Modeling, simulation and experimental validation of a solar dryer for agro-products with thermal energy storage system

Accepted Manuscript MODELING, SIMULATION AND EXPERIMENTAL VALIDATION OF A SOLAR DRYER FOR AGRO-PRODUCTS WITH THERMAL ENERGY STORAGE SYSTEM

José Vásquez, Alejandro Reyes, Nicolás Pailahueque PII:

S0960-1481(19)30239-3

DOI:

10.1016/j.renene.2019.02.085

Reference:

RENE 11217

To appear in:

Renewable Energy

Received Date:

21 June 2018

Accepted Date:

16 February 2019

Please cite this article as: José Vásquez, Alejandro Reyes, Nicolás Pailahueque, MODELING, SIMULATION AND EXPERIMENTAL VALIDATION OF A SOLAR DRYER FOR AGROPRODUCTS WITH THERMAL ENERGY STORAGE SYSTEM, Renewable Energy (2019), doi: 10.1016/j.renene.2019.02.085

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MODELING, SIMULATION AND EXPERIMENTAL VALIDATION OF A SOLAR DRYER FOR AGRO-PRODUCTS WITH THERMAL ENERGY STORAGE SYSTEM

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José Vásquez*, Alejandro Reyes, Nicolás Pailahueque.

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Department of Chemical Engineering, Universidad de Santiago de Chile, Santiago, Chile

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ABSTRACT This paper presents a dynamic model of a solar dryer for agro-products with thermal energy storage system, using paraffin wax as phase change material. The mathematical model of the dryer was separated in three stages: a solar panel, a solar accumulator and a drying chamber. The system of equations was solved using numerical integration. The models were validated with experimental data reported in previous studies on the drying of kiwifruit and mushrooms. Temperatures was measured at the outlet of the solar panel and solar accumulator, solid moisture content and air humidity were measured at the inlet and outlet of the drying chamber. Based on fit evaluations R2 and RMSE, the model accurately predicts temperature and humidity of the drying air, temperature and moisture of the product, behavior of the heat transfer and drying parameters and time variable climatic conditions ambient temperature, air humidity, and solar radiation.

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KEYWORDS: Solar dryer, phase change material (PCM), energy accumulation, modeling and simulation

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*Corresponding author: José Vásquez, [email protected], Department of Chemical Engineering, Universidad de Santiago de Chile, Santiago, Chile.

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HIGHLIGHTS  Thermal efficiency can increase for solar dyers equipped with phase change material  The use of PCM extends operation time into periods of low or no radiation.  A dynamic model of a solar dryer for agro-products with energy accumulation was presented.  The mathematical model integrates the behavior of the solar panel, solar accumulator and drying chamber.  Based on residual analysis the models accounted for experimental data satisfactorily.

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NOMENCLATURE A C D da ds H hc hfg hr hw I k L M N m N Nu Pr Q Re Rh RH SD SL ST T t U u v V W X

area heat capacity diameter dry air dry solid humidity convective heat transfer coefficient latent heat of vaporization radiative heat transfer coefficient convective heat transfer coefficient to ambient air radiation drying rate constant height moisture of the product section number mass control volumes Nusselt number Prandlt number heat Reynolds number hydraulic radio relative humidity diagonal distance between can centers longitudinal distance between can centers transversal distance between can centers temperature time global heat loss coefficient wind velocity air velocity volume mass flow rate axial coordinate

m2 J/kg K m dimensionless dimensionless kg/kg W/m2 K J/kg W/m2 K W/m2 K W/m2 1/s m (water kg/kg db) dimensionless kg dimensionless dimensionless dimensionless J dimensionless m dimensionless m m m K s W/m2 K m/s m/s m3 kg/s m

Greek letters α β δ η θ λ µ ρ σ τ ϕ

absorbance long thickness efficiency angle between surface normal and incident radiation latent heat of fusion viscosity density Stefan–Boltzmann constant transmittance liquid fraction of wax

dimensionless m m % dimensionless J/kg kg/m s kg/m2 W/m2 K4 dimensionless dimensionless

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Subscripts 0 a abs av b e f fin fus g h i L liq max n p pc R s S SA sol SP w x

initial condition ambient air absorbed average absorber plate equilibrium drying air final condition fusion glass cover hydraulic position index latent liquid maximum data identification number product of drying phase change radiation sky sensible solar accumulator solid solar panel paraffin wax position index

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1

INTRODUCTION

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Most foods are perishable, so good storage life (shelf life) is vital if agro-products are to be transported over large distances and stored in warehouses, or by the consumer, for substantial periods of time [1]. Drying is a commonly used process for the preservation of food, since it reduces the water content and therefore biochemical, chemical and microbiological deterioration. However, drying of agro-products is an energy-intensive operation with high operational costs driven primarily by energy consumption.

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The sun is a major source of available energy (i.e., solar energy) for planet Earth. However, despite increased awareness of this huge potential, the contribution of solar energy to the global energy supply is still negligible [2]. Along with rising energy costs, the environmental impact of fossil fuels, and even concerns of fuel depletion, solar energy is an economical alternative that can also virtually eliminate CO2 and CO emissions as well as other contaminants [3] from the drying process. Therefore, it is reasonable that solar energy has been widely used in drying processes. To date, several solar dryer technologies and designs have been implemented [4-5].

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Nevertheless, control and optimization of the drying process is desirable. Recent studies have developed detailed analytical and experimental models of solar drying of food and herbs [6-9] to refine the drying system and to optimize the use of solar energy. Given the complex interactions between the variables involved, complex control strategies are necessary. Vasquez et al. [10] implemented an advanced multivariable control system using fuzzy logic in a solar dryer equipped with a thermal energy storage system.

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One disadvantage of solar energy is that the collector is completely dependent on fluctuations in radiation levels. For example, solar collection diminishes during the winter especially in the higher latitudes. Similarly, solar energy can only be collected during a few hours of the day, when the radiation is high enough to generate potential. Simply put, if the radiation is low or zero, it is not possible to heat the air in the dryer. The use of a thermal energy storage system can extend the period of available energy, making it possible to heat the drying air for a longer time [11-12].

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Phase change materials (PCMs) have been widely adopted in the solar energy field for their thermal energy storage capacity; indeed, they show a significant enthalpy of fusion with the ability to store and release large amounts of energy during melting and solidification processes [13]. One of the materials most frequently used as a PCM is paraffin wax, an organic component that is non-corrosive and chemically stable, with low thermal conductivity and a high heat density at constant temperature during its fusion and solidification periods. Also, it is inexpensive. The melting temperature of paraffin wax and the heat provided through fusion depend on its composition. Several studies have examined the process of solar drying with a solar energy accumulator using paraffin wax as PCM [14-19]. While paraffin wax has an admittedly low thermal conductivity, some researchers have improved the conductivity. Reyes et al. [20] doubled the thermal conductivity of the paraffin wax by mixing it with 5% w/w aluminum strips.

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The studies currently presented, only present specific and independent models for drying with solar panels [21-24] and energy accumulators [25-26]. In addition, most of the studies focus on the operation and efficiency of each equipment. The objective of the present study was to develop a global mathematical model of a solar dryer equipped with a PCM-based solar accumulator and to 4

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simulate its thermal behavior while drying agro-products. The models were validated with experimental data recorded from drying kiwifruit and mushrooms, where the temperature was measured at the outlet of the solar panel and at the solar accumulator, product moisture content and air humidity were measured at the inlet and outlet of the drying chamber.

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2.1 EQUIPMENT

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The dryer used in this study (Figure 1) has a solar panel and an accumulator that uses paraffin wax as a PCM to store energy. The solar panel consists of a chamber 1.2 m wide, 2.9 m long, and 0.07 m high. To increase heat transfer, inside the solar panel are 40 zinc fins painted black, each is 0.03 m in height and with 0.025 m of space between them. The solar panel is thermally insulated and the top is covered by glass with a thickness of 0.007 m (Figure 2a).

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EQUIPMENT AND EXPERIMENTAL PROCEDURES

(a)

(b)

Figure 1. a) Schematic of the solar dryer: (1) drying chamber, (2) blower, (3) vent valve, (4) vent, (5) recirculation valve, (6) solar panel valve, (7) solar accumulator valve, (8) solar accumulator, (9) solar panel, and (10) fresh air inlet. b) P&ID of the solar dryer.

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In the solar dryer system, the solar accumulator consisting of a chamber 1.2 m in width, 2.9 m in length, and 0.12 m high (Figure 2b), may be used to replace or augment heated air from the solar panel. The solar accumulator uses 300 soft drink cans filled with a total of 56 kg of paraffin wax as PCM. Soft drink cans were also cut into thin strips and 4.8 kg of these aluminum strips were placed into the wax in the cans to increase the effective thermal conductivity of the wax (details about aluminum strips procedure can be found in Reyes et al. [20]). These wax-filled cans are used to store thermal energy in order to extend the available drying time. The cans are oriented perpendicular to the air flow, resulting in 30 rows of 10 cans each.

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The drying chamber has a load capacity of 25 kg with dimensions of 1.9 m in length, 0.55 m in width, and 0.46 m in height. It is divided into two zones with 5 perforated trays, each of which has dimensions of 0.58 m x 0.47 m (Figure 2c). 6

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Cans with PCM Zinc Fins

(a)

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(b)

(c) Figure 2.

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a) Solar panel b) Solar accumulator c) Drying chamber

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2.2 EXPERIMENTAL PROCEDURES

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The solar panel and solar energy accumulator were located on the roof of a four-story building at the Department of Chemical Engineering, Universidad de Santiago de Chile, Santiago, Chile. The drying runs were conducted during summer (January 2016), and all runs started at 11:45 am with the drying air introduced from the solar panel to the drying chamber, while the solar energy accumulator simultaneously received solar radiation. Experimental data gathered from the dryer described in this section and reported by Reyes et al. [27] and Reyes et al. [28] was used to validate the mathematical model. The experimental data set consisted of solar radiation measurements, ambient temperature measurements, air temperature measured at the outlet of the solar panel,

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the solar accumulator, and the drying chamber, product moisture measurements, and the humidity measured at the inlet and outlet of the drying chamber.

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The data acquisition system (OPTO 22, model SNAP-PAC-R1) used to monitor the performance of the solar dryer made it possible to record the air temperature at the outlet of the solar panel and solar accumulator with thermocouples (type K), as well as air temperature and relative humidity (RH/°C transmitter, model HI 8666, Hanna Instruments) at the inlet and the outlet of the drying chamber. Dynamic pressure of pitot tubes was measured through pressure sensors in two sectors, one located at the outlet of the centrifugal fan and the other at the outlet of vent valve, to calculate the air velocity. The solar radiation was measured with a pyranometer (LI-200SA) placed at one side of the solar panel on the roof of the building. This information was stored on a PC.

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The solar dryer consists of three main parts that can be modeled separately as a solar panel, a solar accumulator, and a drying chamber. In the development of the model for each part, the following assumptions were made:

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MODELING OF THE SOLAR DRYER

The pressure of the system is constant. The thermo-physical properties of the air are constant. In the solar panel and solar accumulator, the air flow is in the axial direction. Absorption, reflection, and transmission coefficients of the absorber plate, glass cover, and wax cans are constant.  The thermal resistance at the interface between the wax cans and PCM is neglected, as is the effect of radial conduction of the solid wax.    

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3.1

SOLAR PANEL MODEL

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Figure 3 shows a schematic of the solar panel modeled in this study. The mathematical model describes the dynamics of the air temperature 𝑇𝑓, glass cover temperature 𝑇𝑔 and absorber plate temperature 𝑇𝑏.

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Figure 3. Schematic of the solar panel.

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3.1.1

Energy balance in the air

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The dynamics of air temperature inside the solar panel 𝑇𝑓, includes convective heat transfer inside the solar panel, between the glass cover surface and the air and also between the absorber plate and the air. 𝐴𝑏,𝑆𝑃 includes zinc fins. Considering a longitudinal element dx in the solar panel at a distance x from the inlet, the energy balance of the solar panel components is given by Equation (1) [22]. ∂𝑇𝑓 ∂𝑇𝑓 𝜌𝑓𝐴𝑔𝛿𝑆𝑃𝐶𝑓 + 𝛽𝑊𝑓𝐶𝑓 = 𝐴𝑔ℎ𝑐,𝑔𝑓(𝑇𝑔 ― 𝑇𝑓) + 𝐴𝑏,𝑆𝑃ℎ𝑐,𝑏𝑓(𝑇𝑏 ― 𝑇𝑓) ∂𝑡 ∂𝑋

(1)

