Empirical models in the description of prickly pear shoot (Nopal) drying kinetics

Pereira, Emmanuel M.; Silva, Wilton P. da; Gomes, Josivanda P.; Silva, Cleide M. D. P. da S. e; Formiga, Anderson dos S.; Costa, Franciscleudo B. da

doi:10.1590/1807-1929/agriambi.v21n11p798-802

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ARTICLE • Rev. bras. eng. agríc. ambient. 21 (11) • Nov 2017 • https://doi.org/10.1590/1807-1929/agriambi.v21n11p798-802 copy

Empirical models in the description of prickly pear shoot (Nopal) drying kinetics

Modelos empíricos na descrição da cinética de secagem do broto da palma (Nopal)

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The objective of this study was to describe the technological process involved in the drying kinetics of fresh-cut prickly pear shoots through numerical and analytical solutions. Shoots of two different prickly pear species were used, ‘Gigante’ and ‘Miúda’. Drying was performed at different temperatures (50, 60, 70 and 80 °C) and weighing procedures were made continuously. The experimental data were expressed as moisture ratio. The Page model showed the best fit to the drying kinetics of minimally processed ‘Gigante’ and ‘Miúda’ prickly pear shoots, with the best coefficients of determination and Chi-square. Peleg and Wang & Singh models can not be used to simulate the drying of ‘Gigante’ and ‘Miúda’ prickly pear shoots within the evaluated range of temperatures, showing an incoherent graphic pattern.

Key words:
mathematical modeling; Opuntia; Nopalea; minimal processing

Model	Name	Empirical expression
1	Lewis (1921)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = exp(-a t^{b})\sigma e^{-at} \] \end{document}	(2)
2	Henderson & Pabis (1961)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = a exp(-k t) \] \end{document}	(3)
3	Wang & Singh (1678)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = 1 + a \cdot t + b \cdot t^{2} \] \end{document}	(4)
4	Peleg (1993)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = 1 -t/(a + bt) \] \end{document}	(5)
5	Page (1949)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = exp(-k t^{n}) \] \end{document}	(6)
6	Silva et al. (2012)	\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} \[ RX = exp(-at - bt^{1/2}) \] \end{document}	(7)

Temperature (°C)	Parameters		R²	χ²
Temperature (°C)	a	b	R²	χ²
Henderson & Pabis
50	0.1013	0.5715	0.9947	0.2301
60	0.1023	0.8536	0.9950	0.1840
70	0.1017	0.1060	0.9929	0.2179
80	0.1030	0.1393	0.9954	0.1339
Lewis
50	0.5611	-	0.9952	0.2399
60	0.8270	-	0.9956	0.2082
70	0.1036	-	0.9937	0.2302
80	0.1339	-	0.9965	0.1649
Page
50	0.2809	0.1134	0.9968	0.1300
60	0.4234	0.1140	0.9970	0.1012
70	0.5324	0.1146	0.9957	0.1242
80	0.7053	0.1149	0.9976	0.6092
Peleg
50	0.1596	0.7304	0.9900	0.3603
60	0.1043	0.7558	0.9868	0.4338
70	0.8717	0.7197	0.9872	0.3350
80	0.6873	0.7072	0.9913	0.2144
Silva et al. (2012)
50	0.6317	-0.8575	0.9953	0.1937
60	0.9576	-0.1307	0.9958	0.1472
70	0.1189	-0.1384	0.9938	0.1804
80	0.1594	-0.2021	0.9965	0.1474
Wang & Singh
50	-0.3793	0.3347	0.9903	0.5590
60	-0.5289	0.6281	0.9807	0.8847
70	-0.6943	0.1110	0.9903	0.4263
80	-0.9112	0.1954	0.9901	0.3357

Temperature (°C)	Parameters		R²	χ²
Temperature (°C)	a	b	R²	χ²
Henderson & Pabis
50	0.1006	0.6119	0.9952	0.2041
60	0.1016	0.9549	0.9949	0.1787
70	0.1021	0.1073	0.9942	0.1805
80	0.1012	0.1683	0.9917	0.1926
Lewis
50	0.6061	-	0.9955	0.2067
60	0.9341	-	0.9953	0.1898
70	0.1042	-	0.9950	0.1993
80	0.1655	-	0.9920	0.1973
Page
50	0.3372	0.1116	0.9969	0.1263
60	0.5310	0.1121	0.9966	0.1118
70	0.5361	0.1146	0.9968	0.1280
80	0.1312	0.1056	0.9919	0.1814
Peleg
50	0.1435	0.7518	0.9890	0.3863
60	0.8895	0.7814	0.9846	0.4900
70	0.8628	0.7235	0.9881	0.3177
80	0.5058	0.7736	0.9865	0.3090
Silva et al. (2012)
50	0.6659	-0.7004	0.9956	0.1791
60	0.1051	-0.1114	0.9955	0.1525
70	0.1209	-0.1505	0.9951	0.1417
80	0.1787	-0.9455	0.9918	0.1865
Wang & Singh
50	-0.3953	0.3578	0.9858	0.8534
60	-0.5289	0.6281	0.9807	0.8847
70	-0.6957	0.1114	0.9888	0.4604
80	-0.1008	0.2308	0.9649	0.1237

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
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[1] josivanda@gmail.com (Corresponding author)