Energy and exergy analysis of an indirect solar dryer based on a dynamic model

Journal Pre-proof Energy and exergy analysis of an indirect solar dryer based on a dynamic model S. Hatami, G. Payehaneh, A. Mehrpanahi PII:

S0959-6526(19)33679-0

DOI:

https://doi.org/10.1016/j.jclepro.2019.118809

Reference:

JCLP 118809

To appear in:

Journal of Cleaner Production

Received Date: 8 May 2019 Revised Date:

6 October 2019

Accepted Date: 8 October 2019

Please cite this article as: Hatami S, Payehaneh G, Mehrpanahi A, Energy and exergy analysis of an indirect solar dryer based on a dynamic model, Journal of Cleaner Production (2019), doi: https:// doi.org/10.1016/j.jclepro.2019.118809. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Energy and Exergy analysis of an indirect solar dryer based on a dynamic model S. Hatami1, G. Payehaneh2, A. Mehrpanahi3* Department of Mechanical Engineering, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran. 1- [email protected] , [email protected] 2- [email protected] 3- [email protected] , [email protected]

Abstract Sun is a clean and available sustainable energy source. The usage of sustainable energy in various industries such as agriculture is taking into consideration during the early years. One application is dehydration by using an indirect solar dryer, which was adopted in this study. A dynamic model was presented in which the calculation of the solar radiation received in the tiled surface of the collector, temperature variation along the collector, the kinetics of moisture reduction and temperature variation of the drying material were taken into consideration. The model was validated and confirmed with high accuracy by test results in three states of mass flow rates of air. The effects of air velocity, the glass cover thickness and the length of the collector took into consideration in the analysis as effective parameters. The thermal analysis was accomplished by using energy and exergy analysis. To energy analysis, the values of received and used energy were calculated in addition to energy utilization ratio and for exergy analysis, the irreversibility at collector was calculated as well as the exergy efficiency of drying in the chamber. Energy and exergy analysis revealed more stream exergy for higher speed air and hence, lower irreversibility. Besides, the defined exergy efficiency was independent of the material mass despite the exergy destruction or energy efficiency, which means a suitable criterion for the system analysis. The model was in good agreement with the experiments so that the deviation from the best fit line (y=x) in the model-experiments curves were 2.37% for radiation estimation, 4% for the outlet air temperature of the collector,1% for the material temperature and 4.8% for the moisture ratio of the drying material. The model also revealed two critical moisture ratio of 0.75 and 0.23 in the drying process so that the maximum exergy destruction was observed at the first one and the maximum exergy efficiency was 22% for the dryer.

Keywords: Solar radiation, Dynamic model, Drying kinetics, Temperature variation, Exergy.

* Corresponding author, Faculty of Mechanical Engineering Shahid Rajaee University, Lavizan, Tehran, Iran., Tel/Fax Number +98-21229738

1

Nomenclatures a

Collector duct height

m

A

Constant of equation

…

Ac

Collector area

m2

Aic

Collector inlet area

m2

b

Collector width

m

B

Atmospheric extinction

…

coefficient C

the

ratio

of

diffusion

…

radiation to the direct ones on the horizontal surface Cg, Cp, Cm

Specific heat of glass cover,

J kg-1 K-1

plate, drying material D

Diffusion coefficient

DE

Activation energy

Dr

exponential

m2s-1 J

equation

...

Coefficient related to the

...

coefficient Fsg

collector angle Fss

ratio

of

the

diffusion

...

radiation on the tilt surface of the collector to the horizontal exp

experimental

...

f

Density ratio

…

g

Gravity

m s-2

h

Enthalpy

J kg-1

2

hga

Convection factor for glass

Wm-2

cover and passing air hgam

Convection factor for glass

Wm-2

cover and ambient air hrpg

Radiation

heat

transfer

Wm-2

factor for absorber plate and glass cover hrpsky

Radiation

heat

transfer

Wm-2

factor for absorber plate and sky Convection factor for drying

hma

Wm-2

material and air hm

Mass transfer coefficient for

ms-1

material gwater g-1dry air

H

Humidity

Hr

Hour angle

Deg

i

Latitude

Deg

Ic

Solar constant

W m-2

IDN

Direct radiation

W m-2

IDθ

Diffuse radiation

W m-2

Irθ

Reflected radiation

W m-2

It

Total radiation

W m-2

Irr

Irreversibility

J

kg

Thermal

conductivity

of

Wm-1K-1

conductivity

of

Wm-1K-1

glass cover km

Thermal material

3

kp

Thermal

conductivity

of

Wm-1K-1

plate L

Collector length

m

m

mass

kg

md

Dried material mass

kg

mm

Drying material mass

kg

.

kg s-1

Mass flow rate

M

Moisture content

gwater g-1dry matter

M0

Initial moisture content

gwater g-1dry matter

Me

Equilibrium

gwater g-1dry matter

moisture

content MR

Moisture Ratio

...

n

Days of the year

...

Nu

Nusselt number

...

s

Entropy

S

collector tilt angle from the

J kg-1 ...

horizon

Sgen

Entropy generation

Sc

Schmidt number

...

Sh

Sherwood Number

...

P

Pressure

Pa

Pr

Prantle Number

...

Q, q

Heat

J

Re

Reynolds Number

...

t

Time

s

Ta Tam Tg Tp, Tm U

Temperature

K (˚C)

Internal Energy

J kg-1

4

V

Volume

m3

V0

Initial volume

m3

V

Velocity

m s-1

X

Exergy

J

x 0v

Vapor molar ratio

...

Z

Height

m

x,z

Direction

in

differential

...

equations αp

Absorbance coefficient

αg

... ...

αm

thermal diffusivity of the

m2s-1

material β

Solar altitude

Deg

δ

Solar declination

Deg

δg

Thickness of glass

m

∆

Variation

...

θ

Incidence angle

ℰ

Emittance

ρp, ρg, ρm

Density of plate, glass and

Deg ... g.cm-3

material γ

Constant

φ

Solar Azimuth

Deg

τg

Transmittance

...

a

air

...

cond

Conductivity

...

c

Collector

...

...

Subscripts

5

e

Outlet

evap

Evaporated

...

f

Saturated liquid

...

g

Saturated vapor

...

H

Heat source

...

i

Inlet

...

m

Material

...

rad

Radiation

...

s

Sun

...

v

Vapor

w

Water

1. Introduction Sun is a clean and available sustainable energy source. Solar energy is being used in various fields such as solar heaters, solar photovoltaic, solar desalination as well as solar dryers (Herez et al., 2016; Singh et al., 2019). Cost and labor consumption is highly required for agricultural products to be maintaining long period or transporting long distances. To solve the problem one solution may be the “dehydration” which is a complicated process involving simultaneous heat and mass transfer. Various authors studied on drying kinetics which is a process that highly depends on temperature, airspeed and the material structure (Dinani and Havet, 2015). Some experimental methods are existed such as Page model (Page, 1949), Modified Page model (Overhults et al., 1973), Wang and Singh model (Wang and Singh, 1978), Henderson and Pabis model (Henderson and Pabis, 1961) and Verma model (Verma et al., 1985), which were adopted in various studies (e.g. Baini and Langrish, 2007; Eltawil et al., 2018; Shamekhi-Amiri et al., 2018). The authors also studied dynamic

6

modeling for various types of dryers. e.g. hot air drying by Karim and Hawlader (2005), and solar drying by Sami et al. (2011a). A thermal system includes available and unavailable parts of energy called as exergy and anergy, respectively (Lior and Zhang, 2007). The importance of thermodynamic analysis especially exergy analysis was studied by various authors e.g. Calise et al. (2018); Rahbari et al. (2018); Said et al. (2016). The main aim of exergy analysis is the calculation of the exergy destruction in different components of a thermal system, and the exergy efficiency is defined as the percentage of energy or exergy of the fuel, which is used to produce the product. Saidur et al. (2012) compared the thermal efficiency, exergetic efficiency, and the exergy destruction sources for various solar energy systems including solar photovoltaic, solar heating devices, solar water desalination system, solar air conditioners and refrigerators, and solar power generation systems. They concluded that the thermal efficiency is not sufficient to select the desired system and reported the air mass flow rate, inlet temperature and time as the most effective parameters on the exergy efficiency. Motevali et al. (2014) studied energy efficiencies in various types of dryers. Sansaniwal et al. (2018) either worked on the importance of thermodynamics analysis in such systems in their review paper, and Shafieian et al. (2019) worked on the performance improvement of heat pipe solar collectors. In the solar dryers, the whole amount of the absorbed energy by the collector is not transferring to the air stream in the collector channel. Besides, the whole transferred energy is not necessarily consumed for the process goal. Studding these discrepancies and optimizing the operational and design parameters are the main purpose of energy and exergy analysis in these types of dryers. Various methods were presented to analyze the energy and exergy efficiency of solar dryers. In a common definition, the energy efficiency is defined as the ratio of the changes in

7

the air enthalpy within the drying chamber to received energy of air during passing the collector channel. Contradictory results were reported using this method: increasing trend with respect to time followed by a decaying pattern in drying Pistachio and Olive mill wastewater were reported by Midilli and Kucuk (2003) and Celma and Cuadros (2009) respectively while; only a decaying trend in drying Pumpkin and Mint leaves, apple and carrot were reported by Akpinar (2010); Akpinar et al. (2006) and Lamnatou et al. (2012) for for energy efficiency. For the exergy efficiency the authors used some different methods. One common approach to quantify the exergy losses is the determination of the airflow exergy losses in the drying chamber. In this regard, the system efficiency is defined as the ratio of the outlet stream exergy to the inlet stream exergy in the drying chamber (Panwar et al., 2012). Contradictory results were reported for exergy efficiency as well: Akbulut and Durmuş (2010) observed a descending trend of exergy efficiency to the time that followed by an ascending trend in the drying of mulberry while, Chowdhury et al. (2011) observed an increase followed by a decaying exchange and again ascending change in drying Jackfruit leather. Some other authors such as Akpinar (2010); Akpinar et al. (2006); Midilli and Kucuk (2003) reported an ascending pattern of exergy efficiency with respect to drying time for drying Pumpkin, Mint leaves and Pistachio respectively. Hamdi and Kooli (2018) observed various trends in exergy efficiency in consecutive days for drying tomato by using a greenhouse solar dryer. The above contradiction, which might be due to the experimental error besides the different structures of the dryers mean a gap in the thermodynamic analysis of solar dryers. In other words, Insulation of the dryer along with the material of the drying chamber may affect the variations in the passing air temperature, and thus influence the air stream enthalpy and exergy in the drying chamber as the result.

8

Using another method by applying the changes of moisture and temperature of the drying material rather than the drying air could be a solution for removing the gap beside the necessity of a suitable model for illustrating the dryer behavior in different conditions which is called a “Dynamic Model” are the efforts of the present study. This study is aimed to use a new approach for energy and exergy efficiency calculation for a solar dryer as well as other types of dryers by using the results of a dynamic model. So the first aim is modeling the dryer and the second aim is the thermodynamic analysis of the dryer by using the income data of the model. The first step of the model was calculating the radiation intensity in the collector tilt angle; then the air temperature in the collector outlet was calculated by modeling the collector parts. Finally, the moisture reduction and temperature variation kinetics in the drying material was calculated by modeling the drying material in the dryer chamber. For the validation of the model, experiments results were used for each parameter and the errors were investigated for the model confirmation. In the end, the data of the model were used for thermodynamic analysis so that the values of received energy by the collector and the passing air were calculated as well as the energy utilization ratio for energy analysis. In addition to exergy analysis, the values of the exergyutilized ratio, the exergy destruction at the chamber and the irreversibility at collector were determined. The effects of air velocity, time of day or drying time were taken into consideration for the comparison as well.

2. The dryer structure The schematic view of the adopted dryer in the present study is being illustrated in Fig. 1 along with its components. The dryer consisted of a solar collector for heating air, a drying

9

chamber, a rotator fan located at top of the chamber for air suction and formation of forced convection in airflow, and an exit duct for conducting the humidified air into the atmosphere. As shown, the entrance air heated by a solar collector, next entered the drying chamber, and finally exited through an outlet duct after receiving the product moisture. The collector consisted of three layers including glass, absorber plate as the dark solid and a layer of fiberglass for insulation. To increase the air turbulence or the velocity, a rotator AC fan was located above the duct. When the fan was off, the air moved under free convective condition. In other words, the air moved up due to the thermal buoyancy effect induced by the difference between the collector and ambient air temperatures. By turning the fan on, i.e. under forced convective conditions, the velocity of the air stream increased and turbulence occurred in the airflow rate. The materials were being kept on the trays of the dryer chamber and lost their water by the passing air.

3. Methodology This section is aimed to describe the methodology of the study. So first, the developed model for the dynamic behaviour of the dryer was described. Then the thermodynamic analysis method was presented for the drying process. A schematic of the study process is shown in Fig. 2. The flowchart of the study procedure.Fig. 2 for a better understanding of the methodology.

