Mathematical modeling and thermodynamic properties in the drying of citron watermelon seeds

Leite, Daniela D. de F.; Queiroz, Alexandre J. de M.; Figueirêdo, Rossana M. F. de; Santos, Francislaine S. dos; Silva, Semirames do N.; Santos, Dyego da C.

doi:10.1590/1807-1929/agriambi.v26n1p67-74

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Articles • Rev. bras. eng. agríc. ambient. 26 (1) • Jan 2022 • https://doi.org/10.1590/1807-1929/agriambi.v26n1p67-74 copy

Mathematical modeling and thermodynamic properties in the drying of citron watermelon seeds¹ 1 Research developed at Laboratory of Processing and Storage of Agricultural Products, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil

Modelagem matemática e propriedades termodinâmicas na secagem de sementes de melancia africana

Authorship SCIMAGO INSTITUTIONS RANKINGS

HIGHLIGHTS:

The increase in drying temperature increases lipids and total sugar.

The temperatures have lower effect on the drying rate after a certain drying time.

The k constant of the Two Terms model increases as a function of the drying air temperature for watermelon seeds.

ABSTRACT

Citron watermelon is an agricultural product of excellent economic potential. Its seeds are widely used for oil extraction, serving as an energy source, showing nutritional characteristics that make them a suitable product to be studied. Thus, the objective was to characterize citron watermelon seeds regarding their physicochemical composition, in addition to determining drying kinetics, fitting mathematical models to the data, and determining the effective diffusivity coefficients and thermodynamic properties. The seeds were dried in a convective dryer, varying the drying temperature, with air velocity of 1.0 m s^-1. With the increase in drying temperature, there were reductions in moisture content, water activity (a_w), ash concentration, total titratable acidity, lipids and reducing sugar. Citron watermelon seeds are rich in lipids and ash, have low sugar concentration and low acidity; their drying kinetics was very well described by the Two Terms and Approximation of Diffusion models, followed by the models of Midilli and Page, which resulted in acceptable fits. Effective diffusivity accompanied the increase in drying temperature, and this behavior was well fitted by an Arrhenius-type equation. Enthalpy and entropy variations were reduced with drying temperature, with increments in Gibbs free energy.

Key words:
Citrullus lanatus var. citroides; agricultural residues; sustainability; unconventional food; effective diffusivity

Models	Equations
Newton	$R X = e x p (- k \cdot t)$	(2)
Thompson	$R X = e x p (\frac{- a - {(a^{2} + 4 b t)}^{0.5}}{2 b})$	(3)
Modified Page	$R X = e x p [- {(k \cdot t)}^{n}]$	(4)
Page	$R X = e x p (- k \cdot t^{n})$	(5)
Henderson and Pabis	$R X = a e x p (- k \cdot t)$	(6)
Two-Term Exponential	$R X = a e x p (- k \cdot t) + (1 - a) e x p (- k \cdot a \cdot t)$	(7)
Logarithmic	$R X = a e x p (- k \cdot t) + c$	(8)
Approximation of Diffusion	$R X = a e x p (- k \cdot t) + (1 - a) e x p (- k \cdot b \cdot t)$	(9)
Two Terms	$R X = a e x p (- k_{0} \cdot t) + b e x p (- k_{1} \cdot t)$	(10)
Midilli	$R X = a e x p (- k \cdot t^{n}) + b \cdot t$	(11)

Variables (d.b.)	Fresh	50	60	70	80
Variables (d.b.)	Fresh	(°C)
Moisture content (%)	54.15 ± 0.38 a	4.37 ± 0.09 b	3.42 ± 0.06 c	1.58 ± 0.07 d	0.81±0.02 e
Water activity (aw)	0.986 ± 0.001 a	0.340 ± 0.001 b	0.328 ± 0.002 c	0.309 ± 0.003 d	0.293 ± 0.09 e
Total titratable acidity (%)	0.21 ± 0.00 a	0.20 ± 0.00 a	0.19 ± 0.00 a	0.18 ± 0.00 a	0.19 ± 0.00 a
pH	5.60 ± 0.07 b	7.10 ± 0.02 a	6.98 ± 0.04 a	6.86 ± 0.04 a	6.81 ± 0.02 a
Ash concentration (%)	1.67 ± 0.04 b	2.29 ± 0.07 a	2.38 ± 0.05 a	2.29 ± 0.04 a	2.29 ± 0.09 a
Lipids (%)	9.41 ± 0.31 d	28.93 ± 0.19 c	30.57 ± 0.27 b	29.88 ± 0.17 b	34.20 ± 0.09 a
Total sugar (g per 100 g)	0.17 ± 0.03 e	8.87 ± 0.03 b	8.35 ± 0.00 c	8.94 ± 0.01 a	8.25 ± 0.00 d
Reducing sugars (g per 100 g)	0.108 ± 0.00 a	0.09 ± 0.09 b	0.07 ± 0.07 c	0.05 ± 0.05 d	0.04 ± 0.04 d
Non-reducing sugars (g per 100 g)	0.06 ± 0.00 e	8.34 ± 0.04 b	7.86 ± 0.00 c	8.45 ± 0.01 a	7.80 ± 0.00 d

