QUALITY, PERFORMANCE ANALYSIS, MASS TRANSFER PARAMETERS AND MODELING OF DRYING KINETICS OF SOYBEAN

Darvishi, H.

doi:10.1590/0104-6632.20170341s20150509

H. Darvishi ^**To whom correspondence should be addressed

Department of Biosystems Engineering; Faculty of Agriculture, University of Kurdistan, P.O. Box: 416, Sanandaj, Iran. Phone: + (98) 087336277724; Fax: + (98) 08733624249. E-mail: H.Darvishi@uok.ac.ir

*To whom correspondence should be addressed

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Figure 1
Schematic diagram of the experimental apparatus.

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Figure 2
Energy aspects of soybean drying.

^a-c Different superscripts in the same column indicate significant differences (P < 0.05)

^A Values in parenthesis show the standard deviations

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Figure 3
Energy consumed in the sensible and evaporation (latent) periods for microwave drying of soybean.

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Figure 4
Exergy aspects of soybean drying.

^a-c Different superscripts in the same column indicate significant differences (P < 0.05)

^A Values in parenthesis show the standard deviations

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Figure 5
Average improvement potential at different microwave powers.

^a-c Different superscripts in the same column indicate significant differences (P < 0.05)

^A Values in parenthesis show the standard deviations

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Figure 6
Comparison between bulk density of fresh and dried soybean at different microwave powers.

^a-c Different superscripts in the same column indicate significant differences (P < 0.05)

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Figure 7
Drying curves of soybean at various microwave powers.

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Figure 8
Variation of drying rates with moisture content soybean seeds.

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Figure 9
Comparison between experimental and predicted moisture ratios using Page's model.

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Figure 10
Variation of effective diffusivity for soybean with microwave power.

^a-e Different superscripts in the same column indicate significant differences (P < 0.05)

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Figure 11
Effect of microwave power on mass transfer coefficient of soybean seeds.

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Figure 12
Fitting of the experimental points to the Arrhenius relationship for the diffusion model.

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Figure 13
Fitting of the experimental points to the Arrhenius relationship for the mass transfer model.

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Table 1
Mathematical models given by various authors for the drying curves.

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Table 2
Measurement uncertainties.

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Table 3
Different quality of soybean drying.

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Table 4
Statistical analysis of the models fitted to the drying data for microwave drying soybean seeds.

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NOMENCLATURE a, b, n experimental constants Ap sample surface area, (m2) Cp specific heat capacity, (J/kg.K) D0 pre-exponential factor of the Arrhenius equation, (m2/s) Dem moisture diffusivity, (m2/s) Dr drying rate, (kg water/kg dry matter, (s) Eab energy absorbed, (J) Ead activation energy for the diffusion model, (W/g) Eam activation energy for the mass transfer model, (W/g) Eloss specific energy loss, (J/kg water) Eref energy reflected, (J) Etran energy transmition, (J) Esc specific energy consumption, (J/kg water) ex specific exergy, (J/kg) exevap rate of exergy evaporation, (J/s) EXloss specific exergy loss, (J/kg) EXref exergy reflected, (J) EXtran exergy transmission, (J) F0 Fourier number, (dimensionless) h hue angle, (degree) h0 pre-exponential factor of the Arrhenius equation, (m/s) hm mass transfer coefficient, (m/s) IP improvement potential, (J) k drying rate constant, (1/s) m mass of sample, (kg) mt mass of sample at any time, (kg) m0 initial mass of sample, (kg) md mass of dry product, (kg) mw mass of evaporated water, (kg) m·w rate of evaporated water, (kg/s) M0 initial moisture content,(kg water/kg dry matter) Me equilibrium moisture content, (kg water/kg dry matter) Mt moisture content at any time, (kg water/kg dry matter) MR moisture ratio, (dimensionless) MRexp,i ith experimental moisture ratio MRpre,i ith predicted moisture ratio N number of observations P microwave power, (W) Pin microwave power emitted by the magnetron, (W) r radius of sample, (m) R2 coefficient of determination RMSE root mean square error Rr Rehydration ratio Sh shrinkage, (-) t time, (s) T temperature, (K) To ambient temperature, (K) Tp temperature of product, (K) Vc volume of the cylinder, (m3) Vd volume of the dry sample, (m3) Vf volume of the fresh sample, (m3) Vp sample volume, (m3) z number of constants in the drying model

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Greek Symbols ηen energy efficiency, (%) ηex exergy efficiency, (%) λfw latent heat of free water, (J/kg) λwp latent heat of product, (J/kg) ρb bulk density, (kg/m3) ΔE total colour change

