DRYING KINETICS OF BARU FRUITS (<i>Dipteryx alata</i> Vogel)

Resende, Osvaldo; Oliveira, Daniel E. C. de; Costa, Lílian M.; Ferreira Júnior, Weder N.

doi:10.1590/1809-4430-Eng.Agric.v38n1p103-109/2018

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Scientific Paper, Post-Harvest Science and Technology • Eng. agríc. (Online) 38 (1) • Jan-Feb 2018 • https://doi.org/10.1590/1809-4430-Eng.Agric.v38n1p103-109/2018 copy

DRYING KINETICS OF BARU FRUITS (Dipteryx alata Vogel)

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study aimed to fit different mathematical models to the experimental data on drying of baru fruits (Dipteryx alata Vogel), determine and assess the effective diffusion coefficient, as well as obtain the activation energy and thermodynamic properties for the drying process under different air temperature conditions. Baru fruits with an initial moisture content of 0.429 ± 0.044 (dry basis, db) were dried in a forced air ventilation oven under four temperature conditions (40, 60, 80, and 100 °C) until reaching a moisture content of 0.065 ± 0.018 (decimal db). These data were fitted to mathematical models frequently used to represent the drying of vegetal products. The Logarithmic model presented the best fit to describe the phenomenon. The effective diffusion coefficient increased as temperature increased, being described by the Arrhenius equation, with an activation energy of 37.64 kJ mol^-1. Enthalpy and entropy decreased, while Gibbs free energy increased as drying temperature increased.

KEYWORDS
mathematical modeling; liquid diffusivity; logarithmic

Model designation	Model
${RX =1+a t+b t}^{2}$	Wang and Sing	(3)
$RX=a \cdot exp(-k \cdot t)+ (1 - a) \exp (- k_{1} \cdot t)$	Verma	(4)
$RX=exp ((- a- {(a^{2} + 4 \cdot b \cdot t \cdot)}^{0, 5}) \frac{}{2 \cdot b})$	Thompson	(5)
$RX=exp (- k \cdot t^{n})$	Page	(6)
$RX=exp (- k \cdot t)$	Newton	(7)
$RX=a \cdot \exp (- k \cdot t^{n}) + b \cdot t$	Midilli	(8)
$RX=a \cdot \exp (- k \cdot t) + c$	Logarithmic	(9)
$RX=a \cdot \exp (- k \cdot t)$	Henderson and Pabis	(10)
$RX=a \cdot \exp (- k \cdot t) + (1 - a) \exp (- k \cdot a \cdot t)$	Exponential of two terms	(11)
$RX=a \cdot \exp (- k_{o} \cdot t) + b \cdot \exp (- k_{1} \cdot t)$	Two terms	(12)
$RX=a \cdot \exp (- k \cdot t) + (1 - a) \cdot \exp (- k \cdot b \cdot t)$	Diffusion approximation	(13)

Model	40 °C		60 °C		80 °C		100 °C
Model	χ²	SE	χ²	SE	χ²	SE	χ²	SE
Wang and Sing	46.4	0.068	145.4	0.121	19.4	0.044	18.3	0.043
Verma	20.0	0.045	19.0	0.044	4.0	0.020	4.3	0.021
Thompson	8.9	0.030	3.2	0.018	5.8	0.024	6.5	0.025
Page	8.7	0.029	8.4	0.029	7.7	0.028	6.6	0.026
Newton	18.5	0.043	17.4	0.042	7.4	0.027	6.4	0.025
Midilli	8.7	0.030	2.0	0.014	1.4	0.012	1.7	0.013
Logarithmic	10.7	0.033	1.9	0.014	1.5	0.012	1.8	0.013
Henderson and Pabis	15.7	0.040	16.8	0.041	7.1	0.027	5.3	0.023
Exponential of two terms	9.1	0.030	7.6	0.027	5.7	0.024	6.4	0.025
Two terms	9.2	0.030	0.1	0.003	1.6	0.013	1.9	0.014
Diffusion approximation	8.9	0.030	0.3	0.005	4.0	0.020	4.3	0.021

Model	40 °C		60 °C		80 °C		100 °C
Model	P	R²	P	R²	P	R²	P	R²
Wang and Sing	20.466	96.53	49.06	90.33	12.29	97.94	8.90	98.15
Verma	14.200	98.56	24.81	98.79	2.90	99.60	2.44	99.60
Thompson	4.090	99.34	9.93	99.78	5.24	99.39	6.43	99.35
Page	6.829	99.35	15.78	99.44	7.27	99.18	7.84	99.33
Newton	14.200	98.56	24.81	98.79	7.89	99.16	7.39	99.31
Midilli	3.918	99.40	6.23	99.88	2.58	99.87	2.25	99.86
Logarithmic	3.737	99.23	7.49	99.88	1.58	99.85	1.53	99.83
Henderson and Pabis	13.170	98.82	23.96	98.88	8.10	99.25	7.43	99.46
Exponential of two terms	9.308	99.32	17.15	99.50	5.39	99.39	6.35	99.36
Two terms	8.054	99.37	0.86	99.99	1.83	99.85	1.54	99.84
Diffusion approximation	7.951	99.36	0.79	99.98	2.89	99.60	2.44	99.60

Parameter	Temperature (°C)
Parameter	40	60	80	100
	Thompson
a	−6.72844^ Significant at 1% by the t-test;	−4.75078^ Significant at 1% by the t-test;	−9.08335^* * Significant at 5% by the t-test.	−13.6793^ns ns Non-significant by the t-test.
b	0.37770^ Significant at 1% by the t-test;	0.51890^ Significant at 1% by the t-test;	1.01066^ Significant at 1% by the t-test;	1.5261^* * Significant at 5% by the t-test.
	Midilli
a	1.007300^ Significant at 1% by the t-test;	1.024445^ Significant at 1% by the t-test;	1.020260^ Significant at 1% by the t-test;	1.022305^ Significant at 1% by the t-test;
k	0.030846^ Significant at 1% by the t-test;	0.071452^ Significant at 1% by the t-test;	0.109998^ Significant at 1% by the t-test;	0.171084^ Significant at 1% by the t-test;
n	0.833390^ Significant at 1% by the t-test;	0.844882^ Significant at 1% by the t-test;	1.045745^ Significant at 1% by the t-test;	1.038561^ Significant at 1% by the t-test;
b	0.000103^ns ns Non-significant by the t-test.	0.000421^ Significant at 1% by the t-test;	0.003104^ Significant at 1% by the t-test;	0.003414^ Significant at 1% by the t-test;
	Logarithmic
a	0.911724^ Significant at 1% by the t-test;	0.917230^ Significant at 1% by the t-test;	0.944254^ Significant at 1% by the t-test;	0.962794^ Significant at 1% by the t-test;
k	0.017255^ Significant at 1% by the t-test;	0.051663^ Significant at 1% by the t-test;	0.130410^ Significant at 1% by the t-test;	0.197454^ Significant at 1% by the t-test;
c	0.070180^ Significant at 1% by the t-test;	0.082451^ Significant at 1% by the t-test;	0.086418^ Significant at 1% by the t-test;	0.070809^ Significant at 1% by the t-test;
	Two terms
a	0.820626^ Significant at 1% by the t-test;	0.796116^ Significant at 1% by the t-test;	0.061104^ns ns Non-significant by the t-test.	0.037974^ns ns Non-significant by the t-test.
k₀	0.011334^ Significant at 1% by the t-test;	0.063355^ Significant at 1% by the t-test;	-0.011338^ns ns Non-significant by the t-test.	-0.027937^ns ns Non-significant by the t-test.
b	0.186481^ Significant at 1% by the t-test;	0.211949^ Significant at 1% by the t-test;	0.968744^ Significant at 1% by the t-test;	0.993755^ Significant at 1% by the t-test;
k₁	0.092732^* * Significant at 5% by the t-test.	0.008508^ Significant at 1% by the t-test;	0.126721^ Significant at 1% by the t-test;	0.189091^ Significant at 1% by the t-test;
	Diffusion approximation
a	0.188057^* * Significant at 5% by the t-test.	0.805022^ Significant at 1% by the t-test;	0.987270^ Significant at 1% by the t-test;	0.99904^ Significant at 1% by the t-test;
k	0.081676^* * Significant at 5% by the t-test.	0.060455^ Significant at 1% by the t-test;	0.110474^ Significant at 1% by the t-test;	0.16608^ Significant at 1% by the t-test;
b	0.137565^ Significant at 1% by the t-test;	0.129341^ Significant at 1% by the t-test;	-0.518596^ns ns Non-significant by the t-test.	-1.09801^ns ns Non-significant by the t-test.

Temperature (°C)	Thermodynamic properties
Temperature (°C)	H	S	G
40	35031.45	-175.93	90122.65
60	34865.17	-176.44	93646.37
80	34698.89	-176.93	97180.08
100	34532.61	-177.38	100723.21
Equation	H = 35364.01 -8.31T	S = -174.97 - 0.024T	G= 83050.7 + 176.7T
R² (%)	99.99	99.93	99.99

Associação Brasileira de Engenharia Agrícola SBEA - Associação Brasileira de Engenharia Agrícola, Departamento de Engenharia e Ciências Exatas FCAV/UNESP, Prof. Paulo Donato Castellane, km 5, 14884.900 | Jaboticabal - SP, Tel./Fax: +55 16 3209 7619 - Jaboticabal - SP - Brazil
E-mail: revistasbea@sbea.org.br

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[1] *Corresponding author. Instituto Federal de Educação, Ciência e Tecnologia Goiano - Campus Rio Verde/Rio Verde - GO, Brasil. E-mail: osvaldo.resende@ifgoiano.edu.br

Parameter	Temperature (°C)
Parameter	40	60	80	100
	Thompson
a	−6.72844^ Significant at 1% by the t-test;	−4.75078^ Significant at 1% by the t-test;	−9.08335^* * Significant at 5% by the t-test.	−13.6793^ns ns Non-significant by the t-test.
b	0.37770^ Significant at 1% by the t-test;	0.51890^ Significant at 1% by the t-test;	1.01066^ Significant at 1% by the t-test;	1.5261^* * Significant at 5% by the t-test.
	Midilli
a	1.007300^ Significant at 1% by the t-test;	1.024445^ Significant at 1% by the t-test;	1.020260^ Significant at 1% by the t-test;	1.022305^ Significant at 1% by the t-test;
k	0.030846^ Significant at 1% by the t-test;	0.071452^ Significant at 1% by the t-test;	0.109998^ Significant at 1% by the t-test;	0.171084^ Significant at 1% by the t-test;
n	0.833390^ Significant at 1% by the t-test;	0.844882^ Significant at 1% by the t-test;	1.045745^ Significant at 1% by the t-test;	1.038561^ Significant at 1% by the t-test;
b	0.000103^ns ns Non-significant by the t-test.	0.000421^ Significant at 1% by the t-test;	0.003104^ Significant at 1% by the t-test;	0.003414^ Significant at 1% by the t-test;
	Logarithmic
a	0.911724^ Significant at 1% by the t-test;	0.917230^ Significant at 1% by the t-test;	0.944254^ Significant at 1% by the t-test;	0.962794^ Significant at 1% by the t-test;
k	0.017255^ Significant at 1% by the t-test;	0.051663^ Significant at 1% by the t-test;	0.130410^ Significant at 1% by the t-test;	0.197454^ Significant at 1% by the t-test;
c	0.070180^ Significant at 1% by the t-test;	0.082451^ Significant at 1% by the t-test;	0.086418^ Significant at 1% by the t-test;	0.070809^ Significant at 1% by the t-test;
	Two terms
a	0.820626^ Significant at 1% by the t-test;	0.796116^ Significant at 1% by the t-test;	0.061104^ns ns Non-significant by the t-test.	0.037974^ns ns Non-significant by the t-test.
k₀	0.011334^ Significant at 1% by the t-test;	0.063355^ Significant at 1% by the t-test;	-0.011338^ns ns Non-significant by the t-test.	-0.027937^ns ns Non-significant by the t-test.
b	0.186481^ Significant at 1% by the t-test;	0.211949^ Significant at 1% by the t-test;	0.968744^ Significant at 1% by the t-test;	0.993755^ Significant at 1% by the t-test;
k₁	0.092732^* * Significant at 5% by the t-test.	0.008508^ Significant at 1% by the t-test;	0.126721^ Significant at 1% by the t-test;	0.189091^ Significant at 1% by the t-test;
	Diffusion approximation
a	0.188057^* * Significant at 5% by the t-test.	0.805022^ Significant at 1% by the t-test;	0.987270^ Significant at 1% by the t-test;	0.99904^ Significant at 1% by the t-test;
k	0.081676^* * Significant at 5% by the t-test.	0.060455^ Significant at 1% by the t-test;	0.110474^ Significant at 1% by the t-test;	0.16608^ Significant at 1% by the t-test;
b	0.137565^ Significant at 1% by the t-test;	0.129341^ Significant at 1% by the t-test;	-0.518596^ns ns Non-significant by the t-test.	-1.09801^ns ns Non-significant by the t-test.