Mathematical modeling for drying flint corn in a thin layer

Costa, Leonardo Alves da; Souza, José Leôncio Fonseca de; Huebner, Rudolf; Rodrigues Filho, Fernando Antônio; Ferreira, André Guimarães; Azalim Júnior, Fernando

doi:10.1590/S1678-3921.pab2022.v57.02845

Leonardo Alves da Costa Corresponding author

Universidade Federal de Minas Gerais, Escola de Engenharia, Departamento de Engenharia Mecânica, Programa de Pós-Graduação em Engenharia Mecânica, Avenida Antônio Carlos, nº 6.627, Pampulha, CEP 31270-901 Belo Horizonte, MG, Brazil. Email: leonardoalves.costa@yahoo.com.br, rudolf@demec.ufmg.br

http://orcid.org/0000-0002-1257-2677

José Leôncio Fonseca de Souza

Centro Federal de Educação Tecnológica de Minas Gerais, Departamento de Engenharia Mecânica, Campus 2, Avenida Amazonas, nº 7.675, Nova Gameleira, CEP 30510-000 Belo Horizonte, MG, Brazil. Email: jleonciofs@gmail.com, 77frodrigues@gmail.com, agferreira@cefetmg.br, fernandoazalim.junior@gmail.com

http://orcid.org/0000-0003-2319-0540

Rudolf Huebner

Universidade Federal de Minas Gerais, Escola de Engenharia, Departamento de Engenharia Mecânica, Programa de Pós-Graduação em Engenharia Mecânica, Avenida Antônio Carlos, nº 6.627, Pampulha, CEP 31270-901 Belo Horizonte, MG, Brazil. Email: leonardoalves.costa@yahoo.com.br, rudolf@demec.ufmg.br

http://orcid.org/0000-0003-2613-304X

Fernando Antônio Rodrigues Filho

Centro Federal de Educação Tecnológica de Minas Gerais, Departamento de Engenharia Mecânica, Campus 2, Avenida Amazonas, nº 7.675, Nova Gameleira, CEP 30510-000 Belo Horizonte, MG, Brazil. Email: jleonciofs@gmail.com, 77frodrigues@gmail.com, agferreira@cefetmg.br, fernandoazalim.junior@gmail.com

http://orcid.org/0000-0003-1786-4158

André Guimarães Ferreira

Centro Federal de Educação Tecnológica de Minas Gerais, Departamento de Engenharia Mecânica, Campus 2, Avenida Amazonas, nº 7.675, Nova Gameleira, CEP 30510-000 Belo Horizonte, MG, Brazil. Email: jleonciofs@gmail.com, 77frodrigues@gmail.com, agferreira@cefetmg.br, fernandoazalim.junior@gmail.com

http://orcid.org/0000-0002-0694-5369

Fernando Azalim Júnior

Centro Federal de Educação Tecnológica de Minas Gerais, Departamento de Engenharia Mecânica, Campus 2, Avenida Amazonas, nº 7.675, Nova Gameleira, CEP 30510-000 Belo Horizonte, MG, Brazil. Email: jleonciofs@gmail.com, 77frodrigues@gmail.com, agferreira@cefetmg.br, fernandoazalim.junior@gmail.com

http://orcid.org/0000-0002-2860-1743

Corresponding author

Test	Drying temperature (°C)	Drying air velocity (m s^-1)	Wet mass corn (g)	Corn layer height (cm)	Initial moisture content (% db)	Time of drying (min)
Test 01	40	0.5	250	3	22	150
Test 02	50
Test 03	60
Test 04	40	1.0	250	3	22	150
Test 05	50
Test 06	60
Test 07	40	1.5	250	3	22	150
Test 08	50
Test 09	60

Model	Model equation	Reference
Lewis	MR = exp(−kt)	Khanchi & Birrell (2017)KHANCHI, A.; BIRRELL, S. Drying models to estimate moisture change in switchgrass and corn stover based on weather conditions and swath density. Agricultural and Forest Meteorology, v.237/238, p.1-8, 2017. DOI: https://doi.org/10.1016/j.agrformet.2017.01.019. https://doi.org/10.1016/j.agrformet.2017...
Page	MR = exp(−ktⁿ)	Sun et al. (2016)SUN, L.-X.; LIU, S.-X.; WANG, J.-X.; WU, C.-L.; LI, Y.; ZHANG, C.-Q. The effects of grain texture and phenotypic traits on the thin-layer drying rate in maize (Zea mays L.) inbred lines. Journal of Integrative Agriculture, v.15, p.317-325, 2016. DOI: https://doi.org/10.1016/S2095-3119(15)61052-8. https://doi.org/10.1016/S2095-3119(15)61...
Thompson	$M R = \exp (\frac{- a - {(a^{2} + 4 b t)}^{0.5}}{2 b})$	Kucuk et al. (2014)KUCUK, H.; MIDILLI, A.; KILIC, A.; DINCER, I. A review on thin-layer drying-curve equations. Drying Technology, v.32, p.757-773, 2014. DOI: https://doi.org/10.1080/07373937.2013.873047. https://doi.org/10.1080/07373937.2013.87...
Overhults	MR = exp((−kt)ⁿ)	Souza et al. (2015)SOUZA, G.F.M.V.; MIRANDA, R.F.; LOBATO, F.S.; BARROZO, M.A.S. Simultaneous heat and mass transfer in a fixed bed dryer. Applied Thermal Engineering, v.90, p.38-44, 2015. DOI: https://doi.org/10.1016/j.applthermaleng.2015.06.088. https://doi.org/10.1016/j.applthermaleng...
Brooker	MR = c exp(−kt)	Doymaz (2017)DOYMAZ, İ. Drying kinetics, rehydration and colour characteristics of convective hot-air drying of carrot slices. Heat and Mass Transfer, v.53, p.25-35, 2017. DOI: https://doi.org/10.1007/s00231-016-1791-8. https://doi.org/10.1007/s00231-016-1791-...
Midilli	MR = c exp(−ktⁿ) + dt	Doymaz (2017)DOYMAZ, İ. Drying kinetics, rehydration and colour characteristics of convective hot-air drying of carrot slices. Heat and Mass Transfer, v.53, p.25-35, 2017. DOI: https://doi.org/10.1007/s00231-016-1791-8. https://doi.org/10.1007/s00231-016-1791-...

Model	Air Temp. (°C)	R²			SE			P			χ² (× 10^-3)
Model	Air Temp. (°C)	0.5 m s^-1	1.0 m s^-1	1.5 m s^-1	0.5 m s^-1	1.0 m s^-1	1.5 m s^-1	0.5 m s^-1	1.0 m s^-1	1.5 m s^-1	0.5 m s^-1	1.0 m s^-1	1.5 m s^-1
Lewis	40	0.942	0.951	0.951	0.048	0.045	0.045	5.3	5.0	5.0	2.293	2.054	2.055
	50	0.957	0.944	0.942	0.053	0.055	0.055	6.7	6.6	6.6	2.783	2.972	3.044
	60	0.946	0.945	0.932	0.058	0.061	0.066	7.5	7.9	8.5	3.407	3.675	4.324
Brooker	40	0.935	0.944	0.944	0.028	0.027	0.027	2.5	2.4	2.4	0.804	0.747	0.748
	50	0.949	0.935	0.933	0.033	0.034	0.034	3.5	3.3	3.2	1.117	1.137	1.128
	60	0.937	0.934	0.920	0.037	0.038	0.041	3.9	4.1	4.2	1.379	1.462	1.680
Thompson	40	0.998	0.996	0.996	0.006	0.010	0.010	0.7	1.1	1.1	0.038	0.099	0.099
	50	0.993	0.997	0.998	0.017	0.010	0.008	1.9	1.0	0.9	0.275	0.091	0.059
	60	0.997	0.997	0.999	0.012	0.011	0.005	1.3	1.2	0.6	0.146	0.114	0.028
Page	40	1.000	1.000	1.000	0.002	0.002	0.002	0.2	0.2	0.2	0.003	0.005	0.005
	50	1.000	1.000	1.000	0.002	0.003	0.002	0.3	0.3	0.2	0.005	0.010	0.003
	60	1.000	1.000	1.000	0.003	0.002	0.002	0.3	0.2	0.3	0.007	0.004	0.004
Midilli	40	1.000	1.000	1.000	0.002	0.002	0.002	0.2	0.2	0.2	0.003	0.006	0.006
	50	1.000	1.000	1.000	0.002	0.003	0.002	0.3	0.3	0.2	0.005	0.010	0.003
	60	1.000	1.000	1.000	0.002	0.002	0.002	0.2	0.1	0.2	0.003	0.002	0.004
Overhults	40	1.000	1.000	1.000	0.002	0.002	0.002	0.2	0.2	0.2	0.003	0.005	0.005
	50	1.000	1.000	1.000	0.002	0.003	0.002	0.3	0.3	0.2	0.005	0.010	0.003
	60	1.000	1.000	1.000	0.003	0.002	0.002	0.3	0.2	0.3	0.007	0.004	0.004

R^{2} = \frac{{[\sum_{i = 1}^{N} (M R_{\exp, i} - {\bar{M R}}_{\exp}) (M R_{p r e, i} - {\bar{M R}}_{p r e})]}^{2}}{\sum_{i = 1}^{N} {(M R_{\exp, i} - {\bar{M R}}_{\exp})}^{2} \sum_{i = 1}^{N} {(M R_{p r e, i} - {\bar{M R}}_{p r e})}^{2}}

[1] Corresponding author

Brasil

Brasil

Mathematical modeling for drying flint corn in a thin layer

Modelagem matemática para secagem de milho “flint” em camada delgada

Abstract