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Model name	Model	References
Henderson and Pabis	MR = a exp (- kt)	*Darvishi et al. (2014a)*Darvishi, H., Zarein, M., Minaei, S. and Khafajeh, H., Exergy and energy analysis, drying kinetics and mathematical modeling of white mulberry drying process. International Journal of Food Engineering, 10(2), 269-280 (2014a).
Newton	MR = exp (- kt)	*Wang et al. (2007)*Wang, Z., Sun, J., Chen, F., Liao, X. and Hu, X., Mathematical modeling on thin layer microwave drying of apple pomace with and without hot air pre-drying. Journal of Food Engineering, 80, 536-544 (2007).
Wang and Singh	MR = 1 +bt + at²	Sarimeseli (2011)Sarimeseli, A., Microwave drying characteristics of coriander (Coriandrum sativum L.) leaves. Energy Conversion and Management, 52, 1449-1453 (2011).
Page	MR = exp (- ktⁿ)	Lee and Kim (2009)Lee, J. H. and Kim, H. J., Vacuum drying kinetics of Asian white radish (Raphanus sativus L.) slices. LWT - Food Science and Technology, 42, 180-186 (2009).
Logarithmic	MR = a exp (- kt) + b	*Kingsly et al. (2007)*Kingsly, R. P., Goyal, R. K., Manikantan, M. R. and Ilyas, S. M., Effects of pretreatments and drying air temperature on drying behavior of peach slice. International Journal of Food Science and Technology, 42, 65-69 (2007).
Midilli	MR = a exp (- ktⁿ) + bt	*Midilli et al. (2002)*Midilli, A., Kucuk H. and Yapar Z., A new model for single layer drying. Drying Technology, 20(7), 1503-1513 (2002).

Parameter	unit	Value
Uncertainty in mass loss measurement	g	±0.5
Uncertainty in moisture quantity measurement	g	±0.0141
Uncertainty in the time measurement	s	±0.141
Uncertainty in microwave power measurement	W	±0.10
Uncertainty in temperature measurement	ºC	±2.12

P (W)	ΔE (-)	h (degree)	Shrinkage	Rehydration ratio
200	14.68 (±2.59^A A Values in parenthesis showed their standard deviations )^a	88.07 (±5.11)^a	0.948 (±0.021)^a	0.618 (±0.019)^a
300	18.80 (±3.90)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	90.52 (±3.14)^a	0.897 (±0.024)^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	0.716(±0.017)^b a–b Different superscripts in the same column indicate significant differences (P < 0.05) c
400	18.13 (±3.54)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	91.51 (±7.41^)ab	0.885 (±0.034^)b	0.745 (±0.027^)c
500	19.61 (±7.46)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	91.73 (±9.47)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	0.860 (±0.011)^b a–b Different superscripts in the same column indicate significant differences (P < 0.05) c	0.703 (±0.039)^b a–b Different superscripts in the same column indicate significant differences (P < 0.05) c
600	19. 89 (±5.83)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	90.85 (±3.16)^a a–b Different superscripts in the same column indicate significant differences (P < 0.05) ^b a–b Different superscripts in the same column indicate significant differences (P < 0.05)	0.880 (±0.033)^b a–b Different superscripts in the same column indicate significant differences (P < 0.05) c	0.799(±0.029)^d

Model	P (W)	Coefficients and constants	R²	χ²	RMSE
Newton	200	k = 0.0664	0.9176	0.00328	0.05656
	300	k = 0.1301	0.8583	0.00710	0.08249
	400	k = 0.2147	0.8295	0.00892	0.09101
	500	k = 0.2966	0.922	0.00467	0.06515
	600	k = 0.4596	0.9601	0.00313	0.05277
Henderson and Pabis	200	a = 1.1224, k = 0.0827	0.9684	0.00168	0.03997
	300	a = 1.1697, k = 0.1719	0.9336	0.00441	0.06358
	400	a = 1.1775, k = 0.2873	0.9100	0.00658	0.07507
	500	a = 1.1264, k = 0.3647	0.9485	0.00351	0.05362
	600	a = 1.1036, k = 0.5291	0.9842	0.00209	0.04031
Page	200	k = 0.0154, n = 1.704	0.9977	0.00005	0.00690
	300	k = 0.0256, n = 2.116	0.9980	0.00009	0.00913
	400	k = 0.0601, n = 2.260	0.9974	0.00066	0.02386
	500	k = 0.1762, n = 1.781	0.9992	0.00004	0.00572
	600	k = 0.3791, n = 1.462	0.9940	0.00038	0.01726
Wang and Singh	200	b = -0.0301, a = -0.0016	0.9990	0.00270	0.05067
	300	b = -0.0291, a = -0.0129	0.9889	0.00241	0.04701
	400	b = -0.0239, a = -0.0468	0.9990	0.00164	0.03752
	500	b = -0.1168, a = -0.0422	0.9940	0.00128	0.03232
	600	b = -0.2959, a = - 1.012×10^-9	0.9819	0.00246	0.04370
Logarithmic	200	a = 1.505, b = -0.409, k = 0.0521	0.9777	0.00108	0.03169
	300	a = 1.539, b = -0.395, k = 0.1114	0.9522	0.13272	0.34078
	400	a = 1.392, b = -0.240, k = 0.2120	0.9231	0.00751	0.07682
	500	a = 1.291, b = -0.183, k = 0.2861	0.9579	0.00304	0.04702
	600	a = 1.314, b = -0.234, k = 0.3846	0.9881	0.00159	0.03252
Midilli	200	a= 0.994, b= 0.030, k= 0.019, n= 1.958	0.9990	0.00026	0.00560
	300	a= 0.993, b= 0.025, k= 0.037, n= 2.069	0.9991	0.00019	0.01261
	400	a= 0.995, b= 0.039, k= 0.092, n= 2.024	0.9995	0.00007	0.00714
	500	a= 1.000, b= 0.002, k= 0.178, n= 1.781	0.9997	0.00006	0.00060
	600	a= 1.009, b= 0.095, k= 0.556, n= 1.605	0.9993	0.00011	0.00807