3.1.

The dryer model

In this section, the model methodology was described. The model divided into three parts: First, solar radiation received by the collector surface. Second, the variation of the temperature in collector parts such as the absorber, the glass cover and the air passing through the channel. Third, the kinetics of temperature and moisture content variation during drying 10

the material. At the end of this section, the experimental setup, how the model validated with experimental results and the error analysis were described. 3.1.1. The solar radiation modeling The total radiation on any tilt or horizontal surface is divided into three types of direct, diffuse and reflected radiation (Jamil and Khan, 2014). Each type was calculated as follows: The “Direct radiation” was calculated by equation 1. I DN = I c .e

−B sin( β )

(1)

Ic is the “Solar constant” assumed 1357 W.m-2 and B is the “Atmospheric extinction coefficient” varies from 0.14 in the winter to 0.21 in the summer (Iqbal, 2012; Jamil and Khan, 2014). β is the “Solar altitude angle” which was calculated as equation (2).

sin ( β ) = cos ( i ) . cos ( Hr ) . cos (δ )  +  sin ( i ) . sin (δ ) 

(2)

The parameters i, Hr and δ are the “Latitude”, “Hour angle” and “Solar declination” respectively. The “Hour angle” is defined as the hour before or after the noontime multiplied by 15 and “Solar declination” were also calculated by equation (3) (Gunerhan and Hepbasli, 2007; Hay, 1979; Jamil and Bellos, 2019).

 

δ = 23.45 sin  360

284 + n   365 

(3)

Where n in the equation (3) is the day of the year. The “Diffuse radiation” which is the reason for the beautiful blue color of the sky was calculated as equation (4). I dθ = C. I DN . FSS

(4)

C coefficient in equation (4) is the ratio of diffusion radiation to the direct ones on the horizontal surface which is equal to 0.058 for winter and 0.135 for the summer season (Annuk et al., 2011; Jamil and Khan, 2014). Fss is the ratio of the diffusion radiation on the

11

tilted surface of the collector to the horizontal ones and was calculated by equation (5) (Chandel and Aggarwal, 2011). 1 + cos ( S )  FSS =  2

(5)

Where S in the collector tilt angle from the horizon. The “Reflected radiation”, which means the reflected radiation from the environment surface, was calculated by equation (6).

I rθ = ( I DN + Idθ ) .krθ .Fsg

(6)

k rθ is the reflect coefficient of the environment and is equal to 0.2 for the vegetation region

and

is related to the collector angle and calculated by equation (7).

1 − cos ( S )  Fsg =  2

(7)

Finally, the “Total radiation” was calculated by equation (8). (Jamil Ahmad and N Tiwari, 2009)

It = I DN . cos (θ ) + I dθ + I rθ (8) Where θ is “Incidence angle” and calculated as follow:

cos (θ ) = cos ( β ) . cos (ϕ ) . sin ( S )  +  sin ( β ) . cos ( S ) 

(9)

Φ is “Solar Azimuth” and calculated as follow: (Jamil and Khan, 2014) sinϕ =

cosδ sinHr cos β

(10)

3.1.2. The collector modeling As mentioned in the “dryer structure” part, the collector consists of three parts of glass cover, absorber plate, and the passing air. The energy balance was written for each part

12

consequently. Equations (11) to (13) are the energy balance for the glass, absorber plate and the passing air (Sami et al., 2011a). The following assumptions were taken into consideration for the modeling: 1. Air was considered as ideal gas. 2. The system was assumed isolated and the thermal dissipation was not taken into consideration. 3. The black plate was assumed as a black body. 4. The thermal change along the plate thickness was not taken into consideration.

∂Tg ∂t

=

kg

∂ 2Tg

ρ g Cg ∂z

2

+

I tα g

ρ g Cgδ g

(11)

∂Tp ∂t

=

I tτ gα P

h h  h  +  Pa  (Ta − TP ) − rpsky (TP − Tsky ) − rpg (TP − Tg ) ρ P C P lP  ρ P C P lP  ρ P CP l P ρ P CP lP

hpa b ∂Ta ∂T  h b  = −V a +  ga  (Tg − Ta ) + (T − T ) ∂t ∂x  ρ a Ca Ac  ρ PCP Ac P a

(12)

(13)

Where Tg, Tp, Ta are the glass, absorber and the air temperatures. z is the direction along the glass cover thickness and x is along with the collector length, V is air velocity. The parameters k, C, α, ρ, τ, l and δ present the conductivity, specific heat, the absorbance coefficient, density, transient coefficient, length and thickness of glass, absorber plate and air with indexes g, p and a respectively. hga and hpa are the heat transfer coefficients for glass cover-air and absorber plate-air which determined by equation (14) (Knudsen et al., 1959). Nu = 7.6; Re Pr . a / L > 70 Nu = 1.85( Re Pr . a / L )1/ 3

(14)

Re Pr . a / L < 70

hrpsky is the radiation coefficient and was determined by equation (14). (Bala, 1998)

13

hrpsky =

2 σ (TP2 + Tsky ) (TP + Tsky )

(15)

 1 1   + − 1  εP τ g 

While Tsky which is related to ambient air temperature (Tam) was calculated by

Tsky = 0.0552 (Tam )

1.5

(Swinbank, 1964).

The initial and boundary condition for equations (11) to (13) was written as follow: t=0

Tg=Tp=Tam

z=0

kg

∂Tg ∂z

z=

z =0

(16)

= hga ( Tg

|

=ℎ

z =0

− Ta )

−

(17)

|

(18)

Where hgam the heat transfer coefficients for the glass cover and the ambient air and calculated with the determined equation by Sparrow and Liu (1979) as follow:

Nu = 0.86Re1/ 2 Pr1/ 3

(19)

3.1.3. The material kinetics modeling Since drying the material is the aim of the dryer, the modeling seems to be important. Therefore, it was modeled in both aspects of moisture reduction kinetics and temperature variation as well. The following assumptions were taken into consideration for the modeling: 1. No chemical reaction occurred during the dehydration process. 2. Uniform air distribution was considered in the dryer chamber. 3. One direction heat and mass transfers were taken into consideration. Fick's second law was used for moisture kinetics modeling (equation 20) and the energy equation was written in the material for finding the temperature distribution during the drying process (equation 21).

14

∂M ∂2M =D 2 ∂t ∂x ∂Tm ∂ 2Tm = αm ∂t ∂x 2

(20)

(21)

Where M is the moisture content of the material dry basis (g.gdb-1). Tm is the material temperature. D is the diffusion coefficient of mass transfer αm is the thermal diffusivity of the material. Diffusion coefficient which exponentially relates to material temperature, defines by equation (22) (Zogzas et al., 1994).

 DE  D = Dr exp  −   Tm + 273 

(22)

Where Dr is the exponential equation coefficient and DE is the activation energy of the drying material, which is the equivalent energy for dehydrating one mole of the moisture content of the material. The constants of equation (22) were determined by Baini and Langrish (2007) for banana fruit which was the case study of the experiments. Therefore, equation (22) changed to equation (23) for the considered fruit in this study.

 1610  D = 1.36 ×10−7 exp  −   Tm + 273 

(23)

The thermal diffusivity of the material was defined by equation (24). km, ρm and Cm in this equation are the conductivity coefficient, density and the heat capacity of the material respectively. The material density was defined base on the moisture content by Talla et al. (2004) in equation (25) and the values of the heat capacity and the conductivity coefficient were determined for banana fruit by Karim and Hawlader (2005) base on the moisture content in equations (26) and (27).

αm =

15

km ρmCm

(24)

ρm = ρm 0

M +1  1    M0 +1  A + γ M 

Where A =

1 1 + fM 0

γ=

(25)

ρ f f = d 1 + fM 0 ρw

C m = 0.008 M + 0.20

(26)

k m = 0.00493M + 0.148

(27)

M0 is the initial moisture content, ρd and ρw are the dried material and water density respectively. The initial and the boundary conditions for equations (20) and (21) were written as follow: t=0,

M=M0 , T=Tam

x=0;

∂Tm ∂x

x=b;

∂M −D ∂x

x=b;

 ∂Tm   km ∂x   

x =0

=0

x =b

x =b

(28)

∂M ∂x

&

x =0

=0

= hm ( M − M e )

x =b

= hma (Ta − T )

−hm ρ( M − M e ) h fg

x =0

(29)

(30)

x =b

(31)

where Me is the equilibrium moisture content, hm is the mass transfer coefficient and was defined for laminar and turbulent flow by equation (32-a) and (32-b) respectively (Karim and Hawlader, 2005). hma is the heat transfer coefficient determined by equation (33) (McAdams, 1961).

Sh =

hm L = 0.332 Re0.5 Sc0.33 D0

Sh =

hm L = 0.0296 Re4 / 5 Sc1/ 3 D0

(32-b)

Nu = 0.37 Re0.6 ; 17 < Re < 70000

(33)

16

(32-a)

Hence, the moisture ratio (MR) was used as a dimensionless value for moisture rather than the moisture content. It was defined in equation (34) and varies between one for the beginning of the drying operation and zero for the end.

MR =

M − Me M0 − Me

(34)

3.1.4. Model validation Experimental results were used for the model validation. The dryer appearance and function was the same as explained dryer in “Dryer structure” section and the method of the testing was as follows as described by Hatami et al. (2017): "Air temperature in the drying chamber was measured by T-type thermocouples and recorded once a minute in a data logger (Sapcon Company, China) with the accuracy of ±0.1°C. Weighing of the samples was conducted every 15 min using a digital balance (AND GF400, CA, USA) with the accuracy of ±0.01 g. The air mass flow rate was controlled by varying the fan speed using an AC fan inverter and was measured by a hot wire anemometer (Lutron AM-4204, Taipei, Taiwan) with the accuracy of 0.1 m s−1. Drying experiments were performed at airspeed of 0.4 m.s-1, 1m.s-1 and 2m.s-1. " (Hatami et al., 2017) The radiation intensities during the day were either been measured by a solar power meter (TES1333) with the accuracy of 1W.m-2 perpendicular to the collector surface. Banana slices were the drying material in the experiments. For the model validation, the model results compared with the income data of the experiments. For the error analysis of the model, the minimum, average and maximum errors were measured for each parameter. For having a clearer slight on the errors, the line of “Measured-Model” curve was either been drawn so that the measured and the model data were the horizontal and vertical axis respectively. The deviation of the slope of the trend line from the best-fit line (which is y=x) can present how the model validated. 17

3.2.

Thermodynamic analysis

The first and second laws of thermodynamics were used for thermodynamic analysis. The main goal of this part was to calculate energy and exergy efficiencies. So, the energy conservation law was developed for energy analysis and the second law was used for exergy analysis. (Cornelissen, 1997).

3.2.1. Energy analysis In each system, the inlet and consumed energies are the parameters, which are studied in energy analysis. The first law efficiency in a thermal system is the part of inlet energy that is used for the system goal. In terms of drying, the goal is to dry the product, and thus the energy efficiency is that part of the inlet energy which the product should gain to lose its moisture content. In a solar dryer, the absorber plates absorb solar energy. These plates operate as a black body that absorbs solar energy. The amount of this energy is calculated by equation (35) (Sami et al., 2011b). Qc = I tτ gα P Ac

(35)

The solar energy absorbed by the absorbing plates is transferred to the air passing through the collector channel. The amount of the received energy by the air was calculated by equation (36).

Qa,c = maCP.a (Te,c − Ti,c )

(36)

Where Ti,coll and Te,coll are the air temperatures in the inlet and outlet of the collector and ma is the passing mass air in the considered time interval (15minutes in this study) and calculated by multiplying the mass flow rate by the time interval.

18

The heated air enters the drying chamber and exits through the outlet duct after receiving the moisture content of the product. The energy used to evaporate the water from the material was calculated by equation (37) (Jindarat et al., 2011). Qevap = mevap h fg

(37)

Where mevap is the evaporated water mass. Besides, hfg is the latent heat of evaporation, which is equal to the dispute of liquid and vapor in the saturated state. The values obtained from thermodynamics tables for steam pressure at different temperatures. Finally, the energy efficiency was defined as the ratio of the energy used for evaporating the product water to the energy received by the passing air through the collector channel. It was calculated by equation (38):

EnergyEfficiency =

Qevap Qa ,c

(38)

3.2.2. Exergy analysis Exergy can transport in the form of work, heat, and stream. The main goal of exergy analysis is exergy efficiency and irreversibility calculations. Different definitions were used to calculate exergy efficiency in the dryers. One of the most common definitions is based on air stream exergy in which the exergy efficiency is defined as the ratio of outlet stream as the simple exergy efficiency by Cornelissen (1997) and is useful in steady-state processes. It must be noticed that the evaporation process is not a steady-state process. Moreover, this metod is directly depended on the amount of the drying product while the best definition of drying process efficiency should be independent of the material amount to be able to present the quality of the energy used in the process. Also, as mentioned in the Introduction section, different results were obtained in terms of the drying process efficiency by this method. Also, the high value of error is another disadvantage, which influences any kind of exergy

