlet and outlet of the solar collector, in the absorber and the irradiance. The curves are presented as function of time.Figure2 shows the design of the indirect solar dryer with dimensions of different compartments. The volume of the drying room is 0.125 m3. The chamber has three trays with 20 cm between two trays.Figure 2
Design of the indirect solar dryer.


### 2.3. Synoptic of the Regulated Dryer with Solar Energy Source

The synoptic diagram (Figure3) gives the relations between different compartments. We have the sun that provides all the energy available for the whole system, namely, solar-thermal through the glass v, black volcanic stone, and solar photovoltaic, through solar cells.Figure 3
Synoptic of the regulated dryer with solar energy source.Then, the fan (3W, 12V, 16.94 g/s) will act as a hot air speed controller in the dryer (enclosure where the product is exposed) through the control (regulator).Ventilation control varies the temperature and humidity simultaneously because there is only one control parameter. Since the two parameters are linked, it will be a question of regulating the temperature and measuring the path 1 comprising the sun, absorber, glass, and/or storage, and drying chamber is commonly used; path 2 including the solar, cell photovoltaic (30 Wc), control unit, fan, absorber, glass, and/or storage, and drying chamber ensures the control of temperature and measurement of humidity.Table1 provides properties of the material used in the solar system.Table 1
Thermophysical properties of materials.
Calorific capacity (J·kg−1·K−1)Density (kg·m−3)Thermal conductivity (W·m−1·K−1)CoefficientAbsorptionReflectionEmissivitySteel4657833540.950.050.98Aluminium8962707204Glass700250010,10.04White wood31473750,12


### 2.4. Instrumentation

It presents the various measurement sensors and transmitters involved in the conversion of random (nondeterministic) signals. We cannot predict their evolution until we have observed them. Consequently, they can only be described by their statistical properties.As shown in Figure4, we will control the humidity to mark the end of the drying by emitting a sound signal, and the renewal of the air will regulate the temperature. Because, it is the same actuator that controls the process.Figure 4
Instrumentation diagram.


### 2.5. Temperature and Humidity Control in the Dryer

The temperature control and the humidity measurement in the forced convection dryer are done, as shown in Figure5. A humidity sensor and a temperature sensor are placed in a system (process) to send the physical information to a processing circuit in order to realize the regulation loop. Indeed, the excess of moisture in the dryer chamber involves condensation, and the renewal of air in it influences the temperature. This means that because the two parameters are related, regulating the humidity by ventilating strongly influences the stabilization of the temperature. Thus, Figure 4 shows the regulation of the temperature and the measurement of the relative humidity to fix the end of drying of the product. This experiment was performed by Kamta et al. (2010) in an indirect solar dryer with crossing mode and one tray. The temperature is regulated in a range of Tmax to Tmin corresponding to the supply voltages Vcmax and Vcmin of the fans. The set temperature Tc corresponds to the voltage Vc given by the following formula:(1)Vc=Vcmax+Vcmin2.Figure 5
Diagram of electrical control of temperature and relative humidity.Experience has shown that this range is optimal for a difference of 2°C around the set pointTc [33].Here, the negative temperature coefficient (NTC) as sensor closes the loop and thus performs the regulation, while the humidity sensor (HIH 4030 humidity type) is on an open-loop chain and allows a measurement to be made to control the end of the process. This control will sound a buzzer if the humidity set pointVch is reached.Let us consider the thermal sensor as a black box whose input parameters and output parameters are known. Figure6 shows the thermal phenomena in the solar collector when it receives sunshine, ambient temperature, and ambient relative humidity.Figure 6
Phenomenon of solar energy transformation in the thermal collector.By making a thermal balance on the air, we can express, as a function of time, the equation of the temperature of the outlet airTfs (t) and compare it with the theoretical curve to explain the present phenomenon.(2)macpadTfsdt=ShnTn−Tfs+ShvTv−Tfs,where ma is the mass of air (kg), cpa is the specific heat of the air (J./kg.K), Tfs is the inlet fluid temperature (°C), t is the time (s), S is the surface (m2), hn is the conductivity heat transfer coefficient (W/m2 °C), Tn is the absorber plate temperature (°C), hv is the convective heat transfer coefficient (W/m2 °C), and Tv is the cover temperature (°C).


### 2.6. Determination of Heat Exchange Coefficients

Convection exchange coefficient is given in the following equation, whereDh is the characteristic length (hydraulic diameter).(3)hv=NuλfDh.This convection coefficient is performed by considering the predominant natural convection [34].In the case where the fluid circulates on a plate inclined at an angleα, the calculation of the Nusselt number is expressed.For an inclined plate, ifα<80°,105<GrLPr<1011, and the heating surface facing down,(4)Nu=0.56GrLPrcosα1.4,where Gr is the Grashof number, Nu is the Nusselt number, Pr is the Prandtl number, Re is the Reynolds number.Conduction exchange coefficient is(5)hn=λnen.


### 2.7. Determination of the Temperature Controller’s Model

Figure7 shows the block diagram of the process in order to propose an ideal regulator to adapt in such a way to ensure a compromise between accuracy and speed. Using the PID corrector setting by the reference model (Granjon, 2010), the following equations are obtained.Figure 7
Block diagram of regulation giving the transfer function.(6)Fp=XpWp=KpHp1+KpHp,(7)Kp=FpHp1−Fp.According to Prouvost [35], one can apply the ideal criteria by expressing the transfer function as(8)Fp=11+θdp.By replacing equation (5) in (4), the new equation is(9)Kp=θGsθd1+θpθp.By identification with the type of corrector, the PID setting to be designed is actually a PI series with following characteristics.(10)Kp=Gr1+TipTipavecGr=θGsθdetTi=θ.By applying a PI corrector, we can make a good regulation.By replacingTfs (p) with X(p), we can define the transfer function H(p).(11)Hp=XpYpwithYp=Cp;Xp=Tfsp1/Cp+1,(12)Hp=Gs1/Cp+1,where(13)Gs=TfC,is the static gain of the system(14)θ=1Ctime constant.In the transfer equation, there is no integration, and the process is said to be naturally stable or self-regulating, according to the Streje model.


## 2.1. Measuring Equipment

Data acquisition is done by an acquisition station (ALMEMO 2690–8). It allows storing the drying parameters with the appropriate sensors every five minutes. The measurements of the parameters were made using sensors of temperature (NiCr-Ni thermocouple), humidity (FHAD 46), and irradiance (Lux Probe Head FLA 603), all connected to the ALMEMO.


## 2.2. Synoptic of Indirect Solar Dryer

Figure1 shows the model of the dryer used for the experiments. It consists of three compartments (solar collector, drying chamber with three trays, and chimney). However, the chamber gives the possibility of drying in three different ways based on the air circulation mode. Thus, we can distinguish the crossing, licking, and mixed mode.Figure 1
Indirect solar dryer with airflow oriented (ISDAO) [32].The first experimentation was carried out to characterize the equipment without regulation. It consists of measuring temperature at inlet and outlet of the solar collector, in the absorber and the irradiance. The curves are presented as function of time.Figure2 shows the design of the indirect solar dryer with dimensions of different compartments. The volume of the drying room is 0.125 m3. The chamber has three trays with 20 cm between two trays.Figure 2
Design of the indirect solar dryer.


## 2.3. Synoptic of the Regulated Dryer with Solar Energy Source

The synoptic diagram (Figure3) gives the relations between different compartments. We have the sun that provides all the energy available for the whole system, namely, solar-thermal through the glass v, black volcanic stone, and solar photovoltaic, through solar cells.Figure 3
Synoptic of the regulated dryer with solar energy source.Then, the fan (3W, 12V, 16.94 g/s) will act as a hot air speed controller in the dryer (enclosure where the product is exposed) through the control (regulator).Ventilation control varies the temperature and humidity simultaneously because there is only one control parameter. Since the two parameters are linked, it will be a question of regulating the temperature and measuring the path 1 comprising the sun, absorber, glass, and/or storage, and drying chamber is commonly used; path 2 including the solar, cell photovoltaic (30 Wc), control unit, fan, absorber, glass, and/or storage, and drying chamber ensures the control of temperature and measurement of humidity.Table1 provides properties of the material used in the solar system.Table 1
Thermophysical properties of materials.
Calorific capacity (J·kg−1·K−1)Density (kg·m−3)Thermal conductivity (W·m−1·K−1)CoefficientAbsorptionReflectionEmissivitySteel4657833540.950.050.98Aluminium8962707204Glass700250010,10.04White wood31473750,12


## 2.4. Instrumentation

It presents the various measurement sensors and transmitters involved in the conversion of random (nondeterministic) signals. We cannot predict their evolution until we have observed them. Consequently, they can only be described by their statistical properties.As shown in Figure4, we will control the humidity to mark the end of the drying by emitting a sound signal, and the renewal of the air will regulate the temperature. Because, it is the same actuator that controls the process.Figure 4
Instrumentation diagram.


## 2.5. Temperature and Humidity Control in the Dryer

The temperature control and the humidity measurement in the forced convection dryer are done, as shown in Figure5. A humidity sensor and a temperature sensor are placed in a system (process) to send the physical information to a processing circuit in order to realize the regulation loop. Indeed, the excess of moisture in the dryer chamber involves condensation, and the renewal of air in it influences the temperature. This means that because the two parameters are related, regulating the humidity by ventilating strongly influences the stabilization of the temperature. Thus, Figure 4 shows the regulation of the temperature and the measurement of the relative humidity to fix the end of drying of the product. This experiment was performed by Kamta et al. (2010) in an indirect solar dryer with crossing mode and one tray. The temperature is regulated in a range of Tmax to Tmin corresponding to the supply voltages Vcmax and Vcmin of the fans. The set temperature Tc corresponds to the voltage Vc given by the following formula:(1)Vc=Vcmax+Vcmin2.Figure 5
Diagram of electrical control of temperature and relative humidity.Experience has shown that this range is optimal for a difference of 2°C around the set pointTc [33].Here, the negative temperature coefficient (NTC) as sensor closes the loop and thus performs the regulation, while the humidity sensor (HIH 4030 humidity type) is on an open-loop chain and allows a measurement to be made to control the end of the process. This control will sound a buzzer if the humidity set pointVch is reached.Let us consider the thermal sensor as a black box whose input parameters and output parameters are known. Figure6 shows the thermal phenomena in the solar collector when it receives sunshine, ambient temperature, and ambient relative humidity.Figure 6
Phenomenon of solar energy transformation in the thermal collector.By making a thermal balance on the air, we can express, as a function of time, the equation of the temperature of the outlet airTfs (t) and compare it with the theoretical curve to explain the present phenomenon.(2)macpadTfsdt=ShnTn−Tfs+ShvTv−Tfs,where ma is the mass of air (kg), cpa is the specific heat of the air (J./kg.K), Tfs is the inlet fluid temperature (°C), t is the time (s), S is the surface (m2), hn is the conductivity heat transfer coefficient (W/m2 °C), Tn is the absorber plate temperature (°C), hv is the convective heat transfer coefficient (W/m2 °C), and Tv is the cover temperature (°C).


## 2.6. Determination of Heat Exchange Coefficients

Convection exchange coefficient is given in the following equation, whereDh is the characteristic length (hydraulic diameter).(3)hv=NuλfDh.This convection coefficient is performed by considering the predominant natural convection [34].In the case where the fluid circulates on a plate inclined at an angleα, the calculation of the Nusselt number is expressed.For an inclined plate, ifα<80°,105<GrLPr<1011, and the heating surface facing down,(4)Nu=0.56GrLPrcosα1.4,where Gr is the Grashof number, Nu is the Nusselt number, Pr is the Prandtl number, Re is the Reynolds number.Conduction exchange coefficient is(5)hn=λnen.


## 2.7. Determination of the Temperature Controller’s Model

Figure7 shows the block diagram of the process in order to propose an ideal regulator to adapt in such a way to ensure a compromise between accuracy and speed. Using the PID corrector setting by the reference model (Granjon, 2010), the following equations are obtained.Figure 7
Block diagram of regulation giving the transfer function.(6)Fp=XpWp=KpHp1+KpHp,(7)Kp=FpHp1−Fp.According to Prouvost [35], one can apply the ideal criteria by expressing the transfer function as(8)Fp=11+θdp.By replacing equation (5) in (4), the new equation is(9)Kp=θGsθd1+θpθp.By identification with the type of corrector, the PID setting to be designed is actually a PI series with following characteristics.(10)Kp=Gr1+TipTipavecGr=θGsθdetTi=θ.By applying a PI corrector, we can make a good regulation.By replacingTfs (p) with X(p), we can define the transfer function H(p).(11)Hp=XpYpwithYp=Cp;Xp=Tfsp1/Cp+1,(12)Hp=Gs1/Cp+1,where(13)Gs=TfC,is the static gain of the system(14)θ=1Ctime constant.In the transfer equation, there is no integration, and the process is said to be naturally stable or self-regulating, according to the Streje model.


## 3. Results and Discussion

### 3.1. Regulation of Temperature

#### 3.1.1. Characteristic of the Dryer

It is shown on Figure8 that for 250 minutes after exposing the dryer on the sun, the average absorber temperature is 75°C when the average irradiance is 700 W/m2. However, the fluctuation of the irradiance of the outlet absorber temperature is up to 50°C.Figure 8
Temperature and irradiance profiles in dryer without regulation.


#### 3.1.2. Temperature Regulation of the Vacuum Chamber in Crossing Mode

Figure9 shows that during 2.2 hours, the temperature was kept stable in the three trays at 40.60 ± 1.06°C, 39.42 ± 0.83°C, and 36.15 ± 0.71°C, respectively. Thus, there is a nonuniform temperature distribution in the multitrays indirect solar dryer for the crossing mode with regulation. It should be noted that during the handling period, the irradiance was fluctuated, but since it was sufficient to provide the necessary energy, it could be regulated without difficulty. The average ambient temperature is 31°C. The differences between the temperatures on each stray during the test show the difficulty to uniformly removal moisture on crops inside a multitray solar dryer within a limited time [36]. This would also affect the drying performance when the crop would be introduced in the drying chamber. In fact, without the control system, trays near to the outlet of the solar collector, corresponding to the entry of the drying chamber, have higher drying potentials compared to those situated far from that entry [37, 38].Figure 9
Temperature and irradiance profiles in crossing mode with regulation.


#### 3.1.3. Influence of the Position of the Sensor (NTC) on the Temperature Control

Table2 provides the average air temperatures on the trays for different positions of the temperature sensor (NTC) in relation to the trays in order to find the best position for good regulation. For the crossing mode, there is a vertical gradient of temperature, and the position of the NTC does not make it possible to regulate on the trays while keeping this gradient. As for the crossing mode, we will choose the optimal position that gives the best results by licking mode. It is noted that for good temperature regulation, the temperature sensor (NTC) should be placed on the tray 2. The same result is observed in the case of mixed mode.Table 2
Temperature reading on the trays in licking mode for different NTC positions.
ParameterMean and standard deviationSet pointMean ambient temperatureNTC positionTray 1Tray 2Tray 3Temperature (°C)65.9 ± 2.3a61.5 ± 1.4b59.9 ± 1.4b6042Tray 351.3 ± 1.5a52.18 ± 1.4a51.9 ± 1.2a5241Tray 251.6 ± 1.5a53.4 ± 1.3b54.08 ± 1.37b5141Tray 1


#### 3.1.4. Temperature Regulation of the Vacuum Chamber in Licking Mode

In licking mode, the temperatures are the same on the three trays with the same gap. In Figure10, the temperature is regulated at 52°C. Despite the variation of irradiance, the curve of the temperature presents a flat zone for which the regulation is effective.Figure 10
Temperature and irradiance profiles in linking mode.


#### 3.1.5. Temperature Regulation of the Vacuum Chamber in Mixed Mode

Figure11 shows the temperatures on the three trays for a day where average sunshine reached 928 W/m2. The averages temperature on the three trays are 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C. The temperature is regulated to the value of 51°C as a set point, and it remained there between 11 h 03 and 14 h 48. The average ambient temperature is 40.5°C.Figure 11
Temperature and irradiance profiles in mixed mode with regulation.


### 3.2. Model of the Corrector of Temperature Controller

The theoretical curve is shown in Figure12. Normally, it grows to a maximum ideally located at solar noon and then decreases until sunset.Figure 12
Experiment temperature profiles in the dryer chamber.The resolution of equation (2) allows us to have the following expression of the temperature as a function of time which explains the profile of the curve of Figure 12.(15)Tfst=Tfe+BA1−e−A/macpat,with(16)A=Shn+hvandB=ShvTv+hnTn.The variation of the temperature strongly depends on the convective exchange coefficients.Thus, the time constantC can be expressed as(17)C=Amacpa.This constantC depends on the properties of the coolant and the convective exchanges, and it influences the rapid attainment of the maximum temperature.For average temperature values on the glass and the absorber (Tv = 37°C and Tn = 60°C), the curve (Figure 12) resembles a usual curve if the input is an amplitude step B/A.Since the studied method has a first-order transfer function, it can be controlled by a proportional regulator with or without integral.By using the choice graph of the regulator proposed by the method of Broida, this process has no delayτ, and the ratio θ/τ will tend towards infinity. This corresponds to the domain of proportional actions. Thus, we can write(18)Kp=θGsθd.


### 3.3. Control of Relative Humidity

#### 3.3.1. Variation of Humidity during Temperature Control

Figure13 shows that moisture curve varies in the opposite direction to the temperature. The humidity is stable at 10% after 4 hours, while the temperature also becomes stable at 56.4°C on the tray 2 after 2 hours. This shows that if the temperature is stable for a period of time, moisture will follow the same trend, and this information can be used to set the end of drying. This manipulation is done at the average relative humidity of 40%.Figure 13
Temperature and irradiance profiles with regulation in the mixed mode.


#### 3.3.2. Control the End of Drying

The majority of industrial drying systems makes it easy to control the parameters and sometimes offer the possibility to control several parameters simultaneously [27, 39]. These different parameters are controlled over time. Thus, time is considered as a control signal of drying. All food products use time to mark the end of their drying. The system may stop automatically if drying is complete.In solar dryers where the energy source is not mastered, the heat source pumps the heat into the chamber to dry the products. Using the time to set the end of drying while the input parameters are stochastic can skew the results. The use of a system parameter to set the end of drying makes it possible to follow the stochastic variations of these parameters.Relative humidity, which is a measurable, controllable, and stochastic quantity, can be used to control the drying of products. Indeed, it is possible to signal the end of drying of a product which has dried quickly or slowly.


## 3.1. Regulation of Temperature

### 3.1.1. Characteristic of the Dryer

It is shown on Figure8 that for 250 minutes after exposing the dryer on the sun, the average absorber temperature is 75°C when the average irradiance is 700 W/m2. However, the fluctuation of the irradiance of the outlet absorber temperature is up to 50°C.Figure 8
Temperature and irradiance profiles in dryer without regulation.


### 3.1.2. Temperature Regulation of the Vacuum Chamber in Crossing Mode

Figure9 shows that during 2.2 hours, the temperature was kept stable in the three trays at 40.60 ± 1.06°C, 39.42 ± 0.83°C, and 36.15 ± 0.71°C, respectively. Thus, there is a nonuniform temperature distribution in the multitrays indirect solar dryer for the crossing mode with regulation. It should be noted that during the handling period, the irradiance was fluctuated, but since it was sufficient to provide the necessary energy, it could be regulated without difficulty. The average ambient temperature is 31°C. The differences between the temperatures on each stray during the test show the difficulty to uniformly removal moisture on crops inside a multitray solar dryer within a limited time [36]. This would also affect the drying performance when the crop would be introduced in the drying chamber. In fact, without the control system, trays near to the outlet of the solar collector, corresponding to the entry of the drying chamber, have higher drying potentials compared to those situated far from that entry [37, 38].Figure 9
Temperature and irradiance profiles in crossing mode with regulation.


### 3.1.3. Influence of the Position of the Sensor (NTC) on the Temperature Control

Table2 provides the average air temperatures on the trays for different positions of the temperature sensor (NTC) in relation to the trays in order to find the best position for good regulation. For the crossing mode, there is a vertical gradient of temperature, and the position of the NTC does not make it possible to regulate on the trays while keeping this gradient. As for the crossing mode, we will choose the optimal position that gives the best results by licking mode. It is noted that for good temperature regulation, the temperature sensor (NTC) should be placed on the tray 2. The same result is observed in the case of mixed mode.Table 2
Temperature reading on the trays in licking mode for different NTC positions.
ParameterMean and standard deviationSet pointMean ambient temperatureNTC positionTray 1Tray 2Tray 3Temperature (°C)65.9 ± 2.3a61.5 ± 1.4b59.9 ± 1.4b6042Tray 351.3 ± 1.5a52.18 ± 1.4a51.9 ± 1.2a5241Tray 251.6 ± 1.5a53.4 ± 1.3b54.08 ± 1.37b5141Tray 1


### 3.1.4. Temperature Regulation of the Vacuum Chamber in Licking Mode

In licking mode, the temperatures are the same on the three trays with the same gap. In Figure10, the temperature is regulated at 52°C. Despite the variation of irradiance, the curve of the temperature presents a flat zone for which the regulation is effective.Figure 10
Temperature and irradiance profiles in linking mode.


### 3.1.5. Temperature Regulation of the Vacuum Chamber in Mixed Mode

Figure11 shows the temperatures on the three trays for a day where average sunshine reached 928 W/m2. The averages temperature on the three trays are 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C. The temperature is regulated to the value of 51°C as a set point, and it remained there between 11 h 03 and 14 h 48. The average ambient temperature is 40.5°C.Figure 11
Temperature and irradiance profiles in mixed mode with regulation.


## 3.1.1. Characteristic of the Dryer

It is shown on Figure8 that for 250 minutes after exposing the dryer on the sun, the average absorber temperature is 75°C when the average irradiance is 700 W/m2. However, the fluctuation of the irradiance of the outlet absorber temperature is up to 50°C.Figure 8
Temperature and irradiance profiles in dryer without regulation.


## 3.1.2. Temperature Regulation of the Vacuum Chamber in Crossing Mode

Figure9 shows that during 2.2 hours, the temperature was kept stable in the three trays at 40.60 ± 1.06°C, 39.42 ± 0.83°C, and 36.15 ± 0.71°C, respectively. Thus, there is a nonuniform temperature distribution in the multitrays indirect solar dryer for the crossing mode with regulation. It should be noted that during the handling period, the irradiance was fluctuated, but since it was sufficient to provide the necessary energy, it could be regulated without difficulty. The average ambient temperature is 31°C. The differences between the temperatures on each stray during the test show the difficulty to uniformly removal moisture on crops inside a multitray solar dryer within a limited time [36]. This would also affect the drying performance when the crop would be introduced in the drying chamber. In fact, without the control system, trays near to the outlet of the solar collector, corresponding to the entry of the drying chamber, have higher drying potentials compared to those situated far from that entry [37, 38].Figure 9
Temperature and irradiance profiles in crossing mode with regulation.


## 3.1.3. Influence of the Position of the Sensor (NTC) on the Temperature Control

Table2 provides the average air temperatures on the trays for different positions of the temperature sensor (NTC) in relation to the trays in order to find the best position for good regulation. For the crossing mode, there is a vertical gradient of temperature, and the position of the NTC does not make it possible to regulate on the trays while keeping this gradient. As for the crossing mode, we will choose the optimal position that gives the best results by licking mode. It is noted that for good temperature regulation, the temperature sensor (NTC) should be placed on the tray 2. The same result is observed in the case of mixed mode.Table 2
Temperature reading on the trays in licking mode for different NTC positions.
ParameterMean and standard deviationSet pointMean ambient temperatureNTC positionTray 1Tray 2Tray 3Temperature (°C)65.9 ± 2.3a61.5 ± 1.4b59.9 ± 1.4b6042Tray 351.3 ± 1.5a52.18 ± 1.4a51.9 ± 1.2a5241Tray 251.6 ± 1.5a53.4 ± 1.3b54.08 ± 1.37b5141Tray 1


## 3.1.4. Temperature Regulation of the Vacuum Chamber in Licking Mode

In licking mode, the temperatures are the same on the three trays with the same gap. In Figure10, the temperature is regulated at 52°C. Despite the variation of irradiance, the curve of the temperature presents a flat zone for which the regulation is effective.Figure 10
Temperature and irradiance profiles in linking mode.


## 3.1.5. Temperature Regulation of the Vacuum Chamber in Mixed Mode

Figure11 shows the temperatures on the three trays for a day where average sunshine reached 928 W/m2. The averages temperature on the three trays are 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C. The temperature is regulated to the value of 51°C as a set point, and it remained there between 11 h 03 and 14 h 48. The average ambient temperature is 40.5°C.Figure 11
Temperature and irradiance profiles in mixed mode with regulation.


## 3.2. Model of the Corrector of Temperature Controller

The theoretical curve is shown in Figure12. Normally, it grows to a maximum ideally located at solar noon and then decreases until sunset.Figure 12
Experiment temperature profiles in the dryer chamber.The resolution of equation (2) allows us to have the following expression of the temperature as a function of time which explains the profile of the curve of Figure 12.(15)Tfst=Tfe+BA1−e−A/macpat,with(16)A=Shn+hvandB=ShvTv+hnTn.The variation of the temperature strongly depends on the convective exchange coefficients.Thus, the time constantC can be expressed as(17)C=Amacpa.This constantC depends on the properties of the coolant and the convective exchanges, and it influences the rapid attainment of the maximum temperature.For average temperature values on the glass and the absorber (Tv = 37°C and Tn = 60°C), the curve (Figure 12) resembles a usual curve if the input is an amplitude step B/A.Since the studied method has a first-order transfer function, it can be controlled by a proportional regulator with or without integral.By using the choice graph of the regulator proposed by the method of Broida, this process has no delayτ, and the ratio θ/τ will tend towards infinity. This corresponds to the domain of proportional actions. Thus, we can write(18)Kp=θGsθd.


## 3.3. Control of Relative Humidity

### 3.3.1. Variation of Humidity during Temperature Control

Figure13 shows that moisture curve varies in the opposite direction to the temperature. The humidity is stable at 10% after 4 hours, while the temperature also becomes stable at 56.4°C on the tray 2 after 2 hours. This shows that if the temperature is stable for a period of time, moisture will follow the same trend, and this information can be used to set the end of drying. This manipulation is done at the average relative humidity of 40%.Figure 13
Temperature and irradiance profiles with regulation in the mixed mode.


### 3.3.2. Control the End of Drying

The majority of industrial drying systems makes it easy to control the parameters and sometimes offer the possibility to control several parameters simultaneously [27, 39]. These different parameters are controlled over time. Thus, time is considered as a control signal of drying. All food products use time to mark the end of their drying. The system may stop automatically if drying is complete.In solar dryers where the energy source is not mastered, the heat source pumps the heat into the chamber to dry the products. Using the time to set the end of drying while the input parameters are stochastic can skew the results. The use of a system parameter to set the end of drying makes it possible to follow the stochastic variations of these parameters.Relative humidity, which is a measurable, controllable, and stochastic quantity, can be used to control the drying of products. Indeed, it is possible to signal the end of drying of a product which has dried quickly or slowly.


## 3.3.1. Variation of Humidity during Temperature Control

Figure13 shows that moisture curve varies in the opposite direction to the temperature. The humidity is stable at 10% after 4 hours, while the temperature also becomes stable at 56.4°C on the tray 2 after 2 hours. This shows that if the temperature is stable for a period of time, moisture will follow the same trend, and this information can be used to set the end of drying. This manipulation is done at the average relative humidity of 40%.Figure 13
Temperature and irradiance profiles with regulation in the mixed mode.


## 3.3.2. Control the End of Drying

The majority of industrial drying systems makes it easy to control the parameters and sometimes offer the possibility to control several parameters simultaneously [27, 39]. These different parameters are controlled over time. Thus, time is considered as a control signal of drying. All food products use time to mark the end of their drying. The system may stop automatically if drying is complete.In solar dryers where the energy source is not mastered, the heat source pumps the heat into the chamber to dry the products. Using the time to set the end of drying while the input parameters are stochastic can skew the results. The use of a system parameter to set the end of drying makes it possible to follow the stochastic variations of these parameters.Relative humidity, which is a measurable, controllable, and stochastic quantity, can be used to control the drying of products. Indeed, it is possible to signal the end of drying of a product which has dried quickly or slowly.


## 4. Conclusion

For regulation to be possible in the indirect solar dryer, there must be solar energy that can exceed the set point temperature by more than 5%. With NTC fixed on tray number 2, the average temperature on three trays is 51.3 ± 1.5a°C, 52.18 ± 1.4a°C, and 51.9 ± 1.2a°C, respectively, and 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C, respectively, when the set point is 52°C and 51°C in the linking and mixed air flow mode, respectively, whereas, in the crossing airflow mode, the temperature gradient does not allow regulation on all trays. During storage, the time constant C depends on the properties of the coolant and the convective exchanges, and it influences the rapid attainment of the maximum temperature.In solar dryers where the energy source variation is stochastic, relative humidity, which is a measurable, controllable, and stochastic quantity is the best parameter to fix the end of drying products instead of time.



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*Source: 6668095-2021-12-16.xml*