	NOMENCLATURE
a, b, n	experimental constants
A_p	sample surface area, (m²)
C_p	specific heat capacity, (J/kg.K)
D₀	pre-exponential factor of the Arrhenius equation, (m²/s)
D_em	moisture diffusivity, (m²/s)
Dr	drying rate, (kg water/kg dry matter, (s)
E_ab	energy absorbed, (J)
E_ad	activation energy for the diffusion model, (W/g)
E_am	activation energy for the mass transfer model, (W/g)
E_loss	specific energy loss, (J/kg water)
E_ref	energy reflected, (J)
E_tran	energy transmition, (J)
E_sc	specific energy consumption, (J/kg water)
ex	specific exergy, (J/kg)
ex_evap	rate of exergy evaporation, (J/s)
EX_loss	specific exergy loss, (J/kg)
EX_ref	exergy reflected, (J)
EX_tran	exergy transmission, (J)
F₀	Fourier number, (dimensionless)
h	hue angle, (degree)
h₀	pre-exponential factor of the Arrhenius equation, (m/s)
h_m	mass transfer coefficient, (m/s)
IP	improvement potential, (J)
k	drying rate constant, (1/s)
m	mass of sample, (kg)
m_t	mass of sample at any time, (kg)
m₀	initial mass of sample, (kg)
m_d	mass of dry product, (kg)
m_w	mass of evaporated water, (kg)
m·_w	rate of evaporated water, (kg/s)
M₀	initial moisture content,(kg water/kg dry matter)
M_e	equilibrium moisture content, (kg water/kg dry matter)
M_t	moisture content at any time, (kg water/kg dry matter)
MR	moisture ratio, (dimensionless)
MR_exp,i	i^th experimental moisture ratio
MR_pre,i	i^th predicted moisture ratio
N	number of observations
P	microwave power, (W)
P_in	microwave power emitted by the magnetron, (W)
r	radius of sample, (m)
R²	coefficient of determination
RMSE	root mean square error
Rr	Rehydration ratio
Sh	shrinkage, (-)
t	time, (s)
T	temperature, (K)
T_o	ambient temperature, (K)
T_p	temperature of product, (K)
V_c	volume of the cylinder, (m³)
V_d	volume of the dry sample, (m³)
V_f	volume of the fresh sample, (m³)
V_p	sample volume, (m³)
z	number of constants in the drying model

*Greek Symbols*
η_en	energy efficiency, (%)
η_ex	exergy efficiency, (%)
λ_fw	latent heat of free water, (J/kg)
λ_wp	latent heat of product, (J/kg)
ρ_b	bulk density, (kg/m³)
ΔE	total colour change

\begin{matrix} \overset{energyinput}{\overset{︷}{P_{in} \times t}} = \\ \overset{≅ energy absorption}{\overset{︷}{(\overset{energy of dry product}{\overset{︷}{{({mC}_{p} T)}_{dp}}} - \overset{energy of wet product}{\overset{︷}{{({mC}_{p} T)}_{dp}}}) \overset{latent heat}{\overset{︷}{+ λ_{wp} m_{w}}}}} \\ \overset{≅ energy loss}{\overset{︷}{+ E_{ref} + E_{tra}}} \end{matrix}

\begin{matrix} \overset{energy input}{\overset{︷}{P_{in} \times t}} = \\ \overset{exergy absorption}{\overset{︷}{(\overset{exergy of dry product}{\overset{︷}{{(m \times ex)}_{dp}}} - \overset{exergy of wet product}{\overset{︷}{{(m \times ex)}_{wp}}}) + {ex}_{evap} \times t}} \\ \overset{≅ {EX}_{loss}}{\overset{︷}{+ {EX}_{ref} + {EX}_{tra}}} \end{matrix}

[1] *To whom correspondence should be addressed

Brasil

Brasil

QUALITY, PERFORMANCE ANALYSIS, MASS TRANSFER PARAMETERS AND MODELING OF DRYING KINETICS OF SOYBEAN

Abstract