19

exchange when applying this method. This exchange could be with the environment or the product. However, in dryers only the exergy exchange with the product is useful. Conceptually, the exergy efficiency is the percentage of the fuel exergy that is used for producing the product. In a solar dryer, the sun, the inlet air to the collector and the fresh material are the used sources, and the dried material is the process product. The solar exergy transfers to the air through heat transfer in the collector and increases the air stream exergy. The high-empowered airstream enters the dryer chamber and reduces the moisture content of the material via receiving it. Radiation exergy (Xrad) (Sami et al., 2011b), airstream exergy (Xa) (Niksiar and Rahimi, 2009), and exergy for the water content of the product (Xw) (Dincer and Sahin, 2004) were calculated by equations (39 to 41), respectively.

 T  X rad = I tτ gα P Ac 1 − a   TS 

(39) (40)

 m   1+ a H0     m  mv m T  H     X a = ma CP.a  T − T0 − T0ln  + RaT0 × 1 + a H  ln + 1 + a Hln T0  mv H0   mv  1 + ma H      mv   (41)   Pg (T0 )   X w = m w  ( h f (T ) − h f (T0 ) ) + v f ( P − Pg (T ) ) − T0 ( s f (T ) − s g (T0 ) ) + T0 Rw ln  0     xv P0  

Where, Ts is the sun temperature (4350 K) (Bejan et al., 1981), Ma and Mv are the molecular mass of the air and vapor (29 g mol-1 and 18.153 g mol-1, respectively, H is the absolute humidity of the air (kgwater kgdry air), h is the enthalpy (kJ kg-1), s is the entropy (kJ kg-1 K-1), 0, a, v, f, and g are the indices related to thermodynamics dead state, air, vapor, saturated liquid, and saturated vapor, respectively, R is the gas constant (0.278 kJ kg-1 K-1 for air, and 0.446 kJ kg-1 K-1 for vapor), x0v is the vapor molar ratio in the air (0.0038 under our 20

experiments condition), and P is the internal water pressure of the product. The amount of P determined by the multiplication of the water activity of the product and saturated pressure. The water activity values of banana is given by Yan et al. (2008). In the present study, the exergy efficiency of the drying process was defined as the ratio of the changes in the moisture exergy of the product to its initial moisture exergy as indicated by equation (42). This definition is a qualitative explanation of the exergy efficiency, which is independent of the material amount. As a result, we can understand how much exergy consumed in a specific period and how much moisture empowerment utilized in the drying process.

Drying Exergetic Efficienty =

XW 1 − XW 2 XW 1

(42)

Irreversibility can create in different parts of a system. The main part of irreversibility a solar dryer created in the collector channel. Radiation exergy received by the collector and transferred to the passing air through the collector in the form of heat exergy (equation 39) and stream exergy (equation 40). One of the main reasons for irreversibility in thermodynamics processes is heat transfer due to a heat source, which is the sun in a solar collector. Reducing in irreversibility in this part means better use of the radiation exergy. Irreversibility in a system appears as entropy generation which its amount can be calculated by equation (43) Sonntag et al., 1998. ∙

=

(43)

.

Where S gen is the entropy generation (kJ.K-1) that was calculated by equation (44). In fact, every thermodynamics process in the nature tends to more disordering which is called entropy generation. The entropy generation is created because of the stream entropy in a process and heat transfer with a heat source (here the sun) in processes, which are the first and the second terms in equation (44), respectively.

21

∙

=

−

!

∙

"−

#$%& '

(44)

4. Results and Discussion 4.1.

Model results

The radiation values of the model and the experiments at the latitude of 32° and in August are being shown in Fig. 3-a and b; where the continuous line means the model result in Fig. 3-a. The model was validated with the measured radiation. The radiation values in the figure collector angle (37° from the horizon) increased up to 1050 W.m-2 at noontime. The mean error of the model was 5.9% with the maximum and the minimum error of 13.5% and 0.4% respectively. The model validation with the experimental results was either shown in Fig. 3-b that presents the measured and the model data in the horizontal and vertical axis respectively. The deviation of the slope from the best-fit line (y=x) in the figure was only 2.37%, which means a good agreement of the model and the measured data. The error bars of data are either being shown base on the mean error for all comparison figures to show the range of deviation of the model. As presented in “The collector modeling” section, the glass cover, the absorber plate and the outlet air of the collector were taken into consideration. Fig. 4 shows the temperature variation in the glass cover thickness. These results are presented in the air mass flow rate of 0.016kg.s-1 at the end of the collector. The figure shows higher rage of temperature in the boundary of the collector duct (z=0). It decreased gradually up to ambient temperature at the boundary of ambient (z=4mm). Fig. 5 presents the average temperature of the glass cover in different thicknesses. The effect of thickness on temperature was studied at four levels. The results showed the overlap of different curves that indicates the mean temperature of the glass cover was not affected by its thickness. The same result was either been reported by Bakari et al. (2014). 22

The outlet air temperature at three levels of airspeed was shown in Fig. 6-a. The continuous lines that show the model results were in good agreement with the experiment data due by the mean relative error of 7.4%, the maximum relative error of 13.4% and the minimum relative error of 0.36%. this validation also been shown in Fig. 6-b where the slope of the trend line between the experiment data (the horizontal axis) and the model results (the vertical axis) is 1.04 with only 4% deviation from the best-fit line (y=x). The figure also presents higher range of temperature for lower airspeed wherein the natural condition state (0.016kg.s-1), the air temperature rose to 65°C at noontime when the most radiation could be received by the collector and hence the passing air. The effect of the collector length and the air velocity are being shown in Fig. 7-a and b respectively. Where the collector length and the air velocity change had linear and exponential effect on the air temperature exchanges. The equations of which are presented in the figures. Therefore, more outlet temperature could be achieved in long collectors with lowspeed air. Take note the limitations would not let to have those ideal collectors. The model results of the material temperature and the experiment data are being shown in Fig. 8-a and b. The model was in good agreement with the experimental data. Where the mean, Maximum and minimum errors were 4.8%, 16.6%, and 0.33% respectively. The model validation was either shown in Fig. 8-b that presents the experimental data and the model results in the horizontal and vertical axis. The slope of the trend line had only 1% deviation with the best-fit line. It should be noted that the material temperature along with the thickness of the material and along with the drying chamber was negligible due to the uniform air distribution and the small size of the chamber. The error bars of data are either being shown base on the mean error for all comparison figures to show the range of deviation of the model.

