MATHEMATICAL MODELING FOR DETERMINATION OF THE MAXIMUM MASS TRANSFER CAPACITY OF COWPEA BEANS

Franco Junior, Hélio C.; Morais, Romulo A.; Silva, Warley G. da; Oliveira, Maria O. S.; Martins, Glêndara A. de S.

doi:10.1590/1809-4430-Eng.Agric.v40n2p201-206/2020

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Scientific Paper, Post-Harvest Science and Technology • Eng. agríc. (Online) 40 (2) • Mar-Apr 2020 • https://doi.org/10.1590/1809-4430-Eng.Agric.v40n2p201-206/2020 copy

MATHEMATICAL MODELING FOR DETERMINATION OF THE MAXIMUM MASS TRANSFER CAPACITY OF COWPEA BEANS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Cowpea beans are of great socioeconomic expression for the rural population in North and Northeastern Brazil. This legume is rich in essential nutrients and exhibits great resistance to water stress. However, for grain processing, it is fundamental to study legume behavior during the hydration process. This study aims to evaluate the mass transfer of different cowpea beans via mathematical modeling to determine the viability of hydration for commercialization as a canned product. Physical and chemical analyses of lipids and moisture were performed. The soaking process was performed in a water bath with distilled water at 30, 40, and 50 °C. The mathematical model of Peleg presented satisfactory adjustments, with R² values ranging between 99.78% and 99.99% and relative error (P) of <3.74%. In addition, the influence of binomial time/temperature was observed during hydration.

KEYWORDS
Leguminous; Peleg model; hydration; beans

Causes of Variation	Mean square of variables
Causes of Variation	GL	Lipids	Moisture
Treatments	13	0.00059^* * Significance at the 5% level determined by the F test.	0.71258^* * Significance at the 5% level determined by the F test.
Residue	28	0.0003^* * Significance at the 5% level determined by the F test.	0.03646^* * Significance at the 5% level determined by the F test.
Total Adjusted	41	-	-
CV (%)		8.44	2.50
Overall Average		0.06517	7.62294

	BRS Milênio	BRS Itaim	BRS Potengi	BRS Pujante	BRS Novaera	BRS Cauamé	BRS Aracê	BRS Tum.	BRS Juruá	BRS Roux.	BRS Mar.	BRS Xiq	BRS Pajeú	BRS Guariba
Moisture	14.94a ± 0.21	12.87c ± 0.22	12.60d ± 0.09	13.90b ± 0.48	11.84e ± 0.04	12.6d ± 0.34	12.58d ± 0.30	12.17e ± 0.19	14.48a ± 0.41	13.09c ± 0.00	13.14c ± 0.20	14.01b ± 0.54	13.17c ± 0.12	13.24c ± 0.12
Lipids	2.29a ± 0.22	2.47a ± 0.17	1.88b ± 0.09	1.86b ± 0.05	1.83b ± 0.19	2.44a ± 0.33	1.92b ± 0.26	1.52c ± 0.56	2.19a ± 0.34	1.27d ± 0.12	1.55c ± 0.12	1.22d ± 0.37	1.94b ± 0.46	1.52c ± 0.17

Treatment	Temperature (°C)	C1	C2	R² (%)	SE (decimal)	P (%)
BRS PUJANTE	30	0.6228^ Significant at the 1% probability level by Scott-Knott.	0.8672^ Significant at the 1% probability level by Scott-Knott.	99.977	0.0097	0.61
	40	0.3182^ Significant at the 1% probability level by Scott-Knott.	0.8907^ Significant at the 1% probability level by Scott-Knott.	99.947	0.0153	0.89
	50	0.2225^ Significant at the 1% probability level by Scott-Knott.	0.8684^ Significant at the 1% probability level by Scott-Knott.	99.979	0.0102	0.55
BRS POTENGI	30	0.7727^ Significant at the 1% probability level by Scott-Knott.	1.2822^ Significant at the 1% probability level by Scott-Knott.	99.982	0.0054	0.37
	40	0.4409^ Significant at the 1% probability level by Scott-Knott.	1.3430^ Significant at the 1% probability level by Scott-Knott.	99.977	0.0076	0.57
	50	0.0639^ Significant at the 1% probability level by Scott-Knott.	1.3361^ Significant at the 1% probability level by Scott-Knott.	99.954	0.0098	0.78
BRS JURUÁ	30	0.1494^ Significant at the 1% probability level by Scott-Knott.	0.8964^ Significant at the 1% probability level by Scott-Knott.	99.968	0.0113	0.56
	40	0.1678^ Significant at the 1% probability level by Scott-Knott.	1.0279^ Significant at the 1% probability level by Scott-Knott.	99.783	0.0204	1.26
	50	0.1234^ Significant at the 1% probability level by Scott-Knott.	1.0544^ Significant at the 1% probability level by Scott-Knott.	99.945	0.0150	0.85
BRS ROUXINOL	30	2.5361^ Significant at the 1% probability level by Scott-Knott.	0.9549^ Significant at the 1% probability level by Scott-Knott.	99.898	0.0138	1.27
	40	3.3518^ Significant at the 1% probability level by Scott-Knott.	0.8372^ Significant at the 1% probability level by Scott-Knott.	99.811	0.0133	1.20
	50	0.5060^ Significant at the 1% probability level by Scott-Knott.	0.9707^ Significant at the 1% probability level by Scott-Knott.	99.924	0.0150	1.01
BRS PAJEÚ	30	2.1799^ Significant at the 1% probability level by Scott-Knott.	0.9479^ Significant at the 1% probability level by Scott-Knott.	99.974	0.0072	0.62
	40	1.0227^ Significant at the 1% probability level by Scott-Knott.	0.9038^ Significant at the 1% probability level by Scott-Knott.	99.998	0.0016	0.10
	50	0.2622^ Significant at the 1% probability level by Scott-Knott.	0.9735^ Significant at the 1% probability level by Scott-Knott.	99.983	0.0080	0.50
BRS MARATOÃ	30	2.2241^ Significant at the 1% probability level by Scott-Knott.	0.6461^ Significant at the 1% probability level by Scott-Knott.	99.947	0.0143	0.89
	40	0.5475^ Significant at the 1% probability level by Scott-Knott.	0.9463^ Significant at the 1% probability level by Scott-Knott.	99.930	0.0104	0.68
	50	0.1003^ Significant at the 1% probability level by Scott-Knott.	1.0219^ Significant at the 1% probability level by Scott-Knott.	99.977	0.0093	0.57
BRS GUARIBA	30	0.4753^ Significant at the 1% probability level by Scott-Knott.	1.1142^ Significant at the 1% probability level by Scott-Knott.	99.862	0.0127	0.96
	40	0.1591^ Significant at the 1% probability level by Scott-Knott.	1.2059^ Significant at the 1% probability level by Scott-Knott.	99.978	0.0049	0.36
	50	0.0374^ Significant at the 1% probability level by Scott-Knott.	1.2730^ Significant at the 1% probability level by Scott-Knott.	99.990	0.0008	0.05
BRS TUMUCUMAQUE	30	0.3064^ Significant at the 1% probability level by Scott-Knott.	1.0749^ Significant at the 1% probability level by Scott-Knott.	99.970	0.0089	0.59
	40	0.0792^ Significant at the 1% probability level by Scott-Knott.	1.0985^ Significant at the 1% probability level by Scott-Knott.	99.989	0.0218	1.58
	50	0.0696^ Significant at the 1% probability level by Scott-Knott.	1.2244^ Significant at the 1% probability level by Scott-Knott.	99.999	0.0010	0.06
BRS XIQUEXIQUE	30	0.2619^ Significant at the 1% probability level by Scott-Knott.	1.0999^ Significant at the 1% probability level by Scott-Knott.	99.930	0.0134	0.86
	40	0.0987^ Significant at the 1% probability level by Scott-Knott.	1.1399^ Significant at the 1% probability level by Scott-Knott.	99.986	0.0047	0.32
	50	0.0899^ Significant at the 1% probability level by Scott-Knott.	1.2924^ Significant at the 1% probability level by Scott-Knott.	99.991	0.0029	0.21
BRS ITAIM	30	0.4397^ Significant at the 1% probability level by Scott-Knott.	1.2979^ Significant at the 1% probability level by Scott-Knott.	99.997	0.0024	0.17
	40	0.2141^ Significant at the 1% probability level by Scott-Knott.	1.3341^ Significant at the 1% probability level by Scott-Knott.	99.976	0.0072	0.54
	50	0.1756^ Significant at the 1% probability level by Scott-Knott.	1.3315^ Significant at the 1% probability level by Scott-Knott.	99.999	0.0018	0.12
BRS NOVAERA	30	0.7698^ Significant at the 1% probability level by Scott-Knott.	1.2929^ Significant at the 1% probability level by Scott-Knott.	99.994	0.0035	0.26
	40	0.7303^ Significant at the 1% probability level by Scott-Knott.	1.4455^ Significant at the 1% probability level by Scott-Knott.	99.990	0.0039	0.28
	50	0.3780^ Significant at the 1% probability level by Scott-Knott.	1.1061^ Significant at the 1% probability level by Scott-Knott.	99.943	0.0129	0.91
BRS MILENIO	30	0.6613^ Significant at the 1% probability level by Scott-Knott.	1.1806^ Significant at the 1% probability level by Scott-Knott.	99.991	0.0043	0.29
	40	0.1161^ Significant at the 1% probability level by Scott-Knott.	1.3690^ Significant at the 1% probability level by Scott-Knott.	99.939	0.0114	0.86
	50	0.0559^ Significant at the 1% probability level by Scott-Knott.	1.4080^ Significant at the 1% probability level by Scott-Knott.	99.972	0.0077	0.51
BRS CAUAMÉ	30	0.3169^ Significant at the 1% probability level by Scott-Knott.	1.0680^ Significant at the 1% probability level by Scott-Knott.	99.986	0.0061	0.42
	40	0.1732^ Significant at the 1% probability level by Scott-Knott.	1.1189^ Significant at the 1% probability level by Scott-Knott.	99.963	0.0107	0.64
	50	0.2424^ Significant at the 1% probability level by Scott-Knott.	1.0902^ Significant at the 1% probability level by Scott-Knott.	99.994	0.0049	0.29
BRS ARACÊ	30	0.3841^ Significant at the 1% probability level by Scott-Knott.	1.2546^ Significant at the 1% probability level by Scott-Knott.	99.906	0.0147	1.00
	40	0.4811^ Significant at the 1% probability level by Scott-Knott.	1.6304^ Significant at the 1% probability level by Scott-Knott.	98.829	0.0424	3.74
	50	0.0670^ Significant at the 1% probability level by Scott-Knott.	1.2682^ Significant at the 1% probability level by Scott-Knott.	99.981	0.0078	0.49

Variety	Temperature (°C)			Variety	Temperature (°C)
Variety	30	40	50	Variety	30	40	50
BRS PUJANT^e	5,9695^b	5,9550 ^b	6,1649^a	BRS TUMUCUMAQU^e	5,0515^e	5,2505^d	4,7984^f
BRS POTENGI	4,2825^g	3,5350^h	4,3595^g	BRS XIQUEXIQU^e	5,0185^e	5,0555^e	4,7207^f
BRS JURUÁ	6,2960^a	5,8470^b	5,5678^c	BRS ITAIM	4,2320^g	4,3530^g	4,4226^g
BRS ROUXINOL	4,5550^f	4,7080^f	5,4399^c	BRS NOVAER^a	4,1290^g	4,3690^g	4,8756^e
BRS MARATAOÃ	5,7010^c	5,6185^c	5,4631^c	BRS MILENIO	4,7420^f	4,2015^g	4,3585^g
BRS PAJEÚ	4,7895^f	5,5930^c	5,6198^c	BRS CAUAMÉ	5,1405^d	4,6300^f	5,0540^e
BRS GUARIB^a	4,8955^e	4,7350^f	4,4704^g	BRS ARACÊ	4,4015^g	4,1875^g	4,5685^f

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[1] *Corresponding author. Federal University of Tocantins/ Palmas - TO, Brazil. E-mail: romuloitallo2505@gmail.com