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For analysis the solar panel is divided into 10 a number of control volume sub-sections (NSP) along the panel (𝛽 =2.9 m), 0.29 m each section (control volumes, NSP=10), as separating it into more sections does not result in any appreciable differences in the simulation; where 𝑥 is the position index (when 𝑥 = 0; 𝑇𝑓,0 = 𝑇𝑎 ), Equation (1) can be expressed as Equation (2) [22]. 𝐴𝑔 𝑑𝑇𝑓,𝑥 𝐴𝑔 𝐴𝑏,𝑆𝑃 𝜌𝑓 𝛿𝑆𝑃𝐶𝑓 = 𝑊𝑓𝐶𝑓(𝑇𝑓,0 ― 𝑇𝑓,𝑥) + ℎ𝑐,𝑔𝑓(𝑇𝑔 ― 𝑇𝑓,𝑥) + ℎ (𝑇 ― 𝑇𝑓,𝑥) 𝑁 𝑑𝑡 𝑁 𝑁 𝑐,𝑝𝑓 𝑏

(2)

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3.1.2

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The dynamics behavior of the glass cover temperature 𝑇𝑔, includes:

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Energy balance on the glass cover

 Convective heat transfer between the glass cover surface and the air inside the solar panel ℎ𝑐,𝑔𝑓 and between the glass cover surface and the ambient air ℎ𝑤,𝑔𝑎.  𝑇𝑓 is the average air temperature at the inlet and outlet temperatures of the panel.  Radiative heat transfer between the glass cover surface and absorber plate surface 𝐴𝑏ℎ𝑟,𝑏𝑔 and between the glass cover surface and the sky 𝐴𝑔ℎ𝑟,𝑔𝑠.  Solar radiation absorbed by the glass cover 𝐴𝑔𝛼𝑔𝐼.  The glass absorptivity 𝛼𝑔 has the same value for both solar radiation and for thermal radiation. The energy balance on the glass cover is given by Equation (3) [22]. 𝑑𝑇𝑔 𝜌𝑔𝐴𝑔𝛿𝑔𝐶𝑔 = 𝐴𝑔,𝑆𝑃ℎ𝑟,𝑏𝑔𝛼𝑔(𝑇𝑏 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑐,𝑔𝑓(𝑇𝑓 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑤,𝑔𝑎(𝑇𝑎 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑟,𝑔𝑠(𝑇𝑠 ― 𝑇𝑔) + 𝐴𝑔𝛼𝑔𝐼 𝑑𝑡

(3)

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3.1.3 Energy balance on the absorber plate

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The dynamics of absorber plate temperature 𝑇𝑏, includes:

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 Convective heat transfer between the absorber plate surface and the air inside the solar panel ℎ𝑐,𝑏𝑓.  Radiative heat transfer between the glass cover surface and absorber plate surface ℎ𝑟,𝑏𝑔.  Heat loss from the absorber plate 𝐴𝑔𝑈𝑏(𝑇𝑎 ― 𝑇𝑏), 𝐴𝑔 is equal to the external area of the absorber plate (the zinc fins are not considered).  Radiation absorbed by the absorber plate 𝐴𝑔𝜏𝑏𝛼𝑏𝐼. The energy balance on the absorber plate is given by Equation (4) [22]. 𝜌𝑏𝐴𝑏,𝑆𝑃𝛿𝑏𝐶𝑏

𝑑𝑇𝑏 𝑑𝑡

= 𝐴𝑏,𝑆𝑃ℎ𝑐,𝑏𝑓(𝑇𝑓 ― 𝑇𝑏) + 𝐴𝑔,𝑆𝑃ℎ𝑟,𝑏𝑔(𝑇𝑔 ― 𝑇𝑏) + 𝐴𝑔𝑈𝑏(𝑇𝑎 ― 𝑇𝑏) + 𝐴𝑏,𝑆𝑃𝜏𝑔𝛼𝑏𝐼

(4)

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3.1.4 Heat transfer coefficient

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The radiative heat transfer coefficient ℎ𝑟,𝑔𝑠 between the glass cover and the sky is given by Equation (5) [29].

181 ℎ𝑟,𝑔𝑠 = 𝜀𝑔𝜎(𝑇𝑔2 + 𝑇𝑠2)(𝑇𝑔 + 𝑇𝑠)

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(5)

In Equation (5), 𝑇𝑠 is the equivalent temperature of the sky, calculated based on the correlation proposed by [30], which is given by Equation (6). 𝑇𝑠 = 0.0552𝑇𝑎1.5

(6)

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The radiative heat transfer coefficient ℎ𝑟,𝑏𝑔 between the glass cover and the absorber plate is given by Equation (7) [29]. ℎ𝑟,𝑏𝑔 =

𝜎(𝑇𝑏2 + 𝑇𝑔2)(𝑇𝑏 + 𝑇𝑔)

(7)

1 (1 ― 𝜀𝑏)𝐴𝑔 + 𝜀𝑔 𝜀𝑏𝐴𝑏,𝑆𝑃

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The convective heat transfer coefficient to the ambient air ℎ𝑤,𝑔𝑎 at the upper surface of the glass cover where it contacts the ambient air is given by Equation (8) [29]. (8)

ℎ𝑤,𝑔𝑎 = 2.8 + 3.0𝑢

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The Nusselt number is a correlation factor given by Equation (9), which is valid for turbulent flow, and for L/Dh >10 [31]. (9)

𝑁𝑢 = 0.0158𝑅𝑒0.8

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The Reynolds number is given by Equation (10) [31]. 𝑅𝑒 =

𝐷ℎ𝑣𝜌𝑓

(10)

µ𝑓

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The hydraulic diameter 𝐷ℎ,𝑆𝑃 is calculated from the relationship given by Equation (11) [31].

(

𝐷ℎ,𝑆𝑃 = 4𝑅ℎ,𝑆𝑃 = 4

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𝑊𝑆𝑃𝛿𝑆𝑃 2(𝑊𝑆𝑃 +𝛿𝑆𝑃)

)

(11)

Convective heat transfer coefficients between the internal air and either the inner surface of the glass cover ℎ𝑐,𝑔𝑓 or absorber plate ℎ𝑐,𝑏𝑓 are dependent on the Nusselt number 𝑁𝑢 from Equation (9) and the hydraulic diameter Dh from Equation (11), as shown in Equation (12) [31]. ℎ𝑐,𝑏𝑓 = ℎ𝑐,𝑔𝑓 =

𝑁𝑢 ∗ 𝑘𝑓

(12)

𝐷ℎ

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3.1.5 Solar panel efficiency

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The efficiency of the solar panel, is given by Equation (15) is calculated as the ratio of the heat absorbed by the air in the solar panel (Equation (13), to the heat from radiation incident on the solar panel during the period of use (Equation (14)) [29]. 𝑄𝑎𝑏𝑠,𝑓 =

∑𝑊

𝑆𝑃𝐶𝑓

(𝑇𝑓 ― 𝑇𝑎) ∗ Δ𝑡𝑛

(13)

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𝑡

𝑄𝑅 = 𝐴𝑆𝑃cos 𝜃

∫𝐼(𝑡) 𝑑𝑡

(14)

0

209 𝜂𝑆𝑃 =

𝑄𝑎𝑏𝑠,𝑓 𝑄𝑅

100%

(15)

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SOLAR ACCUMULATOR

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3.2

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Figure 4 shows a schematic of the solar accumulator modeled in this study. The mathematical model describes the dynamics of the air temperature 𝑇𝑓, glass cover temperature 𝑇𝑔, absorber plate temperature 𝑇𝑏, wax temperature 𝑇𝑤 and liquid fraction of wax 𝜙.

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Figure 4. Schematic of the solar accumulator during the energy discharge stage.

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3.2.1 Energy balance in the air

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Equation (16) gives the air temperature inside the solar accumulator 𝑇𝑓 where 𝑥 is the position index (when 𝑥 = 1; 𝑇𝑓,0 = 𝑇𝑎 ). ). In this equation the air temperature is calculated in the same way as for the solar panel, adding the convective heat transfer between the wax and the air inside the solar accumulator. The solar accumulator volume is subdivided into 30 axial sections (9.67 cm each sections), one for each row of cans (control volumes, NSA=30) [25]. 𝐴𝑤 represents the total area of cans in each section.

227 𝐴𝑔 𝑑𝑇𝑓,𝑥 𝐴𝑔 𝐴𝑏,𝑆𝐴 (16 𝜌𝑓 𝛿𝑆𝐴𝐶𝑓 = 𝑊𝑓𝐶𝑓(𝑇𝑓,0 ― 𝑇𝑓,𝑥) + ℎ𝑐,𝑔𝑓(𝑇𝑔 ― 𝑇𝑓,𝑥) + ℎ (𝑇 ― 𝑇𝑓,𝑥) + 𝐴𝑤ℎ𝑐,𝑤𝑓(𝑇𝑤,𝑥 ― 𝑇𝑓,𝑥) 𝑁 𝑑𝑡 𝑁 𝑁 𝑐,𝑏𝑓 𝑏 )

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3.2.2 Energy balance on the glass cover

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The glass cover temperature in the solar accumulator 𝑇𝑔, given by Equation (17) [25], was calculated in the same way as for the solar panel, adding the radiative heat transfer between the wax and the glass cover. 𝑑𝑇𝑔 𝜌𝑔𝐴𝑔𝛿𝑔𝐶𝑔 = 𝐴𝑏,𝑆𝐴ℎ𝑟,𝑏𝑔(𝑇𝑏 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑐,𝑔𝑓(𝑇𝑓 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑤,𝑔𝑎(𝑇𝑎 ― 𝑇𝑔) + 𝐴𝑔ℎ𝑟,𝑔𝑠(𝑇𝑠 ― 𝑇𝑔) 𝑑𝑡 + 𝐴𝑔ℎ𝑟,𝑤𝑔(𝑇𝑤 ― 𝑇𝑔) + 𝐴𝑔𝛼𝑔𝐼

(17)

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3.2.3 Energy balance on the absorber plate

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The absorber plate temperature in the solar accumulator 𝑇𝑏 is calculated in Equation (18) in the same way as for the solar panel [25]. 𝜌𝑏𝐴𝑏,𝑆𝐴𝛿𝑏𝐶𝑏

𝑑𝑇𝑏 𝑑𝑡

= 𝐴𝑏,𝑆𝐴ℎ𝑐,𝑏𝑓(𝑇𝑓 ― 𝑇𝑏) + 𝐴𝑔,𝑆𝐴ℎ𝑟,𝑏𝑔(𝑇𝑔 ― 𝑇𝑏) + 𝐴𝑔𝑈𝑏(𝑇𝑎 ― 𝑇𝑏) + 𝐴𝑔𝜏𝑔𝛼𝑏𝐼

(18)

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3.2.4 Energy balance in the PCM (paraffin wax)

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Equation (19) represents the energy balance for the sensible and latent heat of the PCM and the heat transfer to or from the air inside the solar accumulator during the charging and discharging process [25]. Radiative energy transfer between the PCM and the absorber was not considered, since the area 𝐴𝑏,𝑆𝐴 is small compared to the area of the 300 cans 𝐴𝑤. 𝑑𝑇𝑤 𝑑𝜙 𝜆𝑤𝑚𝑤 + 𝑚𝑤𝐶𝑤 = 𝐴𝑤ℎ𝑐,𝑤𝑓(𝑇𝑓 ― 𝑇𝑤) + 𝐴𝑔ℎ𝑟,𝑤𝑔(𝑇𝑔 ― 𝑇𝑤) + 𝐴𝑤𝜏𝑔𝛼𝑤𝐼 𝑑𝑡 𝑑𝑡

(19)

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Depending on the wax temperature, Equation (19) takes one of the three possible forms shown in Equations (20) to (22) [25]. 

(𝑻𝒘 < 𝑻𝒇𝒖𝒔) ⋀ (𝝓 = 𝟎) 𝑚𝑤𝐶𝑤,𝑠𝑜𝑙

𝑑𝑇𝑤 𝑑𝑡

= 𝐴𝑤ℎ𝑐,𝑤𝑓(𝑇𝑓 ― 𝑇𝑤) + 𝐴𝑔ℎ𝑟,𝑤𝑔(𝑇𝑔 ― 𝑇𝑤) + 𝐴𝑤𝜏𝑤𝛼𝑤𝐼

(20)

248 249



𝑑𝜙 𝜆𝑤𝑚𝑤 = 𝐴𝑤ℎ𝑐,𝑤𝑓(𝑇𝑓 ― 𝑇𝑤) + 𝐴𝑔ℎ𝑟,𝑤𝑔(𝑇𝑔 ― 𝑇𝑤) + 𝐴𝑤𝜏𝑤𝛼𝑤𝐼 𝑑𝑡

250 251

(𝑻𝒘 = 𝑻𝒇𝒖𝒔) ⋀ (𝟎 ≤ 𝝓 ≤ 𝟏)



(21)

(𝑻𝒘 > 𝑻𝒇𝒖𝒔) ⋀ (𝝓 = 𝟏) 𝑑𝑇𝑤 𝑚𝑤𝐶𝑤,𝑙𝑖𝑞 = 𝐴𝑤ℎ𝑐,𝑤𝑓(𝑇𝑓 ― 𝑇𝑤) + 𝐴𝑔ℎ𝑟,𝑤𝑔(𝑇𝑔 ― 𝑇𝑤) + 𝐴𝑤𝜏𝑤𝛼𝑤𝐼 𝑑𝑡

(22)

252

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253

3.2.5 Heat transfer coefficient

254 255

The radiative heat transfer coefficient ℎ𝑟,𝑤𝑔 between the wax cans and the glass cover is given by Equation (23) [25]. ℎ𝑟,𝑤𝑔 =

𝜎(𝑇𝑤2 + 𝑇𝑔2)(𝑇𝑤 + 𝑇𝑔)

(23)

1 (1 ― 𝜀𝑤)𝐴𝑔 + 𝜀𝑔 𝜀𝑤𝐴𝑤

256 257 258

Convective heat transfer coefficients can be calculated from the correlation given by Equation (24) valid for 1,000>Re>200,000 and 0.7>Pr>500 [32]. (24)

𝑁𝑢 = 𝐶1𝑅𝑒𝑚𝑎𝑥0.6𝑃𝑟0.36

259 260 261

The constant 𝐶1 is given by Equation (25), where 𝑆𝑇, 𝑆𝐿, and 𝑆𝐷 are the transversal, longitudinal and diagonal distances, respectively, between can centers [32]. 𝐶1 = 0.35

0.2

(25)

() 𝑆𝑇 𝑆𝐿

262 263

The Reynolds and Prandlt numbers are given by Equations (26) and (27), respectively [32]. 𝑅𝑒𝑚𝑎𝑥 =

𝐷ℎ𝑣𝑚𝑎𝑥𝜌𝑓

(26)

µ𝑓

264 𝑃𝑟 =

𝐶𝑓µ𝑓

(27)

𝑘𝑓

265 266 267

Considering that the cans are in rows of 10 each, the hydraulic diameter 𝐷ℎ,𝑆𝑃 is calculated from the relationship in Equation (28) [32].

((

𝐷ℎ,𝑆𝑃 = 4𝑅ℎ,𝑆𝑃 = 4

𝑊𝑆𝑃𝛿𝑆𝑃 ― 10𝐷𝑐𝑎𝑛𝐿𝑐𝑎𝑛

)

(28)

2 𝑊𝑆𝑃 +𝛿𝑆𝑃) + 10·2𝐿𝑐𝑎𝑛

268 269 270

The maximum air velocity 𝑣𝑚𝑎𝑥, which is a function of the pitch length arrangement, is given by Equation (29) [32].

𝑣𝑚𝑎𝑥 =

{

𝑆 𝑇𝑣 𝑆𝑇 ― 𝐷 𝑐

If: 2(𝑆𝐷 ― 𝐷𝑐) > 𝑆𝑇 ― 𝐷𝑐

;

𝑆 𝑇𝑣 2(𝑆𝐷 ― 𝐷𝑐)

;

(29)

otherwise

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272 273 274

Convective heat transfer coefficients between the internal air and the wax cans ℎ𝑐,𝑤𝑓 are calculated by Equation (30), using the Nusselt number 𝑁𝑢 from Equation (24) and the hydraulic diameter Dh from Equation (28) [32]. ℎ𝑐,𝑤𝑓 =

𝑁𝑢 ∗ 𝑘𝑓

(30)

𝐷ℎ

275 276

3.2.6 Solar accumulator efficiency

277 278 279 280

The efficiency of the solar accumulator is given by Equation (36) is calculated as the ratio of the heat absorbed by the air in the solar accumulator (Equation (31)) to the heat stored by the paraffin wax (Equation (32)) [29]. The heat stored by the paraffin wax consists of sensible heat (Equations (33) and (35)) and latent heat (Equation (34)) [29]. 𝑄𝑎𝑏𝑠,𝑓 =

∑𝑊

𝑆𝐴𝐶𝑓

(𝑇𝑓 ― 𝑇𝑎) ∗ Δ𝑡𝑛

(31)

281 𝑄𝑎𝑏𝑠,𝑤 = 𝑄𝑆,𝑙𝑖𝑞 + 𝑄𝐿 + 𝑄𝑆,𝑠𝑜𝑙

(32)

𝑄𝑆, 𝑙𝑖𝑞 = 𝑚𝑤 𝐶𝑤,𝑙𝑖𝑞 (𝑇𝑤,0 ― 𝑇𝑤,𝑝𝑐)

(33)

𝑄𝐿 = 𝑚 𝑤 𝜆

(34)

𝑄𝑆,𝑠𝑜𝑙 = 𝑚𝑤 𝐶𝑤,𝑠𝑜𝑙 (𝑇𝑤,𝑝𝑐 ― 𝑇𝑤,𝑓𝑖𝑛)

(35)

𝑄𝑎𝑏𝑠,𝑓

(36)

282

283

284

285 𝜂𝑆𝐴 =

𝑄𝑎𝑏𝑠,𝑤

100%

286 287

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DRYING CHAMBER

288

3.3

289 290 291 292 293 294

Figure 5 shows a schematic of the drying chamber modeled in this study. The mathematical model describes the dynamics of the air temperature and humidity at the inlet and outlet of the drying chamber (𝑇𝑓3, 𝑇𝑓2, 𝐻3 and 𝐻2, respectively), and the dynamics of the temperature and moisture of the drying product 𝑇𝑝 and 𝑀, respectively. The parameters at in the air inflow, air flow 𝑊𝑓1, air temperature 𝑇𝑓1 (resulting temperature between the air heated by the solar panel and solar accumulator) and air humidity 𝐻1, are considered constant for each time interval.

295

296 297

Figure 5. Schematic of the drying chamber.

298 299

3.3.1 Energy balance in the air

300 301 302

The dynamics of the air temperature at the outlet of the drying chamber, 𝑇𝑓2, considering the convective heat transfer between the drying product and the air inside the drying chamber, is given by Equation (37) [22]. 𝜌𝑓𝑉𝑓(𝐶𝑓 + 𝐶𝑣𝐻2)

𝑑𝑇𝑓2 𝑑𝑡

= 𝑊𝑓3(𝐶𝑓 + 𝐶𝑣𝐻1)𝑇𝑓3 ― 𝑊𝑓3(𝐶𝑓 + 𝐶𝑣𝐻2)𝑇𝑓2 + 𝐴𝑝ℎ𝑐,𝑝𝑓(𝑇𝑓2 ― 𝑇𝑝)

(37)

303

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304

3.3.2 Mass balance in the air

305 306 307

Equation (38) represents the dynamics of the drying air humidity at the outlet of the drying chamber 𝐻2, where the humidity gained by the drying air is equal to the moisture loss of the drying product [22]. 𝑑𝐻2 𝑑𝑀 𝜌𝑓𝑉𝑓 = 𝑊𝑓(𝐻3 ― 𝐻2) + 𝑚𝑝 𝑑𝑡 𝑑𝑡

(38)

308 309

3.3.3 Energy balance in the product

310 311 312 313

Equation (39) represents the dynamics of the drying product’s temperature at the outlet of the drying chamber 𝑇𝑝. This calculation includes the convective heat transfer between the drying product and the air inside the drying chamber minus the heat used to evaporate moisture contained in the drying product [22]. 𝑑𝑇𝑝 𝑑𝑀 + 𝐴 ℎ𝑐,𝑝𝑓(𝑇𝑓 ― 𝑇𝑝) 𝑚𝑝𝐶𝑝 = 𝑚𝑝ℎ𝑓𝑔 𝑑𝑡 𝑑𝑡 𝑝

(39)

314 315

3.3.4 Relationship for drying kinetics

316 317 318

In Equation (40), the dynamic of the drying product moisture 𝑀 is determined by Newton’s semitheoretical model, where the drying rate is proportional to the difference between actual and equilibrium moisture content [22]. 𝑑𝑀 = ―𝑘(𝑀 ― 𝑀𝑒) 𝑑𝑡

(40)

319 320 321

3.3.5 Recirculation

322 323 324

A portion of the drying air is recycled depending on the solar dryer’s design, the level of recirculation ranges between 70% and 90%. The humidity and the enthalpy of the mixed air are calculated from Equations (41) to (43). 𝑊3 = 𝑊2 + 𝑊1

(41)

𝑊3𝐻3 = 𝑊2𝐻2 + 𝑊1𝐻1

(42)

𝑊3ℎ3 = 𝑊2ℎ2 + 𝑊1ℎ1

(43)

325

326

327

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328

3.3.6 Heat transfer coefficient

329 330

Convective heat transfer coefficients between the product and the air are a function of the Nusselt number given in Equation (44) [23]. 𝑁𝑢 = 0.37𝑅𝑒0.6

(44)

331 332 333

Convective heat transfer coefficients between the product and the air ℎ𝑐,𝑝𝑓 (45) are given in Equation (44) [23]. ℎ𝑐,𝑝𝑓 =

𝑁𝑢 ∗ 𝑘𝑓

(45)

𝐷ℎ

334

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335

4

SIMULATION AND MODEL VALIDATION

336 337 338

The simulation was developed in MATLAB using the ode15s function to solve the numerical differentiation formulas (NDFs). The model was validated by comparing the numerical results with experimental data corresponding to each part (solar panel, solar accumulator and drying chamber).

339 340 341 342 343 344 345 346

The model-validation simulations make use of the experimental data set described in Section 2. From this set, solar radiation 𝐼 and ambient temperature 𝑇𝑎 are used as inputs for the solar panel model at 15-minute intervals. For the solar accumulator model, the solar radiation and ambient temperature data are used as inputs at a 10-minute interval. Air temperature at the outlet of the solar panel or solar accumulator 𝑇𝑓 and humidity at the inlet 𝐻3 of the drying chamber each taken at 10-minute intervals is used as an input for the drying chamber model. The calculation routines for each model are presented in Figure 6-8. The algorithms are valid for each time interval (𝑛) provided the input values can be considered constant during the time interval.

347 348 349 350 351

Validation calculations for the simulations consist of evaluating the residual (difference between simulated and measured values) at the outlets of each segment of the model. For the solar panel and solar accumulator, the significant parameter is the output temperature. For the drying chamber the significant parameters include the product moisture 𝑀 and humidity at the outlet 𝐻2 of the drying chamber.

Ta,n False

x=1

Tf,0=Tf,x-1

In

True

Tf,0=Ta

Tf,x (Eq. 2) x+1

False

352 353

x=N

True

Tf (oulet SP)

Tg (Eq. 3)

Tb (Eq. 4)

Heat transfer coefficient (Eq. 5-12)

Figure 6. Computational flow diagram of solar panel.

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Ta,n False

x=1

Tf,0=Tf,x-1

Paraffin wa x: initial con ditions (t=0) Tw=Tw0 Φ=1

In

True

Tw
Tf,0=Ta

(Eq. 20)

Tf,x

(Eq. 22)

(Eq. 21)

Tw,x

(Eq. 16)

Tw>Tfu s Φ=0

Tw=Tfu s 0≤Φ≤ 1

Φx

x+1

False

x=N

True

Tf (oulet SA)

Tg (Eq. 17)

Tb (Eq.18)

Heat transfer coefficient (Eq. 23-30)

354 355

Figure 7. Computational flow diagram of the solar accumulator.

356 357

Tf1 (Outlet SP)

Tf2 (Eq. 37)

Tf1 (Outlet SA)

H2 (Eq. 38)

359

Agro p rodu ct’s parameters

Tp (Eq. 39)

H3 (Eq. 42)

358

k-Me

H1

M

(Eq. 40)

T3 (Eq. 43)

Figure 8. Computational flow diagram of the drying chamber.

360

SOLAR PANEL MODEL

361

4.1

362 363 364 365 366

To analyze the effect of air flow on the solar panel, the simulation was repeated at 6 different mass flows 𝑊𝑆𝑃 (0.012 kg/s, 0.021 kg/s, 0.030 kg/s, 0.039 kg/s, 0.048 kg/s and 0.057 kg/s), based on equipment capacities. Figure 9 shows the simulation results for environmental conditions representative of a summer day. Table 1 shows the maximum and average air temperature at the solar panel output, heat absorbed by the air and the efficiency of the solar panel.

367 368 369

Based on these results, efficiency appears to decrease as the airflow decreases. In this simulation, lower airflow corresponds with higher air temperature, favoring heat loss to the environment due to high heat transfer coefficients. However, while for high airflow there is higher efficiency, this does 22

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370 371

not necessarily mean there is also a high drying efficiency, as drying at lower temperatures requires longer drying time to achieve the same product moisture.

372

Table 1. Solar panel simulation results. WSP (kg/s) 0.012 0.021 0.030 0.039 0.048 0.057

T max (K) 360.8 351.4 345.3 340.9 337.4 334.6

T av (K) 340.4 333.8 329.6 326.5 324.2 322.3

Q abs (kJ) 14,935 21,708 26,988 31,287 34,880 37,937

ηSP (%) 25.6 37.2 46.3 53.6 59.8 65.0

373

W=0.012 W=0.021 W=0.030 W=0.039 W=0.048 W=0.057

374 375

Figure 9. Effect of air mass flow 𝑊 on the solar panel.

376 377 378

The solar panel model was validated by comparing the experimental and simulation results for the air temperature at the outlet of the solar panel, for two air mass flows (0.030 kg/s and 0.048 kg/s). 23

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379 380 381

In addition, the results for the glass cover and the absorber plate temperatures are presented, along with the radiative heat transfer coefficient between the glass cover surface and absorber plate surface and between the glass cover surface and the sky.

382 383 384 385 386 387

Figure 10 and 11 show the result of simulation of the solar panel, for air flow of 0.03 kg/s and simulation time of 525 min. Figure 10a shows the simulation of the temperatures of the air, the glass cover and the absorber plate. Figure 10b shows the simulation of the radiative heat transfer coefficients between the glass cover and the sky (ℎ𝑟,𝑔𝑠) and between the glass cover and the absorber plate (ℎ𝑟,𝑏𝑔), for air flow of 0.03 kg/s. As can be seen the heat transfer coefficients vary according to the temperature change in the glass and the absorber.

388

389

390 391 392 393 394 395

(a)

(b)

Figure 10. a) Simulated temperatures of the air, the glass cover and the absorber plate for air flow of 0.030 kg/s in the solar panel model. b) Simulated heat transfer coefficients for air flow of 0.030 kg/s in the solar panel model. Figure 11 compares experimental and simulation results for the solar panel’s air temperature (section 10 corresponds to the solar panel’s output air temperature, according to explained in item 3.1.1) and it shows the values of the radiation and ambient temperature for air flow of 0.03 kg/s. In this simulation the model presents a correlation coefficient (R2) of 0.978 and a root mean squared error (RMSE) of 2.464.

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396 397

Figure 11. Experimental and simulation results for air flow of 0.03 kg/s in the solar panel model.

398 399 400 401 402 403 404

Figure 12 and 13 show the simulation of the solar panel, for air flow of 0.048 kg/s and simulation time of 525 min. Figure 12a shows the simulation of the temperatures of the air, the glass cover and the absorber plate. Figure 12b shows the radiative heat transfer coefficients for air flow of 0.048 kg/s. Figure 13 compares experimental and simulation results for the solar panel air temperature, and it shows the values of the radiation and ambient temperature for air flow of 0.048 kg/s. In this simulation the model presents an R2 of 0.940 and RMSE of 1.999.

405 406 407 408

The results for both air flows present the same tendencies for the experimental data and the simulation, and the absolute difference does not exceed 6 K. The glass cover and absorber plate temperatures were not measured; therefore, the estimated initial conditions can affect the results obtained at the beginning of the simulation.

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409

410

(a)

(b)

Figure 12. a) Simulated temperatures of the air, the glass cover and the absorber plate for air flow of 0.048 kg/s in the solar panel model. b) Simulated heat transfer coefficients for air flow of 0.048 kg/s in the solar panel model.

411 412

Figure 13. Experimental and simulation results for air flow of 0.048 (kg/s) in the solar panel model.

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SOLAR ACCUMULATOR MODEL VALIDATED

413

4.2

414 415 416 417

The aim of the solar accumulator in the drying process is to enable the dryer to continue its operation during periods of low or no solar radiation. That is why for practical purposes, only the discharge of energy to heat the drying air through the stored energy was evaluated. However, the model could also be used to analyze the charging period.

W=0.012 W=0.018 W=0.024 W=0.030 W=0.036 W=0.042

418 419

Figure 14. Effect of air mass flow 𝑊 on the solar accumulator.

420 421 422 423 424 425

To analyze the effect of air flow on the solar accumulator in the energy discharge period (Figure 14), the simulation was performed for 6 different air mass flows 𝑊𝑆𝐴 (0.012, 0.018, 0.024, 0.030, 0.036, 0.42 kg/s) according to the blower capacities, under environmental conditions of a summer day. Table 2 shows the maximum and average air temperature at the solar panel output, the amount of heat absorbed by the air, and the efficiency of the solar accumulator.

426 427 428 429 430

Although the solar accumulator’s efficiency is less than that of the solar panel, using a PCM to store energy allows the continued use of solar energy even when solar radiation is zero. Although the model analyzed only the equipment independently, the solar panel when there is radiation, and the solar accumulator when the radiation is zero, it is possible to optimize the stored heat by operating both devices at the same time. Vasquez et al. [10] implemented a fuzzy logic control system for the 27

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air flows of the solar panel and solar accumulator as a function of the solar radiation and ambient temperature.

433

Table 2. Solar accumulator simulation results. WSA (kg/s) 0.012 0.018 0.024 0.030 0.036 0.042

T max (K) 356.1 352.7 349.9 347.4 345.3 343.4

T av (K) 319.1 312.6 308.6 305.8 303.9 302.4

Q abs (kJ) 10,425 12,101 13,126 13,868 14,442 14,956

ηSA (%) 45.5 51.3 55.4 58.4 60.8 63.0

434 435 436 437 438 439

According to the results obtained in the simulation, it is possible to heat the drying air for a period between 4 to 8 hours, increasing the average temperature of the drying air between 11.0 to 27.7 K above the ambient temperature, depending on the flow used. For an air flow of 0.012 kg/s, the heat absorbed by the air is 10,425 kJ, whereas for a flow of 0.042 kg/s the heat absorbed by the air is 14.956 kJ. As with the solar panel, the solar accumulator’s efficiency decreases for lower air flows.

440 441 442 443 444

The solar accumulator model was validated by comparing experimental and simulation results for the air temperature at the outlet of the solar accumulator at the energy discharge stage, for two air flows (0.018 - 0.030 kg/s). For the energy discharge stage, the glass cover surface of the solar accumulator was covered by an insulator so as to reduce the heat loss; therefore, the radiative heat transfer coefficient between the glass cover surface and the sky is zero.

445 446 447 448 449

(a)

(b)

Figure 15. a) Simulated liquid fraction of wax for air flow of 0.03 kg/s in the solar accumulator model. b) Simulated temperature of wax for air flow of 0.03 kg/s in the solar accumulator model. Figure 15 and 16 show the result of the simulation of the solar accumulator, for air flow of 0.03 kg/s and simulation time of 350 min. Figure 15 shows the liquid fraction "𝜙" and the temperature of the wax as explained in item 3.2.1 (row 30 corresponds to the solar accumulator’s output air 28

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450 451 452 453

temperature) for air flow of 0.03 kg/s in the solar accumulator model validation. Figure 16 compares experimental and simulation results for the solar accumulator air temperature, and it shows the values of the ambient air temperature for air flow of 0.03 kg/s. In this simulation the model presents an R2 of 0.967 and RMSE of 1.945.

454 455 456

Figure 16. Experimental and simulation results for air flow of 0.03 kg/s in the solar accumulator model.

457 458 459 460 461 462 463

Figure 17 and 18 show the result of simulation of the solar accumulator for air flow of 0.018 kg/s and simulation time of 420 min. Figure 17 shows the liquid fraction and temperature of wax for air flow of 0.018 kg/s in the solar accumulator model validation. Figure 18 compares experimental and simulation results for the solar accumulator output air temperature, and it shows the values of the ambient air temperature for air flow of 0.018 kg/s. In this simulation the model present R2 0.945 and RMSE 2.829.

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464

(a)

(b)

Figure 17. a) Simulated liquid fraction of wax for air flow of 0.018 (kg/s) in the solar accumulator model. b) Simulated liquid fraction of wax for air flow of 0.018 (kg/s) in the solar accumulator model.

465 466

467 468 469

Figure 18. Experimental and simulation results for air flow of 0.018 kg/s in the solar accumulator model. 30

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DRYING CHAMBER

470

4.3

471 472 473

The drying chamber model was validated in the drying of kiwifruit and mushrooms. The solid moisture of the drying product and the air relative humidity at the inlet and outlet of the drying chamber were compared between the simulation and experimental data.

474 475 476 477 478 479 480 481 482 483

Figure 19 and 20 show the simulation of the drying chamber when drying kiwifruit, for air flow of 0.18 kg/s, 83% recirculation, and simulation time of 520 min, and also for air flow (Wf3 in Figure 5) of 0.04 kg/s. Figure 19a shows the simulation of the temperatures at the inlet and outlet of the drying chamber along with the product temperature; Figure 19b shows the absolute air humidity at the inlet and outlet of the drying chamber. Figure 20a compares experimental and simulation results for the kiwifruit moisture, in this simulation the model presents an R2 of 0.995 and RMSE of 0.0369. Figure 20b compares experimental and simulation results for the relative air humidity at the inlet and outlet of the drying chamber. The simulation for the relative air humidity at the outlet presents an R2 of 0.878 and RMSE of 1.903, while for the relative air humidity at the inlet it has an R2 of 0.769 and RMSE of 1.332.

484

485

(a)

(b)

Figure 19. a) Simulated temperatures of the kiwi and the inlet and outlet of the chamber in the drying chamber model. b) Simulated absolute air humidity at the inlet (H3) and outlet (H2) of the drying chamber model.

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486 487

(a)

(b)

Figure 20. a) Experimental and simulation results for the kiwi moisture. b) Experimental and simulation results for the relative air humidity.

488 489 490 491 492

Figure 21 and 22 show the simulation of the drying chamber when drying mushrooms, for air flow of 0.18 kg/s, 83% recirculation, simulation time of 520 min and air flow (Wf3 in figure 5) of 0.04 kg/s. Figure 21 shows the simulation results for mushroom drying, the simulation of the temperatures at the inlet and outlet of the drying chamber, and product temperature and absolute air humidity at the inlet and outlet of the drying chamber.

493 494 495 496 497

Figure 22 compares experimental and simulation results for the mushroom moisture and compares experimental and simulation results for the relative air humidity at the inlet and outlet of the drying chamber in the drying of mushrooms. The solid moisture model presents R2 an 0.992 and RMSE of 0.0556. The simulation for the relative air humidity at the outlet yields an R2 of 0.895 and RMSE of 5.472, while for the relative air humidity at the inlet R2 was 0.929 and RMSE was 2.587.

498 499 500 501 502

The experimental and simulation results for the solid moisture of the drying product are similar for both kiwifruit drying and mushroom drying. The simulated results for the relative humidity were calculated from the exit temperature of the solar panel, so these involve a margin of error in the calculation of the inlet and outlet temperatures of the drying chamber and the relative air humidity; in addition, the model assumes an adiabatic state.

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503

504

505 506

(a)

(b)

Figure 21. a) Temperatures of the product at the inlet and outlet of the chamber in the drying chamber model. b) Absolute air humidity at the inlet and outlet of the drying chamber model.

(a)

(b)

Figure 22. a) Experimental and simulation results for the mushroom moisture. b) Experimental and simulation results for the relative air humidity.

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508 509

Table 3 shows in summary the correlation coefficient (R2) and the root mean squared error (RMSE) of the solar panel, solar accumulator and drying chamber models validation.

510 511 512 513 514

The temperature validations at the outlet of the solar panel and solar accumulator and the two solid moisture validations all have a R2 above 0.94, so it can be concluded that they were adjusted satisfactorily. The relative humidity of the air presented an average R2 of 0.87; this variable is highly sensitive to temperature, so errors in its measurement can cause considerable differences between the experimental value and the simulated value.

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Table 3. Validation of the models. Model Solar panel temperature 0.030 kg/s Solar panel temperature 0.048 kg/s Solar accumulator temperature 0.018 kg/s Solar accumulator temperature 0.030 kg/s Kiwifruit moisture Relative air humidity at the inlet in kiwifruit drying Relative air humidity at the outlet in kiwifruit drying Mushroom moisture Relative air humidity at the inlet in mushroom drying Relative air humidity at the outlet in mushroom drying

R2 0.98 0.94 0.95 0.97 0.99 0.88 0.77 0.99 0.90 0.93

RMSE 2.46 (°C) 2.00 (°C) 2.83 (°C) 1.94 (°C) 0.04 (kg/kg) 1.90 (kg/kg) 1.33 (kg/kg) 0.06 (kg/kg) 5.47 (kg/kg) 2.59 (kg/kg)

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CONCLUSIONS

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This paper presents a global mathematical model based on differential equations of a solar dryer with energy accumulation, using paraffin wax to store thermal energy, with variable climatic conditions over time (ambient temperature, air humidity, solar radiation). Numerical simulations using this model provides temperature profiles of the solar panel and solar accumulator, the fraction of liquid wax remaining in the solar accumulator, the moisture of the drying product, the air humidity and temperatures at the inlet and outlet of the drying chamber, among other values. In addition these simulations allow to obtain the efficiency of the solar panel and solar accumulator, for different air flows.

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The simulation and experimental data from solar dryer have allowed validating the numerical model. The simulation of the temperature at the output of the solar panel shows an R2 0.959, the temperature at the outlet of the solar accumulator presents an R2 0. 956 and the humidity of the air in the drying chamber presents an R2 0.868.

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This model could be adjusted to other dimensions of the equipment and to apply to different materials used for energy storage (knowing the physical properties of the material), the drying of any agro-product (knowing the kinetics of drying) and any environmental condition. In addition, this model could be used to define control logic and optimize the use of solar energy, the equipment design and the drying process.

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ACKNOWLEDGMENT

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