23

Fig. 9 shows the diffusion coefficients of the material. It was decreased with the increment in air velocity, which is due to the higher temperatures in lower air speed. The mass diffusion coefficient has an important role in drying rate since more values for the Diffusion coefficients means more speed in drying. The moisture ratio values of the drying chamber during drying time is shown in Fig. 10-a and b the lowest drying time for 0.016kgs-1 confirms the diffusion coefficient effect. The same result was reported by Akbulut and Durmuş (2010). The model validation was also shown in this figure while the mean error was about 15.7%, and the maximum error happened at the early time of drying in natural convection state due to high measuring errors over those times because of the high speed of drying. The trend line between the model and experiments had only 4.8% deviation from y=x. The variation of the moisture ratio along the thickness of the material is being shown in Fig. 11 where X=0 means the center and X=X1 and X=X2 means higher levels of the thickness near the surface. As observed the moisture content at the higher levels of the material evaporated faster than the deep imprisoned moisture at the center of the material and the moisture evaporated after reached the surface by liquid and vapor diffusion and capillary forces. (Arabhosseini et al., 2019) The drying rate curve base on the moisture ratio at various rates of airspeed is being observed in Fig. 12. The constant drying which occurs at initial steps of drying was observed as increment drying rate because of increasing the temperature during drying at the moisture above 0.75 which is marked by a line at the figure. The same result was observed by Arabhosseini et al. (2019) for the solar drying of tomato. Demirel and Turhan (2003) observed the same moisture ratio, which calls the first critical moisture for drying of banana, slices. The second critical moisture ratio which means the boundary between the fast descending and the slow descending period was either been shown in the figure at about 0.25 the experiments confirmed the ratio of 0.23 (Hatami et al., 2017).

24

4.2.

Thermodynamic analysis

This section is aimed at energy and exergy analysis for the presented indirect solar dryer. The variations of the total energy received by the collector (Qrad) and the amount of it that received by the passing air through the collector channel (Qa,c) are being shown in Fig. 13. As observed the increment of mass flow rate caused less energy received by air, which is due to less time for receiving energy at higher speeds of air. This might be the reason for less air temperature at those rates. The energy utilization ratio or the energy efficiency which was defined as the ratio of the consumed energy in moisture evaporation from the material to the received energy by the air in the collector is being shown to time and the moisture ratio in Fig. 14-a and b respectively. As observed the difference in the efficiency was occurred during the initial steps of drying and was more related to the moisture ratio in the second and third steps of drying lower than 0.75 moisture ratio. The reducing of the efficiency may be related to the moisture loss kinetics of the product during drying. In lower levels of the moisture contents, the drying rate and the amount of evaporation energy decrease and therefore, less amount of the received energy in the collector is used for the process, which in turn causes decreasing the efficiency. In other words, if there were another kind of liquid or water in the dryer, another process and a different result would be obtained. This efficiency is affected by the type and the amount of the material. Mousa and Farid (2002) used the same definition in the energy efficiency for drying banana with microwave method and observed similar results in terms of decreasing trend in efficiency with decreasing moisture content. Jindarat et al. (2011) also used the same approach in the microwave and convective drying of two different multi-layered porous materials. Their report complied with our study regarding the decreasing trend at the efficiency of the first law during the drying process of

25

two types of porous media. The reason for this similarity is the porous structure in agricultural products affecting their drying kinetics (Defraeye, 2014). Regarding exergy analysis, irreversible and destroyed exergy in the collector channel, water content empowerment of the product, the exergy efficiency and the exergy destruction during the drying process were calculated and analyzed. As described, more irreversibility in the collector means less use of the received radiation exergy. Fig. 15 shows the amounts of irreversibility (Irr) in the collector at three air mass flow rates to the time. As observed, more irreversibility occurred in lower mass flow rates of air. This result was approved in Fig. 16-a and b which indicates the outlet exergy of the collector to the time and outlet temperature of the collector. The results show that although there was more exergy for airflow in the lower mass flow rate in a specific time, more outlet stream exergy was gained for higher mass flow rates in a specific temperature due to more mass passing the collector duct in a specific time interval which means high-speed air have more power. Fig. 16-b also indicates a second-degree polynomial equation between the temperature and the exergy. Exergy calculations for water content of the product (Xw) indicated that it was not considerably affected by the airflow rate and was more related to the moisture content while that it decreased when moisture content decreased. This is being shown in Fig. 17. Fig. 18-a and b show the exergy efficiency of the material during drying with respect to the time and moisture ratio at various air mass flow rates, respectively. As observed, at all mass flow rates the exergy efficiency increases and then decreases by passing the time. It was either resulted that the highest exergy efficiency occurred in natural convective condition. It had the highest value near the second critical moisture content about 0.25. High value of exergy efficiency in this region means that although the evaporation value was decreased, but

26

more power of the material water content was used for moisture evaporation at lower air speed. Decreasing the exergy efficiency by increasing the air mass flow rate; based on the approach used in this study, may be explained by the point that increases in the air mass flow rate causes reducing the temperature of the drying chamber and product and consequently, enhancing the moisture empowerment of the product. In other words, the ability for evaporation in the product decreased and hence, the exergy efficiency decreased. The exergy destruction of the product which is dependent on its amount reached to the highest value at the moisture ratio of about 0.75 as shown in Fig. 19-a which was indicated as the first critical moisture ratio. The values were linearly dependent on the drying rate of the as shown in Fig. 19-b and were not changed with the mass flow rate although in a specific moisture ratio more exergy destruction was observed for lower mass flow rate which is due to higher drying rate over those conditions. The effect of the material amount on both energy and exergy efficiency was either been studied and the results revealed no effect on the exergy efficiency despite energy efficiency which increased with the mass amount increasing as shown in Fig. 20. This result can approve the fact that the defined definition for exergy efficiency can be useful for understanding the dryer quality. Needs to note that the traditional definition which was based on the variation of air stream exergy were highly related to the amount of the drying material addition to the experimental error. That is why various results were observed in the various study as mentioned in the introduction part. (Celma and Cuadros, 2009; Midilli and Kucuk, 2003, Sami et al., 2011b, Akpinar, 2010; Akpinar et al., 2006)

27

5. Conclusion and future works 5.1.

Conclusion

Solar drying is an appropriate solution for maintaining and transporting the agricultural products. A complete model was presented in this study which was able to show the system behavior with high accuracy. Energy and exergy analysis was either accomplished to calculate the first and second efficiency of thermodynamic addition to exergy destruction in different parts. The results of the study are being presented as bellow:

•

The deviation from the best fit line (y=x) in the model-experiments curves were 2.37%, 4%, 1% and 4.8% for radiation estimation, outlet air temperature of the collector, the material temperature and the moisture ratio of the drying material respectively.