Models	T (°C)	Parameters						R²	MSD	χ²
Newton		K
	50	0.0321						0.9798	0.0372	0.0014
	60	0.0344						0.9550	0.0533	0.0029
	70	0.0409						0.9680	0.0453	0.0021
	80	0.0595						0.9613	0.0466	0.0023
Thompson		a			b
	50	0.0029			0.0042			0.9611	0.0518	0.0029
	60	0.0037			0.0050			0.9830	0.0329	0.0011
	70	0.0023			0.0039			0.9752	0.0398	0.0017
	80	0.0109			0.0129			0.9868	0.0272	0.0008
Modified Page		k			n
	50	0.0298			0.9481			0.9821	0.0351	0.0013
	60	0.0287			0.8888			0.9661	0.0463	0.0023
	70	0.0365			0.9218			0.9733	0.0413	0.0018
	80	0.0530			0.9162			0.9675	0.0428	0.0019
Page		k			n
	50	0.0741			0.7533			0.9926	0.0226	0.0006
	60	0.1181			0.6331			0.9960	0.0159	0.0003
	70	0.1147			0.6781			0.9939	0.0197	0.0004
	80	0.1784			0.6244			0.9969	0.0130	0.0002
Henderson and Pabis		a			k
	50	0.9481			0.0298			0.9821	0.0351	0.0013
	60	0.8888			0.0287			0.9661	0.0463	0.0023
	70	0.9218			0.0365			0.9733	0.0413	0.0018
	80	0.9162			0.0530			0.9675	0.0428	0.0019
Two-Term Exponential		a			k
	50	0.2937			0.0788			0.9904	0.0257	0.0007
	60	0.2400			0.1064			0.9782	0.0372	0.0015
	70	0.2628			0.1144			0.9846	0.0314	0.0010
	80	0.2547			0.1748			0.9811	0.0326	0.0012
Logarithmic		a		k		c
	50	0.9361		0.0334		0.0310		0.9898	0.0265	0.0008
	60	0.8791		0.0341		0.0396		0.9785	0.0369	0.0015
	70	0.9103		0.0420		0.0357		0.9838	0.0322	0.0012
	80	0.9060		0.0607		0.0324		0.9781	0.0351	0.0014
Approximation of Diffusion		a		k		b
	50	0.7899		0.0478		0.1511		0.9995	0.0046	0.0000
	60	0.6428		0.0744		0.1372		0.9994	0.0057	0.0000
	70	0.7218		0.0715		0.1501		0.9991	0.0077	0.0001
	80	0.6592		0.1261		0.1452		0.9996	0.0055	0.0000
Two Terms		a	k0		b		k1
	50	0.2146	0.0073		0.7916		0.0486	0.9996	0.0055	0.0000
	60	0.3537	0.0101		0.6411		0.0732	0.9995	0.0056	0.0000
	70	0.2758	0.0107		0.7205		0.0708	0.9991	0.0077	0.0001
	80	0.3399	0.0183		0.6585		0.1256	0.9996	0.0055	0.0000
Midilli		a	k		n		b
	50	1.0272	0.0805		0.7391		0.0000	0.9935	0.0211	0.0005
	60	1.0176	0.1222		0.6296		0.0000	0.9965	0.0148	0.0002
	70	1.0174	0.1183		0.6752		0.0000	0.9945	0.0188	0.0004
	80	1.0083	0.1796		0.6254		0.0000	0.9972	0.0125	0.0001

Temperatures (°C)	D_ef (m² s^-1)	R²
50	4.21 × 10^-10	0.9829
60	4.44 × 10^-10	0.9783
70	5.38 × 10^-10	0.9812
80	7.97 × 10^-10	0.9790

Temperature (°C)	ΔH (kJ mol^-1)	ΔS (kJ mol^-1 K^-1)	ΔG (kJ mol^-1)
50	17.0943	-0.3645	134.8986
60	17.0112	-0.3648	138.5453
70	16.9280	-0.3650	142.1946
80	16.8449	-0.3653	145.8463

Unidade Acadêmica de Engenharia Agrícola Unidade Acadêmica de Engenharia Agrícola, UFCG, Av. Aprígio Veloso 882, Bodocongó, Bloco CM, 1º andar, CEP 58429-140, Campina Grande, PB, Brasil, Tel. +55 83 2101 1056 - Campina Grande - PB - Brazil
E-mail: revistagriambi@gmail.com

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[1] * Corresponding author - E-mail: danieladantasfl@gmail.com

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Mathematical modeling and thermodynamic properties in the drying of citron watermelon seeds1 1 Research developed at Laboratory of Processing and Storage of Agricultural Products, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil

Modelagem matemática e propriedades termodinâmicas na secagem de sementes de melancia africana

HIGHLIGHTS:

ABSTRACT

Mathematical modeling and thermodynamic properties in the drying of citron watermelon seeds¹ 1 Research developed at Laboratory of Processing and Storage of Agricultural Products, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil