Drying characteristics and kinetics solar drying of Mediterranean mussel (mytilus galloprovincilis) type under forced convection

Renewable Energy 147 (2020) 833e844

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Drying characteristics and kinetics solar drying of Mediterranean mussel (mytilus galloprovincilis) type under forced convection Mounir Kouhila*, Haytem Moussaoui, Hamza Lamsyehe, Zakaria Tagnamas, Younes Bahammou, Ali Idlimam, Abdelkader Lamharrar Team of Solar Energy and Medicinal Plants, Cadi Ayyad University, High School of Trainee Teachers, BO 2400, Marrakech, Morocco

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 February 2019 Received in revised form 30 July 2019 Accepted 14 September 2019 Available online 16 September 2019

Drying is a process of hydration and Elimination of water which allows the proliferation of microorganisms and development of chemical reactions without influencing morphological structure of Food Material. This paper focused on the influence of temperature on drying kinetics of the Mediterranean mussels (mytilus galloprovincilis) as per the requirement for storage seafood. Convective drying kinetics and hygroscopic behavior of Mytilus Galloprovincilis was carried out in a solar dryer operating in forced convection. Experimental drying kinetics were measured at three air temperatures (50, 60, and 70
C), and two air flow rates fixed at (300 and 150 m3 h1) with ambient air temperature in the range of 36 e42 ± 1
C, 8.92 to 18.86 ± 2% for ambient humidity, 422 to 988 w/m2 for solar irradiation. Experimental data of drying are collected to plot the characteristic drying curve. Nine mathematical models available in the literature are used for describing the drying curves. The logarithmic model showed the best fitting of experimental data with a highest value of correlation coefficient (r), and lowest value of reduced chisquare (c2). Effective diffusion coefficient value Deff was obtained between 1.14 109 to 3.61 109m2s1 based on the Fick equation. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Activation energy Diffusion coefficient Drying kinetics Mathematical model Mytilus galloprovincilis Solar dryer

1. Introduction Drying is considered as the oldest food preservation technique, and a common unit operation in many chemical and process industries. The removal of moisture prevents the growth and reproduction of microorganisms causing decay and minimises many of the moisture deteriorative reactions. Drying is also particularly considered an important technique to conserve the perishable food [1]. Mytilus Galloprovincilis contain up to 60% of water and are thus highly perishable where cold preservation techniques are often missing, preservation by cooling is necessary because it is widely used to maintain the quality of fresh product and prevent high enzymatic reactions and bacterial activity in fresh fish [2], most of mussels (Mytilus Galloprovincilis) from Essaouira region (Morocco) are not consumed by merchandiser and transformed into uncultivated product, then it remains superfluous and goes waste. The same problem at India, around 20% of fresh seafood was attenuated

* Corresponding author. E-mail address: [email protected] (M. Kouhila). https://doi.org/10.1016/j.renene.2019.09.055 0960-1481/© 2019 Elsevier Ltd. All rights reserved.

due to deficient technique of cold storage and irregular postharvest practices [3]. Small fish spices in the same of crap (chelwa) and prawn are dried in northern India [4]. Solar dryer is very frequent practice of aquaculture product in many developing countries such as morocco. Drying of Mussels is primarily carried out under open sun. Sun drying produce as clean energy and represents a lowest process on energy consumption to preserve seafood. Natural or direct sun drying has been employed afterwards time immemorial, however this technique has disadvantage in way to determine the drying parameter, Weather trouble, insect infection, contamination owing to air pollution. To preserve aquaculture food, open sun drying is mainly expert in subtropical countries where solar radiation is available [5]. The drying technique can develop product quality, enhance shelf life and support their processing. In this research, the Mussels drying process conducted using solar energy; this process decreases conventional energy consumption, reduces considerably the water and microbiological activity of the material, and minimises physical and chemical changes during its storage [6,7]. The knowledge of all experiment data of drying in different air condition as temperature, humidity and flow rate, gives the

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Abbreviations a,b,c,n,k,k0,k1 constants in drying models B the slope of the straight line CDC characteristic drying curve Deff effective moisture diffusivity (m2.s1) D0 pre-exponential factor of the Arrhenius equation (m2. s1) Dv Drying air flow rate (m3.s1) Ea activation energy (kJ/mol) ESM standard error G dimensionless drying rate () L the half thickness of the product (m) MR moisture Ratio at any time of drying MR () reduced moisture content

homogeneity and correlation points gathered into global curve especially named characteristic drying curve (CDC). A deep knowledge of heat transfer parameters, mass, diffusion and the drying behavior of the product are considered indispensable for the conceptualization, simulation and optimization of the drying process. It is then necessary to have an accurate model that can predict rates of elimination of water and describe the drying of the product, nine statistical models were studied to predict and validate experimental data, and those models are: Logarithmic, Midilli-Kucuk, Newton, page, Handerson and Pabis, Tow-term, Diffusion Approach, Wang and singh, Modified Handerson and Pabis. Moisture diffusivity is an essential transport property required in modeling and determining of various food process mainly drying, rehydration, storage and packing, the property of diffusivity has been found to change considerably with the moisture content in food material, due to the complex structure of food product such as cellulose or protein, and their interaction with water [8]. Theoretical prediction of diffusivity is not feasible in the complex food materials such as Mytilus Galloprovincilis, experimental determination is necessary [9]. Three experimental methods have been developed to predict effective moisture diffusivity in food product: analysis of the drying data, permeability measurement and sorption kinetics, this work is based on the analysis of the drying data, because it can be applied to various shapes of food. The mechanism of moisture transport from the interior to the surface of the product are described by the Fick's Equation, it concerns the food materials which dehydration process take place in the falling rate period [10]. Arrhenius Law [11] reported that all molecules possess minimum amount of energy. Taking into account consideration of molecule collides, the energy kinetics of the molecules leading to chemical reactions. The minimum energy requirement to occur reactions is called activation Energy Ea. According to the consulted literature, there is no published paper concerning the Mytilus Galloprovincilis drying. Thus, the main objectives of this study were: a) To study the drying kinetics of Mytilus Galloprovincilis and the influence of temperature on the drying curves; b) To establish the characteristic drying curve of Mytilus Galloprovincilis; c) To model the diffusion phenomenon occurring in the inner structure of Mytilus Galloprovincilis, through the fitting of drying curves and the estimation of effective diffusivity coefficients at different temperatures.

M0 Me M(t) Mf Ms MReqexp;i

moisture initial content (kg Water kg1d.b) equilibrium moisture content (kg Water kg1d.b) moisture content at any time final moisture content content (kg Water kg1d.b dry mass (g) equilibrium experimental water content

MReqpred;i MBE n r R Rh

equilibrium predict water content mean bias error positive integer constant correlation coefficient universal gas constant (J. mol1. K1) ambiant air relative humidity (%) air absolute temperature (K) drying time (min)

q t

2. Material and method 2.1. Description of the experimental setup The experimental apparatus used for the drying of Mediterranean mussels is an indirect forced convection solar dryer (Fig. 1) available at the laboratory of the ‘’ High School of Trainee Teachers (Morocco) ‘‘. The dryer is the type “cupboard » to activate total or partial recycling drying air with ten polyvalent shelves. This type of dryer provides a hot air flow rate characterized by aero-thermal conditions (temperature, humidity and flow rate) [12]. The mass of the product used in drying experiments was (37.0±2) g, samples were uniformly spread on a drying tray, that was then placed on the first shelf of the drying cabinet [13], Moreover, ambient air is heated in a single glazing connected to a solar collector and allows the heated air to enter to the drying cabinet below the trays and flows upwards through the samples. An auxiliary heater system was used for maintaining the drying air temperature constant. Solarmeter was used to measure the amounts of daily solar radiation. Temperature measurements at different points and recordings in the solar drying were made by Cr-Alumel thermocouples (0.2 mm diameter) connected to a data logger enabling ±0.1
C accuracy and the outlet temperatures were measured with thermometers. The relative humidity was detected bay capacitance sensors and determined by Probes Humicolor±2% [14]. A digital weighing apparatus (±0.001 g) measures the mass loss of the product during the drying process. Uncertainty in experimental measurements has also shown in Figs. (2), (3) and (7) in the form of error bars. Uncertainties in experiments were extracted from used instruments. The experiments were carried out at three air drying temperatures (50, 60 and 70
C) and two drying air flow ratesð150 and 300 m3 :h1 Þ as shown in Table 1. The ambient temperature during the drying period varied from 36 to 42 ± 1
C, ambient air humidity from 8.92 to 18.86 ± 2%. During drying of Mytilus Galloprovincilis for each test, the weight of the sample on the tray was measured each 5 min until the variation of mass get constant. For each product, it is possible to define an optimal value of wet Mass for which the product is not deteriorated and maintains the nutritional and organoleptic properties [15]. The final dry matter mass of each sample was determined by a drying oven whose temperature was fixed at 105
C for 24h. This measurement allows calculating equilibrium moisture content per dry basis for each temperature (50, 60 and 70
C) and

M. Kouhila et al. / Renewable Energy 147 (2020) 833e844

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Fig. 1. Schematic diagram of the solar dryer. (1) Solar collector, (2) ventilation duct, (3) fan, (4) suction line, (5) control box, (6) electrical heating system, (7) floors, (8) drying cabinet, (9) air valve, (10) air inlet, (11) air outlet, (12) humidity probe, (13) thermocouple, (14) clays.

Fig. 2. Horizontal and inclined global irradiation during the drying experiments of Mytilus Galloprovincilis.

different equilibrium moisture content obtained and projected on drying curve for various thermal conditions were approached by nine statistical mathematical models. 2.2. Determination of drying characteristic curve 2.2.1. Drying curves The drying curves are the curves representing the variation of the equilibrium moisture content Me as a function of drying time t, or those giving the drying rate as a function of time versus the water content. These curves are obtained experimentally by following the evolution of the wet mass of the product during the drying process by successive weighing until reaching the final moisture content Mf. To obtain the dry mass Ms, the product is placed at the end of each test in an oven heated to a temperature of 105
C for 24 h. This curve contains all the experimental information [12,15]. Drying conditions must make it possible to achieve this optimum value. Fig. 3. Evolution of the moisture content of Mediterranean mussel versus the drying time for different drying air conditions.

two air flow rate. According to the experimental data, drying rate versus time was consequently observed from the characteristic drying curve fitted of a polynomial degree 3. In the subsequent,

2.2.2. Characteristic drying curve The Van Meel [16] transformation is applied for determining the characteristic drying curve allow to studying the influence of the drying air temperature on drying kinetics of Mytilus Galloprovincilis. Drying rate curve obtained for different air conditions by a single normalized drying rate curve [17]. The moisture content was

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Fig. 4. Evolution of drying rate versus time of the same flow rate at 300 m3 h1.

Fig. 5. Variation of drying rate versus moisture content for different drying air conditions.

converted to the moisture ratio MR, dimensionless drying rate G was calculated using the equation below:

MðtÞ  Me MRðtÞ ¼ M0  Me

(1)




 dM dt t f ¼
dM dt

0

Were f: the dimensionless drying rate.

(2)

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2.3. Fitting of the solar drying curve To predict the most suitable drying model for describing the solar drying curve obtained for Mytilus, nine statistical models used by different authors [18e26] are tested to fit solar drying curve (Table 2). The statistical parameters used for selecting the best equation describing the thin draying curves of Mytilus Galloprovincilis [27], Thus, According the highest coefficient [r] value, the lowest [MBE ] and the lowest [c2], the suitable model could be selected. These parameters are given as following: N  P

   MReqexp;i  MReqexp;i  MReqpred;i  MReqpred;i i¼1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 N  N  P P MReqexp;i  M eqexp;i  MReqpred;i  MReqpred;i i¼1

Fig. 6. Influence of the drying air temperature on drying rate of Mytilus Galloprovincilis.

MReqexp;i ¼

MReqpred;i ¼

c2 ¼

i¼1

N 1 X MReqexp;i N i¼1

(4)

N 1 X MReqpred;i N i¼1

(5)

2 PN  i¼1 MReqexp;i  MReqpred;i

(6)

df

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 XN  MBE ¼ MR  MR eq eq exp;i pred;i i¼1 N MReqexp;i ¼ Where:

(3)

(7)

N 1 X MReqexp;i N

(8)

i¼1

MReqexp;i : experimental moisture ratio MReqpred;i : predicted moisture ratio N: number of experimental point df: degree of regression model Fig. 7. Characteristic drying curve of Mytilus Galloprovincilis.


 : the drying rate at any time of drying (Kg water/Kg d.b dM dt t

Computer softwares (Curve Expert 4.1 and Origin 8.0) were applied to calculate the coefficients for each model describing the drying curves, this program applied by Marquardt-Levenberg using nonlinear optimization method.

min)):

8
2.4. Effective moisture diffusivity

for for for

MR ¼ 0 0  MR  1 MR  1

Diffusivity is generally considered to be the main mechanism for transporting moisture to the surface to be evaporated [10]. The main mechanism describing diffusivity shows that internal mass transfer resistance due to presence of falling rate drying period

Table 1 Drying conditions during experiments in the solar dryer. Exp N


Air flow rate Dv (m3/s)

Drying temperature T±0.1 (
C)

Relative humidity Rh± (%)

Ambient temperature ± 1 (
C)

t (min)

1 2 3 4 5 6

0.083 0.083 0.083 0.042 0.042 0.042

50 60 70 50 60 70

10.52 18.86 9.82 13.69 13.92 14.71

41 36 42 39 39 38

320 230 140 525 330 210

838

M. Kouhila et al. / Renewable Energy 147 (2020) 833e844 Table 2 Mathematical models applied to the drying curve. Model name

Model equation

Newton [18] Page [19] Henderson and Pabis [20] Logarithmic [21] Two-term [22] Wang and Singh [23]

MR MR MR MR MR

¼ expð  ktÞ ¼ expð  kt n Þ ¼ a expð  ktÞ ¼ a expð  ktÞ þ c ¼ a expð  k0 tÞ þ b expð  k1 tÞ

MR MR MR MR

¼ ¼ ¼ ¼

Diffusion approach [24] Modified Henderson and Pabis [25] Midilli-Kucuk [26]

coefficients

1 þ at þ bt 2 a expð  ktÞ þ ð1  aÞexpð  kbtÞ a expð  ktÞ þ b expð  k0 tÞ þ c expð  k1 tÞ a expð  kt n Þ þ bt

K k,n a,k a,k,c a,k0,b,k1 a,b a,b,k a,b,k,k0,k1 a,b,k,n

controls drying time [28]. Moisture transport during falling rate period can be analyzed mathematically by the Second law Fick's diffusion model:

Activation energy (Ea) can be calculated by the plot of Ln (Deff) versus the inverse of temperature 1/q, the slop B of straight plotted gives Ea using the following eq (14):

vMR ¼ Deff V2 MR vt


   Ea 1 Ln Deff ¼ LnðD0 Þ  R q

(9)

According to infinite slab geometry, Crank [10] had recommended a particular solution of this partial differential eq (9). The solution of this equation can be applied undertaking hypothesis such as uniform initial moisture distribution, constant drying temperature, regular diffusivity and negligible shrinkage:

MR ¼

∞ 8 X

p2

1

n¼0 ð2n

þ 1Þ

2

exp



ð2n þ

1Þ2 p2 D 4H 2

eff t

! (10)

In practice, when the drying time is abundant, only the first term of the series is used, thus eq (10) could be reduced:

MR ¼

8

p2

exp



p2 Deff t

! (11)

4L2

Effective moisture diffusivity is calculated from experimental data obtained in drying process [29]. Introduce naturel logarithm from eq (10), the effective moisture diffusivity (Deff) retained by plotted curve that consisting Ln (MR) versus time (min) and determining from the slope B of the straight line corresponding the fit experimental data:


 8 LnðMRÞ ¼ Ln 2 

p

B¼



p2 Deff

p2 Deff  t 4L2

! (12)

!

4L2

(13)

This method used for predicting this constant for the whole process. Furthermore, during drying of Mediterranean Mussels (Mytilus Galloprovincilis), effective moisture diffusivity was found to be dependence function of moisture content and temperature [30]. 2.5. Activation energy The concept of activation energy (Ea) corresponds to the amount of energy that must be brought to a system to initiate chemical reactions, nuclear reaction or various other physical phenomena [31]. This amount energy can be determined by using Arrhenius [11,32] type equation, it is resolved from the correlation between the experimental drying temperatures and the values of the effective moisture diffusivity:

Deff ¼ D0 eðEa =RqÞ

(14)

B¼


 Ea R

(15)

(16)

3. Results and discussion 3.1. Determination of drying kinetics The solar irradiation data of the drying experiments were performed during June 2017 in Marrakech, Morocco. During the experiments, horizontal and inclined solar irradiation varied between 400 and 988 W/m2 (Fig. 2), the entire aero-thermal conditions of temperature, relative humidity and air flow rate were measured. The relative humidity varied between 8.92 and 18.86% (±2%), the ambient air temperature ranged from 36 to 42 ± 1
C, inlet drying air temperature carried out from the range of 50e70
C and air flow rate at 150 and 300 m3 h1. Drying curve represents the evolution of moisture content as function of time, it signified the amount of moisture containing within sample. The drying kinetic of sample indicates the loss of mass and could be presented by drying rate. Drying experiment is performed at three drying air temperatures (50, 60 and 70
C) and two air flow rate (300 and 150 m3 h1) as shown in (Table 1). Six experiments was tested to represent the drying curve, Fig. 3 shows the evolution of the moisture content as function of time from different air condition, it is observed on the drying curve that the moisture content decrease considerably with time and decrease when the temperature of the drying air increase. En general, the drying curve could be represented into three phases, there is absences of initial period (phase 0) were the drying rate period increased. In this phase, the sensible heat is transmitted toward the surface of the product accompanied by the increases of its temperature. To clarify this phase, at the beginning of drying process, the product still relatively to its initial temperature less than the drying air temperature of the flow rate. The energy required in the dried chamber serves to increase the temperature of the product by a sensible heat input, which leads to evaporate the water of the product. Also, it is noticed an absence of phase 1 from Fig. 3, the second phase (phase 1) corresponds to the steady drying phase. During this period, the free water is present on the surface of the dried product. Consequently, the vapor pressure at the surface of the product is equal to the saturation vapor pressure and is therefore only a function of the temperature. Furthermore, the drying rate is constant during this phase, it only depend on the external conditions (temperature, air humidity and flow

M. Kouhila et al. / Renewable Energy 147 (2020) 833e844

characteristics). There is only the presence of the falling drying rate period (phase 2). This phenomenon was interpreted by the amount of free moisture in the initial stage of drying; hence it removed considerably [33]. During phase 2, the enquired energy applied to drying are used to evaporate water from the product in both vapor and liquid state, this effect involves increasing temperature of the product and is represented by the decrease in drying rate [34,35]. This mechanism is governed by the effective diffusion in materials, which depends on the pressure, temperature and moisture content of the product. These results in agreement by other authors [26,36e38]. According to the drying rate in Fig. 4, it represents the ratio
 dM versus time (min). This figure shows the decreasing rate dt period (phase 2) as indicated previously at 70, 60 and the same flow rate 300 m3 h1.

50
C

from

3.2. Influence of the drying air temperature on the drying kinetics According to the results illustrated in Figs. 5 and 6 for three temperatures (50, 60 and 70
C) and for two air flow rate 300 and 150 m3 h1 respectively. The aero thermal conditions of the drying air have a significant impact on the rate of the drying curves. It is observed that, for the same drying air flow rate of 300 m3 h1 the drying rate increases when the temperature of the drying air increases. Similarly, the drying rate decrease continuously with decreasing moisture content. As a result, the highest values in drying rate conduct in the experiment were found at 70
C. The initial moisture content of Drying Mytilus Galloprovincilis varied from 2.30 to 2.81% (d.b), this moisture range was reduced respectively to a final moisture content that varied between 0.36 and 0.46% (d.b), which means an important reduction weight have observed during drying of Mytilus Galloprovincilis under forced

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convection solar dryer at the higher drying air temperature 70
C as shown in Figs. 5 and 6. However, The effect of drying volume flow rate is remarkable for a constant drying air temperature, the higher drying rate at 300 m3h1conduct to reduction of moisture content and the drying time, compared to the drying rate at 150 m3h-1 were the drying time increases. Consequently, the drying kinetics of Mediterranean mussels is influenced by drying air temperature. Generally, this influence depends for the majority of porous hygroscopic in product. Similar results are noted in other work on solar drying [39,40]. 3.3. Characteristic drying curve of mytilus galloprovincilis The results obtained for the six performed experiments are synthetized in order to establish a law of drying called characteristic drying curve, it consists to normalize the kinetics of drying process in a statistical model. The methods adopted allow establishing a correlation based to the nonlinear optimization method of Levenberg-Marquad in the form of a third-degree polynomial equation. Origin 8.0 Software was used to obtain the characteristics drying curve for Mediterranean Mussels. The dimensionless drying rate value G gives some satisfactory knowledge about how the drying kinetics behaves at any condition of the drying air; indeed, it is sufficient to determine the initial moisture and that of the equilibrium state. The main interest of CDC is that reduce all experimental data and put them in a useable form could be exploitable by the experimenter and the scientific community. Experimental drying data are plotted in Fig. 7 to represent dimensionless Drying rate G versus Reduced moisture content G ¼ f (MR ()). This figure shows that for different aero-thermal conditions in drying experiments, all the drying curves obtained with the moisture ratio fall into a tight band, which gathered all experimental points in different conditions of air temperature and flow rate. It indicates that the effect of variation of air conditions is small

Table 3 Coefficients of the models describing the drying kinetics of Mediterranean mussels. Model name Newton

Page

Handerson and Pabis

Logarithmic

Two-term

Wang and Singh

Diffusion Approximation

Modified Handerson and Pabis

Midilli-kucuk

T (
C)


70 C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C 70
C 60
C 50
C

Coefficients k ¼ 0.0137 k ¼ 0.0115 k ¼ 0.0085 k ¼ 0.0110 n ¼ 1.0518 k ¼ 0.0041 n ¼ 1.2350 k ¼ 0.0058 n ¼ 1.0795 a ¼ 1.0530 k ¼ 0.0124 a ¼ 1.0530 k ¼ 0.0124 a ¼ 1.0149 k ¼ 0.0087 a ¼ 1.0523 k ¼ 0.0120 c ¼ 0.0600 a ¼ 1.2571 k ¼ 0.0080 c ¼ 0.2463 a ¼ 1.0893 k ¼ 0.0070 c ¼ 0.0948 a ¼ 0.5047 k0 ¼ 0.0870 b ¼ 0.5074 k1 ¼ 0.0087 a ¼ 0.5269 k0 ¼ 0.0124 b ¼ 0.5296 k1 ¼ 0.0124 a ¼ 0.5074 k0 ¼ 0.0087 b ¼ 0.5074 k1 ¼ 0.0087 a ¼ 0.0120 b ¼ 2.6945 105 a-0.0088 b ¼ 2.0073 105 a ¼ 0.0064 b ¼ 1.0950 105 a ¼ 1.0002 k ¼ 0.0072 b ¼ 1.0000 a ¼ 1.8192 k ¼ 0.0205 b ¼ 1.0245 a ¼ 1.0368 k ¼ 0.0072 b ¼ 1.0000 a ¼ 13.6701 k ¼ 0.0083 b ¼ 10.3290 g ¼ 0.0086 c ¼ 4.3305 h ¼ 0.0087 a ¼ 13.6637 k ¼ 0.0047 b ¼ 10.3366 g ¼ 0.0051 c ¼ 4.3357 h ¼ 0.0051 a ¼ 13.6531 k ¼ 0.0093 b ¼ 10.3327 g ¼ 0.0092 c ¼ 4.3338 h ¼ 0.0093 a ¼ 0.9980 k ¼ 0.0135 n ¼ 0.9779 b ¼ 0.0002 a ¼ 0.9910 k ¼ 0.0055 n ¼ 1.1319 b ¼ 0.0005 a ¼ 1.0029 k ¼ 0.0088 n ¼ 0.9679 b ¼ 0.0002

r

S

c2

MBE 3

0.9979 0.9910 0.9978 0.9983 0.9984 0.9987 0.9935 0.9935 0.9980 0.9990 0.9997 0.9998 0.9980 0.9935 0.9980 0.9929 0.9997 0.9961 0.8362 0.9986 0.9872 0.9990 0.9997 0.9980 0.9991

0.0212 0.0413 0.0212 0.0197 0.0197 0.0197 0.0365 0.0216 0.0365 0.0151 0.0151 0.0151 0.02312 0.02312 0.02312 0.01720 0.01720 0.01720 0.19546 0.19546 0.19546 0.01755 0.01755 0.01755 0.01527

1.162 10 0.00177 4.7600 104 3.8780 102 3.2070 102 2.9840 102 4.7050 104 0.0013 4.4750 104 2.3090 104 5.9800 104 5.2290 105 4.9010 104 1.4540 103 4.9010 104 4.2640 102 1.5450 102 1.1390 103 3.7650 102 2.9640 104 3.0230 103 1.0430 103 6.5780 104 6.9230 104 8.9420 104

3.2014 102 4.1306 102 2.1397 102 1.8566 102 1.7205 102 1.6570 102 2.0449 102 3.5072 102 2.0291 102 1.387 102 7.2730 103 6.7836 103 2.0290 102 3.5072 102 2.0290 102 2.04551 102 1.1941 102 3.2371 102 1.7712 101 1.6194 102 5.1578 102 2.6372 102 2.2449 102 2.2938 102 2.6372 102

0.9998

0.01527

4.3490 105

6.0661 103

0.9999

0.01527

1.6970 104

1.1941 102

840

M. Kouhila et al. / Renewable Energy 147 (2020) 833e844

Table 4 Results of statistical analysis of the mathematical models. Models

r

Newton Page Handerson and Pabis Logarithmic Two-term Wang and Singh Diffusion Approximation Modified Handerson and Pabis Midilli and Kucuk

0.9949 0.9981 0.9947 0.9995 0.9958 0.9969 0.9523 0.9985 0.9996

c2 1.1484 3.4875 6.8020 1.4352 7.5481 2.1644 1.9627 8.5195 3.6918

MBE 3

10 104 104 104 104 102 102 104 104

3.2069 1.8290 2.4066 1.0449 2.4066 1.0842 1.0542 2.4544 1.4793

102 102 102 102 102 102 101 102 102

linear optimization based on the Levenberg-Marquad algorithms. The appropriate model for describing the shape of drying kinetics is selected according to the following criteria: high correlation coefficient (r), minimal mean bias error (MBE) and minimal chi-square (c2 ). The average values of constants models were determined and summarized in Table 3. From Table 4, the Logarithmic model seems to be the best model describing the drying kinetics of Mediterranean mussels because it has the highest value of [r]of 0.9995, the lowest values of chi-square [c2 ] of 1.4352 104 and lowest MBE of 1.0449 102. Fig. 8 shows an excellent agreement between the reduced experimental moisture contents and the predicted Logarithmic model:

over the range tested [39,40].

f ¼ 0:0467 þ 1:509MR  1:751MR2 þ 1:168MR3

(17)

The best smoothing are used to choose two criteria for evaluate the goodness of fit, it concerns the standard error (ESM ¼ 0.017) and the correlation coefficient (R ¼ 0.956). The characteristic drying curve of the Mytilus Galloprovincilis gives valuable information for the prediction of the drying rate for other experimental conditions other than those in which our tests were carried out. 3.4. Modeling of drying curves The moisture content data measured at different drying air temperatures of Mytilus Galloprovincilis were converted to moisture ratio. The drying curves were plotted afterwards in function of time. In drying treatments, modeling of drying curve is necessary to predict moisture content in a product [41]. Nine statistical models or empirical equations were used to describe the shape of drying curve of Mytilus Galloprovincilis. All experimental data and constants drying coefficients [r, MBE andc2 ] was adjusted using non-

MR ¼ aexp(-kt)þc

(18)

Where: a ¼ 2.8293e0.06824T þ 6.54 104T2

(19)

k ¼ 0.047e0.00155T þ 1.5 105T2

(20)

c ¼ 2.6283 þ 0.07502T-5.475 104T2

(21)

Eq 19e21 predicted well the Moisture Ratio (MR) at three drying air temperatures 50, 60 and 70
C.These results as shown in Fig. 9 presents the plotted predicted moisture versus drying time. Indeed, the logarithmic model describes adequately the drying kinetics of Mytilus in forced convection.

3.5. Determination of effective moisture diffusivity and activation energy The Experimental drying curves the Mytilus Galloprovincilis

Fig. 8. Predicted moisture ratio by the Logarithmic model as a function of the experimental moisture ratio of Mytilus Galloprovincilis.

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Fig. 9. Experimental and predicted moisture ratios obtained using the logarithmic model versus drying time.

Fig. 10. Plot of Ln (MR) as a function of the drying time for the flow rate of 300 m3 h1.

demonstrated that the drying rate occurs only in the falling drying rate period, this is due to liquid diffusion which controls the moisture transportation process. The second law by Fick's equation based on the analysis of the drying data could be used to determine the effective moisture diffusivity of food products, thus to describe

the drying behavior. The solution of Fick's equation in slab geometry was defined according to equation (12). Figs. 10 and 11 show the influence of drying temperature and drying air flow on effective moisture diffusivity of Mytilus, the effective diffusivity values are defined from the graphs were drawn

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Fig. 11. Plot of Ln (MR) as a function of the drying time for the flow rate of 150 m3 h1.

between Ln (MR) against drying time for the studied range of temperatures 50e70
C and flow rate 150e300 m3h-1. The values of Deff are shown in Table 5. It apparent at constant drying air flow rate, Deff increases with the increase of drying air temperature. When Mussels dried at high temperature, the raise of heating energy of solar dryer increases the activity of water molecules and lead to high diffusivity. The influence of temperature on effective diffusivity was explained widely in reference [41]. From Table 5, The Deff values obtained for Mytilus Galloprovincilis varied between 1.14 109 to 3.61 109 m2 s1 at 150 m3h-1, and 1.79 109 to 2.66 109 m2 s1 at 300 m3h-1. These values are within the overall margin 108 to 1012 m2/s for effective moisture diffusivity of food products.

3.6. Activation energy Activation energy Ea represents the potential barrier that prohibited the drying process to take place. To dry a food product the required energy must overcome the activation energy value to occur the process. The diffusion phenomenon is activated through the thermal agitation, so the Arrhenius law (Eq. (14)) could totally describe the diffusion coefficients. The activation energy value was determined from the slop of

Table 5 Values of effective moisture diffusivity Deff for different drying condition of the Mediterranean mussels. Exp N


T
(C)

Dv (m3.h1)

Deff (m2.s1)

1 2 3 4 5 6

50 50 60 60 70 70

300 150 300 150 300 150

1.79 1.14 2.13 1.95 2.66 3.61

109 109 109 109 109 109

R 0.9935 0.9825 0.9942 0.9797 0.9931 0.9926

plotted natural logarithm of Deff versus (1/T). By taking into consideration of different air conditions (temperature and drying air flow rate) as shown in Figs. (12 and 13), the value of activation energy was 55.43 kJ mol1 obtained for Mytilus Galloprovincilis [41,42]. 4. Conclusions The convective solar drying experiments were conducted in the temperature range of 50e70
C and two drying air flow rates (300 and 150 m3 h1) in a convective partial solar dryer. The kinetics drying for Mytilus Galloprovincilis and the characteristics of drying process was determined. The evolution of moisture content for different air conditions was checked; the drying curve shows only the presence of phase 2 which corresponds the falling drying rate period. According to the various aero-thermal drying conditions (temperature and drying air flow rate); the drying air temperature was found to be the main factor influencing the drying kinetics of Mytilus Galloprovinvilis. The increasing in drying air temperature causes the drying rate increase. The concept of characteristic drying curve obtained by Van Meel transformation provides valuable information to predict the drying rate for other experimental conditions other than those in which our experiments are performed. In this work, the goodness of fit of experimental data was evaluated using nine drying models. The statistical parameters were analyzed; The Logarithmic model seems to be the best statistical model for describing the convective solar drying kinetics of Mytilus Galloprovincilis. In the covered ranges, the effective moisture diffusivity values (Deff) are obtained from the Fick's diffusion model varying from 1.14 109 to 3.61 109 m2s1. The increase in drying air temperature at a constant drying air flow rate increased the value of Deff, while the

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Fig. 12. Ln (Deff) versus (1/q) at Dv ¼ 300 m3h-1

Fig. 13. Ln (Deff) versus (1/q) at Dv ¼ 150 m3h-1

increase in air flow rate at constant air temperature decreased the value of Deff. An Arrhenuis relation with activation energy values of 55.43 kJ mol1 expressed the effects of drying temperature on the effective diffusivity.

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