•

The effect of the length of the collector and the velocity as effective parameters on the outlet temperature revealed a linear and exponential relationship respectively.

•

The model revealed two critical moisture ratios of 0.75 and 0.23 in the drying process.

•

Energy and exergy analysis showed more stream exergy for higher speed of air and hence, lower irreversibility.

•

It was concluded that exergy efficiency increased up to 22% at around the critical moisture content (0.75) despite the decreasing trend of the energy efficiency

•

Despite the exergy destruction and energy efficiency, the exergy efficiency was able to show the quality of the system because it was not related to the material amount.

5.2.

Recommendation for future works:

•

Dynamic modeling and thermodynamic analysis of greenhouse dryers.

•

Dynamic modeling of a coupled Solar-Geothermal dryer.

•

Economical study on drying agricultural products with the solar dryer at agricultural lands in subtropical areas. 28

Acknowledgements The experiments we used for the validation of the model were accomplished in Isfahan university of technology (IUT), Isfahan, Iran and thanks to Dr. Morteza Sadeghi for best guides in the experiments. (Hatami et al., 2017).

Appendix A The raw parameters:

29

Parameter

Value

Parameter

Value

i

32°

αg

0.1

S

37°

αp

0.96

n

200

τg

0.8

kg

5.9 (W.m-2K-1)

Cp

900 (J.kg.K-1)

Cg

753 (J.kg.K-1)

ρw

1,000 (kg.m-2)

ρg

2’466 (kg.m-2)

L

2 (m)

δg

4 (mm)

b

1 (m)

lp

2 (m)

ρd

960 (kg.m-3)

ρa

1.09 (kg.m-2)

a

0.1 (m)

ka

0.025 (W.m-2K-1)

kp

250 (W.m-2K-1)

Ca

1,005 (J.kg.K-1)

M0

3.5 (gwater g-1dry matter)

Figure Captions Fig. 1.The schematic view of the solar dryer used for the modeling and its parts. ............. 32 Fig. 2. The flowchart of the study procedure. ..................................................................... 33 Fig. 3. The solar radiation intensity. a) During the day. b) Model and experimental comparison ............................................................................................................................... 34 Fig. 4. The glass temperature at the end point of the collector in different depth levels. ... 34 Fig. 5. The mean glass temperature at various thicknesses................................................. 35 Fig. 6.a) The outlet air temperature of the collector at various levels of air velocity. b) The model result versus the experimental data. .............................................................................. 36 Fig. 7. The effects of the collector length. a) On the air velocity. b) On the outlet air temperature. ............................................................................................................................. 37 Fig. 8. The comparison of the experiments and the model for the material temperature in different air speed. a). Versus drying time. b) The model validation. ..................................... 38 Fig. 9. The diffusion coefficients during drying time at different air velocity. .................. 39 Fig. 10. The moisture ratio a) Versus drying time. b) Model and experiments comparison. .................................................................................................................................................. 40 Fig. 11. The moisture content of the material along with its thickness............................... 41 Fig. 12. Variation of drying rate base on the moisture ratio ............................................... 41 Fig. 13. Variation of the received energy of passing air in the collector and absorbed radiation energy by the plates versus drying time at various mass flow rates of air. .............. 42 Fig. 14. Energy efficiency of drying the product at different mass flow rates of air. a) Versus the time. b) Versus moisture ratio. ............................................................................... 43 Fig. 15. Variation in irreversibility of the collector at different air mass flow rates verus the time..................................................................................................................................... 43

30

Fig. 16. The stream exergy in the collector outlet versus a) The time, and b) The collector outlet temperature. ................................................................................................................... 44 Fig. 17. Water exergy of the product. ................................................................................. 45 Fig. 18. The exergy efficiency of drying the product at different air mass flow rates versus a) The drying time b) The moisture ratio ................................................................................. 45 Fig. 19. The water exergy destruction of the product versus a) Moisture ratio b) Drying rate............................................................................................................................................ 46 Fig. 20. The influence of the meterial amount on a) Energy Efficiency b) Exergy Efficiency. ................................................................................................................................ 47

31

Fig. 1.The schematic view of the solar dryer used for the modeling and its parts.

32

Fig. 2. The flowchart of the study procedure.

33

Solar Radiation (Wm-2)

1,100

a)

Model

1,000

Measured

900 800 700 600 8:00 AM

10:00 AM

12:00 PM Hour

2:00 PM

4:00 PM

b)

Model (W.m-2)

1,100 1,000

y = 1.0,237x R² = 0.8,448

900 800

Solar Radiation

700

Linear (Solar Radiation)

600 600

700

800 900 Measured (W.m-2)

1,000

1,100

Fig. 3. The solar radiation intensity. a) During the day. b) Model and experimental comparison

70 65 Glass Temperature (°C)

60 55 50

z=0

45

z=1mm z=2mm

40

z=3mm

35 30 8:00 AM 10:00 AM 12:00 PM 2:00 PM Hour

z=4mm

4:00 PM

6:00 PM

Fig. 4. The glass temperature at the end point of the collector in different depth levels.

34

Glass Temperature (°C)

55 50 45 40

Thinkness=1mm Thinkness=2mm

35

Thinkness=3mm Thinkness=4mm

30 8:00 AM 10:00 AM 12:00 PM 2:00 PM Hour

4:00 PM

6:00 PM

Fig. 5. The mean glass temperature at various thicknesses.

35

70

a)

Air Temperature (°C)

60 50 40 30 20 10 0 8:00 AM

10:00 AM

12:00 PM

2:00 PM Hour

4:00 PM

6:00 PM

b) 70 65 Model (°C)

60

y = 1.044x R² = 0.919

55 50 45

Outlet Collector Temperature

40

Linear (Outlet Collector Temperature)

35 30 30

35

40

45 50 Experimental (°C)

55

60

65

Fig. 6.a) The outlet air temperature of the collector at various levels of air velocity. b) The model result versus the experimental data.

36

Air Temperature (°C)

80

a)

70

y = 8.5,737x + 35 R² = 0.994

60 50 Air Temprature in Different lenghts

40

Linear (Air Temprature in Different lenghts)

30 0

1

2

3

4

5

Lentgh(m)

Average Outlet Temperature (°C)

55

b) Air Temperature in Different Air Velocity

50 Power (Air Temperature in Different Air Velocity)

45 40 y = 44.855x-0.13 R² = 0.917

35 30 0

1

2

3 4 -1 Air Velocity (m.s )

5

6

Fig. 7. The effects of the collector length. a) On the air velocity. b) On the outlet air temperature.

37

80

a)

Material Temprature (°C)

70 60 50 40 30

Experimental, 0.4 m.s m/s-1 Experimental,1 m.s m/s-1 Experimental, 2m.s m/s-1 -1 Model, 0.4 m.s m/s m.s-1 Model,1 m/s Model, 2 m.s m/s-1

20 10 0 0

100

200

300 time (min)

400

500

600

b)

Model (°C)

70

60 y = 0.99x R² = 0.9267

50

40

Material Temprature Linear (Material Temprature)

30 30

40

50 Experimental

60

70

Fig. 8. The comparison of the experiments and the model for the material temperature in different air speed. a). Versus drying time. b) The model validation.

38

9E-10 Diffusion Coefficient (m2.s-1)

8E-10 7E-10 6E-10 5E-10 4E-10 0.016 kg.s kg/s-1

3E-10

0.041 kg.s kg/s-1

2E-10

0.082 kg.s kg/s-1

1E-10 0 0

100

200 300 400 Drying time (min)

500

600

Fig. 9. The diffusion coefficients during drying time at different air velocity.

39

1

a)

0.9 0.8 Moisture Ratio

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

100

200

300 time (min)

400

500

600

Model Moisture Ratio

1.2

b)

1

y = 0.948x R² = 0.977

0.8 0.6

MR Linear (MR)

0.4 0.2 0 0

0.2

0.4 0.6 0.8 Expermental Moisture Ratio

1

Fig. 10. The moisture ratio a) Versus drying time. b) Model and experiments comparison.

40

4 Moisture Content g.gdb-1

3.5 3 Moisture Content,X=0

2.5 2

Moisture Content,X=X1

1.5

Moisture Content,X=X2

1

0.5 0 0

100

200 300 400 Drying Time (min)

500

600

Fig. 11. The moisture content of the material along with its thickness.

Variation of Drying Rate (gw.gd-1.s-1)

0.014

The first critical moisture ratio

0.012 0.01

The second critical moisture ratio

0.008 0.006 0.004

0.016 kg/s kg.s-1

0.002

0.041 kg.s kg/s-1 0.082 kg.s kg/s-1

0 0

0.2

0.4 0.6 Moisture Ratio

0.8

Fig. 12. Variation of drying rate base on the moisture ratio

41

1

1,800

350

1,600 1,400

300

1,200 250 1,000 0.016

200

kg/s kg.s-1

800

kg.s-1 0.041kg/s

150

kg.s-1 0.082 kg/s

600

Qrad

100

400

50 0 8:00 AM

Received Energy by the Collector (kJ)

Recieved Energy Air (kJ)

400

200

10:00 AM

12:00 PM 2:00 PM Time (min)

4:00 PM

0 6:00 PM

Fig. 13. Variation of the received energy of passing air in the collector and absorbed radiation energy by the plates versus drying time at various mass flow rates of air.

42

18

a)

Energy Efficiency (%)

16 14 12 10

kg.s-1 0.016 kg/s

8

0.041kg/s kg.s-1

6

0.082 kg/s kg.s-1

4 2 0 0

100

200 300 400 Drying Time (min)

500

600

18

b)

Energy Efficiency (%)

16 14 12 10 8 6 4 2 0 0

0.2

0.4 0.6 Moisture Ratio

0.8

1

Fig. 14. Energy efficiency of drying the product at different mass flow rates of air. a) Versus the time. b) Versus

Irriversibility at Collector (kJ)

moisture ratio.

250 200 150 100 50 0 0

100

200

300 400 Time (min)

500

600

Fig. 15. Variation in irreversibility of the collector at different air mass flow rates verus the time

43

30

a)

Outlet Air Exergy (kJ)

25 20 15 10 5 0 0

100

200

300 Time (s)

400

500

600

b)

30 y=

Outlet Air Exergy (kJ)

25 20

0.0,217x2

- 1.2,797x + 18.909 R² = 1

y = 0.1,134x2 - 6.7,605x + 100.62 R² = 1 y = 0.0,561x2 - 3.3,356x + 49.52 R² = 1

15 10 5 0 20

30

40 50 60 Outlet Temprature of Collector (°C)

70

Fig. 16. The stream exergy in the collector outlet versus a) The time, and b) The collector outlet temperature.

44

350

Water Exergy (kJ)

300

y = 318.52x + 9.734

250 200 150 100 50 0 0

0.2

0.4

0.6

0.8

1

Moisture Ratio Fig. 17. Water exergy of the product.

25 Exergy Efficiency (%)

a) 20 15 10 5 0 0

100

200

300 Time (min)

400

500

600

b)

25

Outlet Air Exergy (kJ)

20

15

10

5

0 0

0.2

0.4

0.6

0.8

1

Moisture Ratio Fig. 18. The exergy efficiency of drying the product at different air mass flow rates versus a) The drying time b) The moisture ratio

45

50

a)

45 Exergy destruction (kJ)

40 35 30 25 20 15 10 5 0 0

0.2

0.4 0.6 Moisture Ratio

0.8

1

50

b)

Exergy Destruction (kJ)

45 40 35 y = 4,735.5x + 0.0,279 R² = 0.99

30 25 20 15 10 5 0 0

0.002

0.004 0.006 0.008 -1 Drying Rate (min )

0.01

0.012

Fig. 19. The water exergy destruction of the product versus a) Moisture ratio b) Drying rate

46

Energy Efficiency (%)

70

a)

60 m=10g

50

m=30g

40 30

m=70g

20

m=150g

10

m=500g

0 0

100

200

.

300 Time (min)

400

500

600

b)

Exergy Efficiency (%)

25 m=10g

20

m=30g

15

m=70g 10

m=150g m=500g

5 0 0

100

200

300 Time (min)

400

500

600

Fig. 20. The influence of the meterial amount on a) Energy Efficiency b) Exergy Efficiency.

47

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Highlights: • • • •

A dynamic model was developed for an indirect solar dryer. The obtained model was in good agreement with experimental data. Energy and exergy analysis were developed for a solar based dryer. The product exergy was taken into consideration in the dryer exergy analysis.

Declaration of interests ☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: