Performance Analysis and Identification of an Indirect Photovoltaic Thermal Dryer with Aluminum Oxide Nano-Embedded Thermal Energy Storage Modification

Abstract

In the current paper, different thermal energy storage unit-integrated photovoltaic thermal (PVT) air collectors with and without nanoparticles have been designed, fabricated and tested. Aluminum oxide nanoparticles have been integrated into the thermal storage unit to increase the performance of the PVT collector. The developed collectors have been tested in a drying application at two different mass flow rates. The major goals of this work are upgrading the performance of the PVT air collector by employing a nano-embedded thermal energy storage unit and analyzing the impacts of using nanoparticles in the latent heat storage unit in the PVT collector on the drying performance of the system. The drying time was reduced by approximately 15–22% by employing nanoparticles in the thermal storage unit. Moreover, overall exergy efficiency values were obtained in ranges of 12.49–14.67% and 13.64–16.06%, respectively, for modified and unmodified PVT air collectors. It should be indicated that the overall energy and exergy efficiencies of the PVT air collectors were improved in the ranges of 6.91–6.97% and 9.20–9.47%, respectively, by using nanoparticles in the thermal energy storage unit. The combination of increasing the flow rate and integrating nanoparticles into the storage unit improved the overall exergetic efficiency of the PVT air collector by 28.58%. The mean exergetic efficiency of the drying room was between 48.33 and 54.26%. In addition to the experimental analysis, dynamic models for thermal and exergy efficiencies of developed collectors were constructed by employing the system identification method.

1. Introduction

Global energy demand is increasing day by day and results in negative consequences such as environmental pollution [1,2]. Sustainable and inexhaustible energy resources should be utilized to eliminate these negative impacts. In recent years, solar energy has become one of the most popular renewable energy sources because of its widely accessible and easy-to-apply features [3,4]. Both electrical and thermal energy can be produced by using solar irradiance.

One of the most popular methods for simultaneously producing electrical and thermal energies is utilizing hybrid photovoltaic thermal (PVT) collectors. Different working fluids such as air, water and nanofluids can be employed in PVTs. Moreover, various modifications such as fins [5] and obstacles [6] can be integrated to increase the residence time of the working fluid and heat transfer surface area. There are some works about different modifications in PVT systems in the academic literature. Fan et al. [7] investigated a hybrid PVT solar air heating system by employing a multiobjective design optimization approach. The thermal and electrical output values were significantly improved with the optimization study. Fudholi et al. [8] designed a grooved PVT air heating system and tested the collector under different conditions. They achieved an exergy efficiency value in the range of 12.89–13.36%.

In addition to geometrical modifications, the thermal performance of PVT systems can be upgraded by utilizing latent heat thermal energy storage units (TESUs). Generally, paraffin wax is employed in TESUs as a phase change material (PCM) [9]. There are some advantages of paraffin, which are the absence of phase separation and constant latent heat of fusion [10,11]. One of the main characteristics of paraffin wax is its low melting point, which allows its usage in low-temperature systems [12]. Fiorentini et al. [13] developed a PVT air system with PCM to be utilized in a residential HVAC system. They employed a hybrid predictive control model for optimizing the system. In a work published by Ahmadi et al. [14], PCM-integrated PVT systems have been tested under natural and forced convection modes. Energy efficiency values for the best PVT cases were achieved as 67–83% and 13–14%, respectively, for active and passive modes. Carmona et al. [15] designed a PVT system with PCM and a recovery system. The electrical efficiency was improved by 7.43% in comparison to a conventional photovoltaic panel. Fu et al. [16] structured a PVT system using PCM with multilayer heat exchangers. In their work, the mean electrical yield was upgraded by 1% by employing PCM.

It is known that paraffin wax has low thermal conductivity [17,18]. Nanoparticles can be added to PCMs for upgrading their thermal conductivity values. There are some studies that investigate PVT systems modified with nano-enhanced PCM. Al-Waeli et al. [19] investigated a PVT system with nano-embedded PCM. They achieved electrical and thermal efficiencies between 13.2 and 13.7% and 71.3 and 72%, respectively. Kazemian et al. [20] utilized aluminum oxide nano-enhanced PCM in a PVT water heater. They also used response surface methodology in the study. The optimal thermal and electrical exergies were attained as approximately 2.4 and 136 W/m², respectively. There are also some studies that consider the utilization of PVT water heaters with zinc oxide and copper oxide nano-enhanced PCM [21,22]. It should be indicated that these mentioned studies include PVT water heating systems.

PVT collectors can be utilized in various processes such as domestic water heating, space heating and drying. Agricultural product drying by using PVT collectors has become a popular research topic in recent years. Veeramanipriya and Sundari [23] developed a PVT system based on a vacuum tube collector and tested it in a drying application. The drying process was performed for eight hours, and moisture content was reduced from approximately 91.5% to 11%. Tiwari et al. [24] designed a PVT-assisted greenhouse dehumidification system and performed an experimental analysis. They also performed a numerical investigation based on MATLAB. In another study, Mortezapour et al. [25] structured a PVT heater-assisted heat pump dryer for a saffron drying process. According to the experimental results, the maximum drying efficiency was obtained as 72%. Nayak et al. [26] utilized a PVT collector to improve the performance of a greenhouse dryer. The mean efficiency of the dryer was found to be 34.2%. Tiwari and Tiwari [27] developed a mixed-mode PVT air collector integrated greenhouse dryer. They utilized different numbers of collectors in the drying application. The thermal efficiency of the developed system varied approximately between 42% and 61%. In another study, Çiftçi et al. [28] fabricated a vertically placed PVT air heating system, which was utilized in a drying application. The thermal efficiency of the developed PVT was found to be between 47.46% and 58.16%. Gupta et al. [29] analyzed a PVT dryer under forced and natural convection conditions. The thermal efficiency of the PVT collector and payback time of the dryer were between 43.58 and 69.27% and 1.4 and 1.7 years, respectively. Tiwari et al. [30] investigated a solar dryer based on a PV-attached roof and a drying room. The overall yield of the system was attained as 77.98%. In another work, Gupta et al. [31] designed a PVT drying system for a green tea drying process, where the maximum thermal efficiency of the PVT collector was found to be 58.71%.

In recent years, modeling of drying applications by utilizing different modeling approaches has become a popular research topic. Hao et al. [32] analyzed and modeled a solar dehumidifier. They used experimental data including environmental conditions, air flow rate and outlet temperature by using five different machine learning approaches. They obtained higher accuracy between the experimental data and model outputs. Gürel et al. [33] developed and experimentally analyzed a solar-collector-assisted fluidized bed drying system. A modeling approach based on response surface methodology was used for the experimentally obtained moisture content. In another work, Kırbaş et al. [34] employed artificial intelligence to estimate various drying methods of pomelo peel while a smart interface in the model was also provided. In a study performed by Dhalsamant [35], a mixed-mode solar drying process was modeled using an artificial intelligence method by using different parameters such as product diameter, drying time and product temperature. Abdenouri et al. [36] predicted the thermal behavior in a solar dryer by developing a state-space model. A new type of temperature controller was developed for the solar drying system.

In this work, two different PVT air collectors including a paraffin-based TESU and nano-enhanced paraffin-based TESU are designed and produced. In the previous work, the influence of adding copper oxide nanoparticles in the thermal storage component on the thermal and electrical performances of a PVT air heater was explored [37]. Moreover, alumina nanoparticles were utilized in the thermal energy storage unit of a greenhouse drying system [38]. This study also compares the effect of utilizing an alumina nano-enhanced TESU on the performances of greenhouse dryers and PVT dryers. In the present work, a new type of PVT is developed, and its effectiveness in a drying application is experimentally explored. A novel nano-enhanced TESU-integrated PVT air collector has been utilized in a solar drying application. The major aims of this work are to develop a novel nano-enhanced thermal energy storage unit to improve the performance of a PVT air collector and test the newly developed PVT air collector in a drying application. Solar radiation has been employed to meet both the thermal and electricity demands of a drying system by using the present design. By using alumina nanoparticles, the effectiveness of the TESU in the PVT air collector is significantly upgraded. There are many works available in the literature that explain the positive effects of utilizing alumina nanoparticles in various types of solar thermal systems including the solar organic Rankine cycle [39], solar thermal energy storage system [40], solar liquid collector [41] and concentrating solar systems [42] because of their superior thermal properties [43]. The general structure of the current study is presented in Figure 1. Data from the experimental analysis are used to create a dynamic model based on the system identification method, which is also another novelty of the present work. A multi-input multi-output (MIMO) dynamic model is developed for the energetic and exergetic efficiency values of the PVT collectors.

2. Materials and Methods

2.1. Fabrication of Nano-Integrated Latent Heat Storage Unit

In the current study, two different PVT air collectors with different modifications are developed. In this regard, two different thermal energy storage units (TESUs) were prepared. Two basins were fabricated by utilizing 1 mm thick aluminum sheets (dimensions: 620 × 590 × 250). Paraffin was selected as the phase change material in PVT air collectors. The first TESU contains paraffin wax. Paraffin wax was liquefied on a heater at a constant 60 °C and poured into the basin for fabricating the first TESU. The volume expansion rate of the phase change material is indicated as 0.125 by the manufacturing company. In this context, 85% of basins were filled to prevent leakages in the liquid phase. The second TESU includes alumina (Al₂O₃) nanoparticles. A two-step approach was employed to fabricate a nano-embedded TESU (NeTESU) [44,45]. In the initial stage, paraffin was liquefied, and nano-sized particles were added to the paraffin. After that process, the obtained mixture was stirred by a mechanical stirrer for an hour at 500 rpm. An MTOPS brand MS3040 model mechanical mixer was utilized for that purpose. In the last step of the preparation process, nano-embedded paraffin wax was sonicated for three hours to achieve a homogenous dispersion. It should be stated that the entire process was conducted in the liquid phase at a constant temperature (60 °C). Additionally, the weight concentration of the nano-integrated phase change material is 1% (wt/wt). Determination of the weight concentration and the entire preparation process were performed by referring to similar works in the literature that analyzed different types of nano-enhanced PCMs including myoinositol-based nano-PCM [46], oxide nano-enhanced PCM [47] and alumina nano-enhanced paraffin wax [48]. Specifications of the employed PCM and nanoparticles are depicted in

Table 1. Specifications of the utilized paraffin wax and Al₂O₃ nanoparticles.

Material	Specification	Value
Nanoparticles	Manufacturing company	Nanografi Co., Turkey
	CAS No.	1344-28-1
	Mean particle size	78 nm
	Color	white
	Purity	99.5+%
	Morphology	almost spherical
	Crystallographic structure	rhombohedral
	Specific heat capacity	880 J·kg−1·K−1
	Specific surface area	>20,000 m2/kg
Phase change material	Manufacturer	RUBITHERM
	Model	RT42
	Thermal conductivity	0.2 W·m−1·K−1 (both phases)
	Specific heat capacity	2 kJ·kg−1·K−1
	Heat storage capacity	250 kJ·kg−1
	Density	8 kg·L−1 (solid), 7 kg·L−1 (liquid)

. In addition, the SEM image and XRD pattern of utilized alumina nanoparticles are shown in Figure 2. The morphological structure of the Al₂O₃ nanoparticles was examined with the LEO 1430VP model scanning electron microscope (SEM) images (Figure 2a). This micrograph showed that the synthesized nanoparticles are not apart but rather interconnected in chains of beads with primary particles with an average size of ∼130 nm. However, small particles less than 40 nm in size exist in clusters between larger particles as evidenced by Figure 2a. The X-ray diffraction (XRD) pattern of Al₂O₃ nanoparticles (Figure 2b) was recorded at room temperature using Philips X-ray diffractometer with Cu Kα radiation (λ = 1.5406 Å) in 2θ ranging from 20° to 80°. The prepared nanostructures’ XRD pattern confirmed the formation of Al₂O₃ nanostructures with a cubic structure and a face-centered lattice of Al₂O₃ nanoparticles with a lattice constant of a = b = c = 7.94 Å. This is completely consistent with the standard Joint Committee on Powder Diffraction Standards (JCPDS) card (no: 79-1558) [49].

2.2. Experimental Setup

As mentioned before, a copper oxide nanoparticle-integrated TESU has been utilized in a PVT air collector in the previous study [37]. The present work investigates the effects of utilizing alumina nanoparticles on the performance of the PVT air collector. Moreover, the performance of the newly developed collector was tested in a drying application. In this regard, two PVT air heaters with different modifications were developed and fabricated. PV panels (power: 85 W) were employed (brand/model: Lexron/LXR-85P, I_mp = 4.44 A, V_mp = 18.00 V, I_sc = 4.86 A, V_oc = 22.10 V and dimensions: 670 × 780 × 25 mm) in the experimental part of this study. The first PVT collector contains a paraffin-based TESU. The second PVT collector was improved with a nano-enhanced TESU. The depths of air channels are 70 mm for both collectors. Four guiding plates were integrated into each collector. TESUs were put on the back surface of the PV systems. The dimensions of the storage units are 620 × 590 × 25 mm. Impermeability was secured by employing epoxy glue and liquid seal. The guiding fins and the basin of the TESU were fabricated from 1 mm thick aluminum sheets for both collectors. Dimensions of the PVTs are illustrated in Figure 3. Fabricated PVT collectors were coupled with drying chambers with dimensions of 300 × 300 × 200 mm. It should be indicated that the sides and bottom part of the PVT collectors and entire surfaces of drying chambers were thermally insulated. Two identical platforms were manufactured for placing the PVT dryer with a thermal energy storage unit (PVTD/TESU) and nano-embedded thermal energy storage unit (PVTD/NeTESU). The schematic illustration and an image of the test rig are presented in Figure 4 and Figure 5, respectively.

2.3. Experimental Procedure

Performance tests were executed on two consecutive days in August 2021 in Manisa province of Turkey. The developed dryers were tested simultaneously at two mass flow rates of 0.014 and 0.007 kg·s⁻¹. In other words, the developed systems were tested at a higher flow rate on the first day, while on the second day, the developed PVT dryers were tested simultaneously at a lower flow rate. Green apples (Granny Smith) were employed as a drying sample within the scope of this survey. Apples were cleaned and seeds were subtracted and sized into 3 mm slabs by employing a special slicing apparatus. The initial moisture content (5.20 ± 0.12 g_water·g_{dry matter}⁻¹) of the drying sample was determined by using an oven-drying approach, which is a widely utilized method [28,50,51]. The mass of products is taken as 100 g for each drying system. Drying samples were placed on a perforated tray before the tests. Performance tests were started at 10 a.m. in the morning and finished when the variation between two mass measurements was lower than one percent. However, PVT collector performance tests were continued until 17:00 to observe the thermal and electrical behavior of newly developed TESUs. Temperature measurements were taken every five seconds. Other metrics were measured ten-minute intervals.

3. Theoretical Analysis

3.1. Energy Evaluation of the PVT Collector

The energy expressions in a hybrid PVT air collector system can be given as below:

$${\displaystyle \sum }{\dot{E}}_i={\displaystyle \sum }{\dot{E}}_l+{\displaystyle \sum }{\dot{E}}_o$$

(1)

$${\dot{E}}_{m,i}+{\dot{E}}_{su}={\displaystyle \sum }{\dot{E}}_l+{\dot{E}}_{el}+{\dot{E}}_{m,o}$$

(2)

$${\displaystyle \sum }{\dot{E}}_l={\dot{E}}_{l,r}+{\dot{E}}_{l,c}+{\dot{E}}_{l,f}$$

(3)

In the second equation (Equation (2)), ${\dot{E}}_{su}$ represents the receiving solar radiation and could be expressed by employing Equation (4) [52]:

$${\dot{G}}_e=\alpha \times \tau \times \dot{G}\times A$$

(4)

The thermal energy gained by flowing air could be found as

$${\dot{E}}_t={\dot{E}}_{m,o}-{\dot{E}}_{m,i}=\dot{m}\times c_p\times \left(T_{o,ai}-T_{i,ai}\right)$$

(5)

The specific heat capacity of the air can be found as [53]

$$c_p=1009.26-0.0040403\times T+0.00061759\times T^2-0.0000004097\times T^3$$

(6)

Electrical power can be attained as

$${\dot{E}}_{el}=I_{sc}\times V_{oc}\times FF$$

(7)

In Equation (7), $FF$ depicts the fill factor of the PV module, and it could be attained as [54]

$$FF=P_{mx}/\left(I_{sc}\times V_{oc}\right)=\left(I_{mx}\times V_{mx}\right)/\left(I_{sc}\times V_{oc}\right)$$

(8)

The overall energy of the PVT system can be given as

$${\dot{E}}_{ov}={\dot{E}}_{el}+{\dot{E}}_t$$

(9)

Energy losses in the hybrid collector could be shown as follows:

$${\displaystyle \sum }{\dot{E}}_l={\dot{E}}_{su}-{\dot{E}}_t-{\dot{E}}_{el}$$

(10)

The electrical yield of the PVT collector could be attained as [52]

$${\eta }_{el}=\frac{{\dot{E}}_{el}}{{\dot{E}}_{su}}=\frac{I_{sc}\times V_{oc}\times FF}{{\dot{G}}_e}$$

(11)

The thermal efficiency of the PVT system could be given as [55]

$${\eta }_t=\frac{{\dot{E}}_{m,o}-{\dot{E}}_{m,i}}{{\dot{E}}_{su}}=\frac{\dot{m}\times c_p\times \left(T_{o,ai}-T_{i,ai}\right)}{{\dot{G}}_e}$$

(12)

The normalized power output efficiency defines the ratio of outlet power attained under actual conditions to standard test conditions, and it can be achieved as

$${\eta }_{np}=\left(\frac{P_{ms}}{P_{stc}}\right)\times 100$$

(13)

The performance ratio is a widely employed warranty metric for commercial PV facilities. This indicator could be employed to compare the performance of PV plants in different regions and could be found by employing Equation (14) [56]

$$PR=\frac{P_{ms}/P_{stc}}{G/1000}$$

(14)

3.2. Exergy Evaluation of the PVT Collector

The exergy expressions in a PVT air heater at quasi-steady-state conditions could be given as follows [57]:

$${\displaystyle \sum }{\dot{Ex}}_i={\displaystyle \sum }{\dot{Ex}}_o+{\displaystyle \sum }{\dot{Ex}}_l$$

(15)

$${\dot{Ex}}_{su}+{\dot{Ex}}_{m,i}={\dot{Ex}}_{el}+{\dot{Ex}}_{m,o}+{\displaystyle \sum }{\dot{Ex}}_d$$

(16)

$${\displaystyle \sum }{\dot{Ex}}_d={\dot{Ex}}_{d,r}+{\dot{Ex}}_{d,c}+{\dot{Ex}}_{d,f}$$

(17)

Exergy input can be achieved as follows [58]:

$${\dot{Ex}}_{su}=\dot{G}\times \left(1-\frac{T_a}{T_{su}}\right)$$

(18)

Exergy of the air flow rate could be expressed by using Equation (19):

$${\dot{Ex}}_{m,o}-{\dot{Ex}}_{m,i}=\dot{m}\times c_p\times \left({\psi }_o-{\psi }_i\right)$$

(19)

Stream exergy equations could be given as [52]

$${\psi }_o=\left({\overline{h}}_o-{\overline{h}}_a\right)-T_a\left(s_o-s_a\right)$$

(20)

$${\psi }_i=\left({\overline{h}}_i-{\overline{h}}_a\right)-T_a\left(s_i-s_a\right)$$

(21)

The electrical exergy can be found as below [59]:

$${\dot{Ex}}_{el}={\dot{E}}_{el}$$

(22)

Total exergy can be achieved by employing Equation (23):

$${\dot{Ex}}_{ov}={\dot{Ex}}_{el}+{\dot{Ex}}_t$$

(23)

Destroyed exergy of the collector can be found as

$${\displaystyle \sum }{\dot{Ex}}_d={\dot{Ex}}_{su}-{\dot{Ex}}_{el}-{\dot{Ex}}_t$$

(24)

The electrical exergy efficiency could be obtained by employing the expression below [52]:

$${\epsilon }_{el}=\frac{{\dot{Ex}}_{el}}{{\dot{Ex}}_{su}}=\frac{{\dot{E}}_{el}}{\dot{G}\times \left(1-\frac{T_a}{T_{su}}\right)}=\frac{I_{sc}\times V_{oc}\times FF}{\dot{G}\times \left(1-\frac{T_a}{T_{su}}\right)}$$

(25)

Thermal exergy efficiency could be achieved as [52]

$${\epsilon }_t=\frac{{\dot{Ex}}_t}{{\dot{Ex}}_s}=\frac{\dot{m}\times c_p\times \left[\left(T_o-T_i\right)-T_a\ln \left(\frac{T_o}{T_i}\right)\right]}{\dot{G}\times \left(1-\frac{T_a}{T_{su}}\right)}$$

(26)

Total exergy efficiency can be attained as

$${\epsilon }_{ov}={\epsilon }_{el}+{\epsilon }_t$$

(27)

3.3. Exergy Evaluation of the Drying Room

The exergy balance expression for the drying chamber could be attained as

$${\displaystyle \sum }{\dot{Ex}}_{i,dc}-{\displaystyle \sum }{\dot{Ex}}_{o,dc}={\displaystyle \sum }{\dot{Ex}}_{l,dc}$$

(28)

Inlet and outlet exergies for the drying room could be attained by using Equations (29) and (30), respectively [60]:

$${\dot{Ex}}_{i,dc}={\dot{m}}_{ai}{c}_p\left[\left(T_{i,dc}-T_a\right)-T_a\ln \left(\frac{T_{i,dc}}{T_a}\right)\right]$$

(29)

$${\dot{Ex}}_{o,dc}={\dot{m}}_{ai}{c}_p\left[\left(T_{o,dc}-T_a\right)-T_a\ln \left(\frac{T_{o,dc}}{T_a}\right)\right]$$

(30)

The exergy yield of the drying room could be given as [61]

$${\epsilon }_{dc}=\frac{{\dot{Ex}}_{o,dc}}{{\dot{Ex}}_{i,dc}}$$

(31)

3.4. Evaluation of Drying Parameters

The dry basis moisture content could be expressed as [62]

$$X_{db}=\left(\frac{X_i-X_d}{X_d}\right)100$$

(32)

The moisture ratio could be found by employing Equation (33) [34]:

$$MR=\frac{X-X_{eq}}{X_0-X_{eq}}$$

(33)

The drying rate could be achieved as

$$DR=\frac{X_{t+dt}-X_t}{dt}$$

(34)

Fresh agricultural crops have high moisture content. In this context, Equation (33) can be rewritten as [63]

$$MR=\frac{X}{X_0}$$

(35)

3.5. Analysis of Exergy-Based Sustainability Parameters

The sustainability index (SI) depicts the lifetime of the analyzed dehumidifier, and WER expresses the exergy loss per given unit exergy inlet. The SI can be expressed as

$$SI=\frac{1}{\left(1-\epsilon \right)}$$

(36)

The waste exergy ratio can be found as [62]

$$WER=\frac{{\dot{Ex}}_l}{{\dot{Ex}}_i}$$

(37)

3.6. Uncertainty Analysis

Expression of experimental uncertainty in its general form can be given as [64,65]

$$W_R=\sqrt{\left[{\left(\frac{\partial R}{\partial x_1}{w}_1\right)}^2+{\left(\frac{\partial R}{\partial x_2}{w}_2\right)}^2+\dots +{\left(\frac{\partial R}{\partial x_n}{w}_n\right)}^2\right]}$$

(38)

Obtained uncertainty values are depicted in

Table 2. Empirical uncertainties.

Metric	Unit	Uncertainty
Temperature	°C	±0.58
Electrical power	W	±0.37
Solar radiation	W/m2	±16.54
Velocity of air	m/s	±0.41

. The obtained uncertainties are in good agreement with similar surveys that analyzed PVT collectors and solar dryers [52,66,67,68].

4. Dynamic Model with MIMO System Identification

An input–output dynamic model is constructed by using the available data from the experimental study. Models based on artificial intelligence, identification and model order reduction are created by using a data set from the experimental test rig or computational fluid dynamics in diverse energy system technologies [69,70,71,72,73]. These mathematical models are used for fast estimation of the system performance or to capture the dynamic features of the systems.

A multi-input multi-output (MIMO) system is considered by using system identification [74,75,76]. In this method, relevant input and output data sets are collected. Then, a model structure using finite impulse response (FIR), autoregressive with exogenous input (ARX) and output error (OE) is selected. The number of delays in the input and output data set, regressor type, selection of the appropriate model structure and model validation checks are some of the common steps available in dynamics system modeling. The functional form for a multivariable ARX model can be represented as

$$\begin{gathered} A0·y\left(t\right)+A1·y\left(t-T\right)+\dots +An·y\left(t-nT\right)\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}=B0·u\left(t\right)+B1·u\left(t-T\right)+...+Bm·u\left(t-mT\right)+e\left(t\right) \end{gathered}$$

(39)

In Equation (39), $u$ and $y$ denote the input and output data set, respectively.

In the present work, ambient temperature and solar radiation were considered as the input while thermal energy and exergy efficiencies were used as the output for the system at a flow rate of 0.07 kg/s. Time-dependent data from local time between 10:00 to 16:00 with 10 min sampling were used to obtain the input–output dynamic models. Two different MIMO models were constructed—one for the PVT with TESU and the other for the PVT with NeTESU. The MATLAB system identification toolbox was utilized in the investigation. The model order and delays for a 2 input–2 output ARX model were selected as

$$na=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right],\hspace{1em}nb=\left[\begin{array}{cc}10& 10\\ 10& 10\end{array}\right],\hspace{1em}nk=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$$

(40)

5. Results and Discussion

5.1. Experimental Results

In this part, empirical outcomes and results of the modeling study of the present work have been presented and discussed in detail. Experimental evaluation includes thermal, electrical and exergetic analysis of the developed PVT air heating systems, investigation of drying parameters and exergy-based sustainability indicators and exergetic analysis of the drying room.

Change in environmental parameters over time is illustrated in Figure 6. The attained mean environmental temperature values for the tests performed at high and low mass flow rates are 31.8 and 32.0 °C, respectively. Moreover, mean solar radiation values were observed as 866 and 870 W/m², respectively. Environmental parameters are quite similar for both days. The deviation between solar radiation and ambient temperature values are 0.62% and 0.46%, respectively. These similar environmental values allow us to make an accurate comparison of the obtained results.

The variation in outlet temperatures of air over drying time can be found in Figure 7. The average outlet air temperature was attained as 52.9 and 54.4 °C for the PVT with TESU and PVT with NeTESU, respectively, in the tests performed at high air velocity. For a lower air velocity, outlet air temperatures were attained as 59.8 and 61.9 °C, respectively. The highest instantaneous outlet temperature value was obtained in the PVT with NeTESU as 67.50 °C at 13:20 (experiment performed at a lower flow rate). Similar trends in outlet temperature value were achieved by some studies that analyzed PVT collectors [77,78]. In addition, the mean obtained useful thermal energy rate for the PVT with TESU was between 206 and 294 W. For the PVT with NeTESU, useful gain thermal energy values were attained in the range of 221–315 W. Adding nanoparticles in the system improved the useful thermal energy in the range of 7.14–7.28%.

Change in the thermal yield of PVT collectors over time is demonstrated in Figure 8. Mean thermal efficiencies for the PVT with TESU and PVTD with NeTESU were achieved as 65.2% and 69.9%, respectively, in the experiment conducted at a higher velocity. At low air velocity, these values were obtained as 45.6% and 48.9%, respectively. Additionally, the change in electrical efficiencies of PVT collectors over time is illustrated in Figure 9. Mean electrical efficiencies for the PVT with TESU and PVTD with NeTESU were obtained as 12.9% and 13.7%, respectively, in the test performed at a higher velocity. At a low flow rate, these metrics were achieved as 11.2% and 11.8%, respectively. As seen, enhancing the velocity and utilizing nano-doped PCM improved the electrical yield by 22.32%. Integrating nanoparticles into the system enhanced the thermal conductivity of the storage system and led to improvements in both thermal and electrical efficiencies. Gholampour et al. [79] experimentally investigated an unglazed PVT collector, and electrical and thermal efficiencies were enhanced by enhancing the air velocity. Additionally, similar behaviors of thermal and electrical efficiencies were attained in some works about hybrid PVT collectors [80,81].

Average overall energetic efficiency values for the PVT with TESU and PVT with NeTESU were attained as 83.51% and 78.11%, respectively, in the test performed at a higher flow rate. These values were attained as 62.79% and 59.62%, respectively, in the experiment performed at a lower flow rate. By using nanoparticles in the TESU, the overall energetic efficiency values of the PVT air collector were improved by 6.91% and 6.97%, respectively, in the tests performed at higher and lower flow rates. Both modifying the TESU with nanoparticles and enhancing the flow rate improved the overall energetic efficiency by 40.07%.

Figure 10 presents the variation in the performance ratio over time. This metric is generally employed as a warranty value for PV power plant projects. The average performance value was found to be 0.79 and 0.84 for the PVT with TESU and PVT with NeTESU, respectively, in the tests performed at a higher velocity. For a lower velocity, performance ratio values were attained as 0.68 and 0.72, respectively. Moreover, mean normalized power output efficiency values for nano-modified and unmodified PVTs were attained between 62.79 and 72.61% and 59.62 and 68.65%, respectively. As seen, both the performance ratio and normalized power output efficiencies were improved by integrating nanoparticles into the TESU. In the literature, some surveys analyzed conventional and PCM-assisted PV systems and significantly improved the electrical performance by utilizing PCMs [56,82,83]. Different from available works, Al₂O₃ nano-doped PCM was utilized to enhance the effectiveness of a PVT air collector.

The change in moisture contents over time is depicted in Figure 11. The obtained drying process time values for PVTD/TESU and PVTD/NeTESU are 200 and 170 min, respectively, in the test performed at high velocity. These metrics were observed as 330 and 270 min, respectively, in the test performed at low velocity. As seen, utilizing nanoparticles in the system reduced the drying period by between 15 and 22%. Additionally, it can be indicated that the flow rate of air has a crucial influence on the drying time. Increasing the flow rate decreased the drying time by approximately 37–39%. Similar drying behavior can be seen in similar works available in the literature. In a work published by Khanlari et al. [50], a four-flow PV-assisted dehumidification system has been analyzed. Their outcomes showed that drying time was decreased by 21–47% by enhancing the flow rate. Similar drying trends were obtained by some surveys that surveyed solar drying applications [84,85,86].

Drying rate (DR) is a widely utilized performance indicator in solar dehumidification applications. The time-dependent change in DR values is given in Figure 12. The obtained mean DR values for PVTD/TESU and PVTD/NeTESU are 0.00130 and 0.00181 g_water·g_{dry matter}⁻¹·min⁻¹, respectively, in the experiment conducted at a higher velocity. Drying rate values were obtained as 0.00048 and 0.00074 g_water·g_{dry matter}⁻¹·min⁻¹, respectively, in drying test performed at a lower velocity. The moisture content of the drying products is higher during the first period of the drying process. Therefore, it is easier to remove water from the product during this period. However, reducing the moisture content of the product by elapsing time induced a reduction in the DR values. Similar findings were attained by works analyzing solar drying systems performed at flow rates similar to those in this study. Tuncer et al. [67] and Afshari et al. [51] both surveyed sustainable dryers and attained DR values quite similar to those in the current work.

In this work, the exergetic efficiency metric was analyzed on electrical and thermal aspects [52]. The change in thermal exergy yield values of PVT heaters is given in Figure 13. Mean thermal exergy efficiencies for the PVT with TESU and PVTD with NeTESU were achieved as 8.99% and 8.00%, respectively, in the test conducted at high velocity. Additionally, these metrics were achieved as 7.56% and 6.72%, respectively, in the experiment performed at 0.007 kg·s⁻¹. In one work, Abuşka and Şevik [55] investigated grooved solar air heating systems and achieved an exergy efficiency value between 1 and 7%. In another work, Nayak and Tiwari [87] analyzed a PVT collector to improve the performance of a greenhouse dryer. They attained a thermal exergy efficiency of approximately 4%. In another research, Jahromi et al. [88] analyzed a PVT collector under various climatic conditions and found the thermal exergy efficiency value to be between 9.6 and 9.7%.

The change in overall exergy yield over time is given in Figure 14. Total exergy yield is defined as the sum of electrical and thermal efficiency values. The overall exergy efficiencies for the PVT with TESU and PVT with NeTESU were achieved between 12.49 and 14.67% and 13.64 and 16.06%, respectively. In a previous study, a copper oxide nanoparticle-enhanced TESU has been utilized in a PVT collector and compared with conventional and paraffin-based TESU-modified systems [37]. Average overall exergy efficiency values were obtained in the range of 10.52–15.44%. In addition, mean electrical exergy efficiencies were obtained as 6.68% and 7.06%, respectively, in the test performed at high velocity in the current study. At a lower velocity, these values were achieved as 5.77% and 6.08%, respectively. Mean sustainability index values for the hybrid collectors with and without nano-doped modification were attained between 1.16 and 1.19 and 1.14 and 1.16, respectively.

Variation in exergetic efficiencies of the drying room over local time is depicted in Figure 15. Mean exergetic efficiency values of the drying room for PVTD/TESU and PVTD/NeTESU were found to be 51.29% and 54.26%, respectively, in the test performed at high velocity. In the survey conducted at low velocity, these values were attained as 48.33% and 49.85%, respectively. The exergetic efficiency of the drying room is related to inflow and outflow temperature values of the drying room. In the first step of the dehumidification process, the temperature difference of the dryer was high because of the high water content of the product at the initial stage. Therefore, the exergetic efficiency value of the drying room was lower at the beginning stage of the process. In the last step of the process, the water content of the drying product is lower in comparison to the initial stage, and the inlet and outlet temperature values are close to one other, which allows us to achieve a superior exergy efficiency value. The main reason for this issue is the reduction in the difference between outflow and inflow temperature values of the drying chamber. Kesavan et al. [89] analyzed a solar dehumidifying application and found an exergy yield of the drying room between 3 and 87%. Additionally, Panwar [90] analyzed the exergy yield of the drying room of a solar dehumification system and obtained a value between 23 and 73%. In a different research, Karthikeyan and Murugavelh [91] surveyed a tunnel dehumidifier and attained an exergy yield of the drying room in the range of 23–73%. Moreover, similar behavior for the drying room’s exergy efficiency can be found in some recent studies that analyzed various solar drying systems [62,92,93,94,95].

Time-dependent variation in the sustainability index and waste exergy ratio values are given in Figure 16 and Figure 17, respectively. In the dehumidifying test performed at low velocity, the obtained mean SI values for PVTD/TESU and PVTD/NeTESU are 2.57 and 2.64, respectively. Mean SI values of the drying chamber for PVTD/TESU and PVTD/NeTESU were calculated as 2.2% and 2.44, respectively, at low velocity. In addition, average WER metrics for PVTD/TESU and PVTD/NeTESU were achieved between 0.48 and 0.51 and 0.45 and 0.50, respectively. While the highest SI value was found in the nano-enhanced system at a high air flow rate, the WER value obtained was the lowest. Similar values were observed in some studies that analyzed solar dehumidifying processes available in academic literature. Ndukwu et al. [96] analyzed a hybrid dehumidificator and obtained SI and WER values between 2.3 and 6.11 and 0.05 and 0.94, respectively. Akpinar [97] analyzed the pepper drying process in a solar dehumidifier and attained an SI between 0.39 and 6.16. In a different work, Mugi and Chandramohan [62] designed and experimentally tested an indirect solar dryer and attained SI and WER values between 3.69 and 5.1 and 0.41 and 0.44, respectively.

Photographs of undried and dried samples are presented in Figure 18. Additionally, results of the present study were compared with similar papers that analyzed different types of solar dehumidificators as shown in

Table 3. Comparison of attained results with similar works in academic literature.

Ref.	Dryer Type	Modification	Flow Rate (kg·s−1)	Thermal Efficiency of Collector (%)	Exergy Yield of Collector (%)	Exergy Yield of Drying Chamber (%)	SI of Drying Chamber	WER of Drying Chamber
[28]	Indirect PVT dryer	Vertically placed PVT collector, baffles	0.010, 0.012, 0.014	47.46–58.16 (a)	2.32–2.86 (a)	41.85–56.11 (a)	2.16–3.25 (a)	0.43–0.58 (a)
[50]	Indirect solar dryer	Quadruple-flow solar air collector, PV panel assistance	0.007, 0.010, 0.013	73.27–78.19 (a)	3.56–4.40 (a)	44.16–58.38 (a)	1.93–2.73 (a)	0.52–0.56 (a)
[51]	Indirect solar dryer	Compact geometry, obstacles	0.011, 0.014	38.49–49.30 (a)	-	44.91–55.28 (a)	2.23–3.06 (a)	-
[62]	Indirect solar dryer	Corrugated absorber, PV panel assistance	0.0429–0.0690	61.49–74.98 (a)	2.03–2.44 (a)	55.45–59.32 (a)	3.69–5.1 (a)	0.41–0.445 (a)
[91]	Indirect solar dryer	Mixed mode, tunnel geometry	-	-	-	49.12 (a)	-	-
[92]	Indirect solar dryer	Grooved absorber, thermal energy storage, PV panel assistance	0.06	-	-	8.66- 79.02 (i)	-	-
[93]	Indirect solar dryer	Shelved drying chamber	-	-	-	21.35–80.5 (i)	-	-
[94]	Indirect solar dryer	Sensible and latent heat thermal storage	-	9.8–26.10 (a)	0.14–0.81 (a)	30.28 (a)	-	-
[95]	Indirect solar dryer	Parallel-flow drying chamber	-	9.64–40.24 (a)	-	47 (a)	-	-
[96]	Indirect solar dryer	Biomass furnace, copper tubing as a heat exchanger	-	-	-	5.6–95.13 (i)	2.3–6.11 (i)	0.05–0.94 (i)
[97]	Indirect solar dryer	Finned solar heating system	-	-	-	28.22–86.02 (i)	0.393–6.156 (i)	0.13–0.71 (i)
[98]	Indirect solar dryer	Solar absorber extension tube with ball-shaped turbulators	0.008, 0.0012	45.26–64.71 (a)	-	-	-	-
[99]	Direct solar dryer	Auxiliary solar heater, PV panel assistance, black thermal curtain	0.0572–0.0998	35.93–52.70 (a)	-	-	-	-
[100]	Direct solar dryer	Drying chamber with transparent cover	0.006, 0.01, 0.015	8.18–28.87 (a)	0.38–1.65 (a)	1.09–7.49 (a)	-	-
This study	Indirect PVT dryer (PVTD-TESU)	Thermal energy storage unit	0.007, 0.014	45.6–65.2 (a)	12.49–14.67 (a)	48.33–51.26 (a)	2.20–2.57 (a)	0.48–0.51 (a)

a: average; i: instantaneous.

. As it clearly seen, attained results in the current work are quite comparable with similar papers. It should be indicated that selected studies for comparing the obtained results were operated at similar flow rate values.

5.2. System Identification Results

The model coefficients for the analyzed systems are presented in

Table 4. Model coefficients for the analyzed PVTD systems.

Model Coefficient	System Type
	PVTD-TESU	PVTD-NeTESU
A0	$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$	$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
B0	$\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$	$\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
B1	$\left[\begin{array}{cc}-0.0246& 0.5923\\ 0.0002& -0.4397\end{array}\right]$	$\left[\begin{array}{cc}-0.0067& 0.5689\\ 0.0050& -0.5003\end{array}\right]$
B2	$\left[\begin{array}{cc}0.0180& -0.2417\\ -0.0080& -0.0399\end{array}\right]$	$\left[\begin{array}{cc}0.0698& 2.0220\\ 0.0017& 0.4587\end{array}\right]$
B3	$\left[\begin{array}{cc}0.0163& 0.8393\\ 0.0148& 0.2466\end{array}\right]$	$\left[\begin{array}{cc}-0.0975& 0.0564\\ -0.0081& 0.0953\end{array}\right]$
B4	$\left[\begin{array}{cc}-0.0159& 1.0632\\ -0.0073& 0.2998\end{array}\right]$	$\left[\begin{array}{cc}-0.0176& -0.7648\\ -0.0083& -0.1020\end{array}\right]$
B5	$\left[\begin{array}{cc}0.0523& 0.2136\\ 0.0244& 0.2738\end{array}\right]$	$\left[\begin{array}{cc}0.0726& -0.9125\\ 0.0301& 0.0489\end{array}\right]$
B6	$\left[\begin{array}{cc}0.0464& 0.2565\\ 0.0117& 0.0913\end{array}\right]$	$\left[\begin{array}{cc}-0.0747& 0.3967\\ -0.0140& 0.1263\end{array}\right]$
B7	$\left[\begin{array}{cc}-0.0296& -2.0407\\ -0.0047& -0.5761\end{array}\right]$	$\left[\begin{array}{cc}0.1217& 0.2052\\ 0.0282& -0.1018\end{array}\right]$
B8	$\left[\begin{array}{cc}-0.0931& -0.3803\\ -0.0252& -0.3757\end{array}\right]$	$\left[\begin{array}{cc}-0.0561& -0.7408\\ -0.0182& -0.4835\end{array}\right]$
B9	$\left[\begin{array}{cc}-0.0170& 0.4159\\ -0.0057& 0.1480\end{array}\right]$	$\left[\begin{array}{cc}0.0032& 0.8044\\ -0.0020& 0.2383\end{array}\right]$
B10	$\left[\begin{array}{cc}0.0689& 0.7742\\ 0.0342& -0.3137\end{array}\right]$	$\left[\begin{array}{cc}0.0200& -0.3548\\ 0.0263& -0.6019\end{array}\right]$

. To assess the model quality, residual analysis is used. The whiteness test and the independence test are considered. In the first test, the residual autocorrelation function lies inside the confidence interval, and it shows the uncorrelated residuals. In the second test, the correlation of the residuals with past inputs is performed, and for a good model, it should be uncorrelated. The autocorrelation of the residuals and cross correlation between the input and output data set for channels $u_1-y_1$ and $u_2-y_2$ are shown in Figure 19. These can be used for assessment of model quality. The residual autocorrelation function lies within the confidence interval for a good model, and it shows that the residuals are uncorrelated.

Further assessment of model quality can be achieved by using the fit values, which are given as

$$\mathrm{Fit}=\left[1-\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^N{\left(y\left(i\right)-y_m\left(i\right)\right)}^2}{{{\displaystyle \sum }}_{i=1}^{N}y{\left(i\right)}^2}}\right]\times 100$$

(41)

where $y\left(i\right)$ and $y_m\left(i\right)$ are the experimental data and identified model data, respectively. The model fits to the data set for the energy and exergy efficiency values of the MIMO model are shown in Figure 20. The dynamic characteristics of the efficiencies for the base and nano-enhanced system are very well captured with the MIMO dynamic system. The fits between the experimental data and dynamic model are above 85%.

6. Conclusions

In this work, two hybrid PVT air collectors with different types of (paraffin-based and nano-doped paraffin-based) thermal energy storage units have been designed, fabricated and experimentally surveyed in a drying application. The main findings of the current survey are listed as below:

• The drying time was decreased by 5–22% by employing a nano-integrated thermal storage unit.
• The mean electrical efficiency was raised by 22.32% by upgrading the air velocity and adding nano-sized particles into the thermal storage unit.
• By using nanoparticles in the TESU, the overall energetic efficiency values of the PVT air collector were improved by 6.91% and 6.97%, respectively, in the tests performed at higher and lower flow rates. Both modifying the TESU with nanoparticles and enhancing the flow rate improved the overall energetic efficiency by 40.07%.
• The total exergy efficiencies for the PVT collector with TESU and PVT air collector with NeTESU were obtained in the ranges of 12.49–14.67% and 13.64–16.06%, respectively. In addition, mean electrical exergy yield values were achieved as 6.68% and 7.06%, respectively, in the test performed at a higher velocity value.
• The average sustainability index and waste exergy ratio of the drying chamber for PVTD/TESU were found to be between 2.26 and 2.57 and 0.48 and 0.51, respectively. These values for PVTD/NeTESU were obtained as 2.44–2.64 and 0.45–0.50, respectively.
• A multi-input multi-output dynamic model was obtained by using the system identification method for the developed PVT collectors considering energetic and exergetic efficiencies as multiple outputs of systems. The dynamic characteristics of the systems were well captured with dynamic models, and a modeling accuracy above 85% was achieved.

The findings of this work indicated that modifying the thermal energy storage component with nano additives significantly upgraded the electrical, thermal and drying effectiveness of a PVT air collector based indirect solar drying system. Moreover, future studies can include investigations of the effect of different types of nanoadditive modifications in the thermal storage component on the effectiveness of the PVT air collector and the solar drying system. Additionally, various nanoparticle concentration ratios can be tested to determine the optimum configuration. It should be indicated that the present work contains pilot-scale PVT drying systems. For real-time applications, various size arrangements, load capacities and nanoparticle ratios should be analyzed in detail. To improve the performance of the modeling, nonlinear system identification with different model structures can be considered.