An empiric equation for the latent heat of vaporization of moisture in bananas during its isothermal drying
Author(s)
Wilton Pereira da Silva*,
Cleide Maria Diniz Pereira da Silva e Silva,
Fernando José de Almeida Gama,
Josivanda Palmeira Gomes
ABSTRACT
In order to determine the energy needed to artificially dry a product, the latent heat of vaporization of moisture in the product, hfg, must be known. Generally, the expressions for hfg reported in the literature are of the form hfg = h(T)f(M), where h(T) is the latent heat of vaporization of free water, and f(M) is a function of the equilibrium moisture content, M. But expressions of this type contain a simplification because, in this case, the ratio hfg/h would only depend to the moisture content. In this article a more general expression for the latent heat of vaporization, namely hfg = g(M,T), is used to determine hfg for banana. To this end, a computer program was developed which fits automatically about 500 functions, with one or two independent variables, imbedded in its library to experimental data. The program uses nonlinear regression, and classifies the best functions according to the least reduced chi-square. A set of executed statistical tests shows that the generalized expression used in this work given by hfg = g(M,T) produces better results of hfg for bananas than other equations found in the literature.
In order to determine the energy needed to artificially dry a product, the latent heat of vaporization of moisture in the product, hfg, must be known. Generally, the expressions for hfg reported in the literature are of the form hfg = h(T)f(M), where h(T) is the latent heat of vaporization of free water, and f(M) is a function of the equilibrium moisture content, M. But expressions of this type contain a simplification because, in this case, the ratio hfg/h would only depend to the moisture content. In this article a more general expression for the latent heat of vaporization, namely hfg = g(M,T), is used to determine hfg for banana. To this end, a computer program was developed which fits automatically about 500 functions, with one or two independent variables, imbedded in its library to experimental data. The program uses nonlinear regression, and classifies the best functions according to the least reduced chi-square. A set of executed statistical tests shows that the generalized expression used in this work given by hfg = g(M,T) produces better results of hfg for bananas than other equations found in the literature.
Cite this paper
Silva, W. , Silva e Silva, C. , Gama, F. and Gomes, J. (2012) An empiric equation for the latent heat of vaporization of moisture in bananas during its isothermal drying. Agricultural Sciences, 3, 214-220. doi: 10.4236/as.2012.32025.
Silva, W. , Silva e Silva, C. , Gama, F. and Gomes, J. (2012) An empiric equation for the latent heat of vaporization of moisture in bananas during its isothermal drying. Agricultural Sciences, 3, 214-220. doi: 10.4236/as.2012.32025.
References
[1] Liu, J.Y. and Cheng, S. (1991) Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies. International Journal of Heat and Mass Transfer, 34, 1747-1754. doi:10.1016/0017-9310(91)90150-D [2] Kiranoudis, C.T., Maroulis, Z.B. and Marinos-Kouris, D. (1995) Heat and mass transfer model building in drying with multiresponse data. International Journal of Heat and Mass Transfer, 38, 463-480. doi:10.1016/0017-9310(94)00166-S [3] Wang, N., Brennan and J.G. (1995) A mathematical model of simultaneous heat and moisture transfer during drying of potato. Journal of Food Engineering, 24, 47-60. doi:10.1016/0260-8774(94)P1607-Y [4] Wang, Z.H. and Chen, G. (2000) Heat and mass transfer in batch fluidized-bed drying of porous particles. Chemical Engineering Science, 55, 1857-1869. doi:10.1016/S0009-2509(99)00446-7 [5] Chemkhi, S., Zagrouba, F. and Bellagi, A. (2005) Modelling and simulation of drying phenomena with rheological behaviour. Brazilian Journal of Chemical Engineering, 22, 153-163. doi:10.1590/S0104-66322005000200001 [6] Sfredo, M.A., Finzer, J.R.D. and Limaverde, J.R. (2005) Heat and mass transfer in coffee fruits drying. Journal of Food Engineering, 70, 15-25. doi:10.1016/j.jfoodeng.2004.09.008 [7] Nascimento, J.J.S., Lima, A.G.B., Teruel, Bárbara, J. and Belo, F.A. (2006) Transmisión de calor y materia con reducción de volumen durante el secado de ladrillos de cerámica. Información Tecnológica, 17, 125-132. doi:10.1016/j.jfoodeng.2005.09.010 [8] Trujillo, F.J., Wiangkaew, C. and Pham, Q.T. (2007) Drying modeling and water diffusivity in beef meat. Journal of Food Engineering, 78, 74-85. [9] Suvarnakuta, P., Devahastin, S. and Mujumdar, A. S. (2007) A mathematical model for low-pressure super-heated steam drying of a biomaterial. Chemical Engineering and Processing, 46, 675-683. doi:10.1016/j.cep.2006.09.002 [10] Mariani, V.C., Lima, A.G.B. and Coelho, L.S. (2008) Apparent thermal diffusivity estimation of the banana during drying using inverse method. Journal of Food Engineering, 85, 569-579. doi:10.1016/j.jfoodeng.2007.08.018 [11] Meeso, N., Nathakaranakule, A. and Madhiyanon, T., Soponronnarit, S. (2008) Different Strategies of Far-Infrared Radiation Application in Paddy Drying. International Journal of Food Engineering, 4, 1267. doi:10.1016/j.biosystemseng.2003.09.004 [12] Wu, B., Yang, W. and Jia, C. (2004) A three-dimensional numerical simulation of transient heat and mass transfer inside a single rice kernel during the drying process. Bio-systems Engineering, 87, 191-200. [13] Brook, R.C. and Foster, G.H. (1981) Drying, cleaning and conditioning. In: CRC Handbook of Transportation, Marketing and Agriculture, v.2, CRC Press, Boca Raton. [14] Brooker, D.B., Bakker-Arkema, F.W. and Hall, C.W. (1992) Drying and storage of grains and oilseeds. The AVI Publishing Company, Westport. [15] Mata, M.E.R.M.C., Dantas, L.A. and Braga, M.E.D. (1999) Programa computacional para simula?ao de secagem de graos. Revista Brasileira de Produtos Agroindustriais, Campina Grande, 1, 33-50. [16] Cavalcanti Mata, M.E.R.M. and Duarte, M.E.M. (2003) Drying simulation theory of the cowpea considering the grains shrinkage. Revista Brasileira de Produtos Agroin-dustriais, Campina Grande, 5, 179-185. [17] Al-Mahasneh, M.A., Rababah, T.M. and Yang, W. (2007) Moisture sorption thermodynamics of defatted sesame meal (DSM). Journal of Food Engineering, 81, 735-740. doi:10.1016/j.jfoodeng.2007.01.010 [18] Prado, M.M. and Sartori, D.J.M. (2008) Simultaneous heat and mass transfer in packed bed drying of seeds having a mucilage coating. Brazilian Journal of Chemical Engineering, 25, 39-50. doi:10.1590/S0104-66322008000100006 [19] Correa, P.C., Christ, D., Martins, J.H. and Mantovani, B.H.M. (1998) Curvas de dessorcao e calor latente de vaporizacao para as sementes de milho pipoca. Revista Brasileira de Engenharia Agrícola e Ambiental, 2, 75-79. [20] Kaleemullah, S. and Kailappan, R. (2005) Latent heat of vaporization of moisture from red chillies. International Journal of Food Properties, 8, 199-205. doi:10.1081/JFP-200060232 [21] Smith, J.M., Van Ness, H.C. and Abbot, M.B. (2004) Introduction to Chemical Engineering Thermodynamics. Mcgraw-Hill, New York. [22] Phoungchandang, S. and Woods, J.L. (2000) Moisture diffusion and desorption isotherms for banana. Food Engineering and Physical Properties, 65, 651-657. [23] Athié, I., Castro, M.F.P.M., Gomes, R.A.R. and Valentini, S.R.T. (1998) Conservacao de Graos. Fundacao Cargill, Campinas. [24] Shore, H., Brauner, N. and Shacham, M. (2002) Modeling Physical and thermodynamic properties via inverse normalizing transformation. Industrial & Engineering Chemistry Research, 41, 651-656. doi:10.1021/ie010039s [25] Bevington, P.R. and Robinson, D.K. (1992) Data Reduction and Error Analysis for the Physical Sciences. 2nd Edition, WCB/McGraw-Hill, Boston. [26] Taylor, J.R. (1997) An introduction to error analysis. 2nd Edition, University Science Books, Sausalito. [27] Silva, W.P., Precker, J.W., Silva, C.M.D.P.S., Silva, C.D. P.S., Silva, D.D.P.S. and Lima, A.G.B. (2007) Calculation of the uncertainty in the determination of the equilibrium moisture content of pumpkin seed flour. International Journal of Food Engineering, 3, 1098.
[1] Liu, J.Y. and Cheng, S. (1991) Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies. International Journal of Heat and Mass Transfer, 34, 1747-1754. doi:10.1016/0017-9310(91)90150-D [2] Kiranoudis, C.T., Maroulis, Z.B. and Marinos-Kouris, D. (1995) Heat and mass transfer model building in drying with multiresponse data. International Journal of Heat and Mass Transfer, 38, 463-480. doi:10.1016/0017-9310(94)00166-S [3] Wang, N., Brennan and J.G. (1995) A mathematical model of simultaneous heat and moisture transfer during drying of potato. Journal of Food Engineering, 24, 47-60. doi:10.1016/0260-8774(94)P1607-Y [4] Wang, Z.H. and Chen, G. (2000) Heat and mass transfer in batch fluidized-bed drying of porous particles. Chemical Engineering Science, 55, 1857-1869. doi:10.1016/S0009-2509(99)00446-7 [5] Chemkhi, S., Zagrouba, F. and Bellagi, A. (2005) Modelling and simulation of drying phenomena with rheological behaviour. Brazilian Journal of Chemical Engineering, 22, 153-163. doi:10.1590/S0104-66322005000200001 [6] Sfredo, M.A., Finzer, J.R.D. and Limaverde, J.R. (2005) Heat and mass transfer in coffee fruits drying. Journal of Food Engineering, 70, 15-25. doi:10.1016/j.jfoodeng.2004.09.008 [7] Nascimento, J.J.S., Lima, A.G.B., Teruel, Bárbara, J. and Belo, F.A. (2006) Transmisión de calor y materia con reducción de volumen durante el secado de ladrillos de cerámica. Información Tecnológica, 17, 125-132. doi:10.1016/j.jfoodeng.2005.09.010 [8] Trujillo, F.J., Wiangkaew, C. and Pham, Q.T. (2007) Drying modeling and water diffusivity in beef meat. Journal of Food Engineering, 78, 74-85. [9] Suvarnakuta, P., Devahastin, S. and Mujumdar, A. S. (2007) A mathematical model for low-pressure super-heated steam drying of a biomaterial. Chemical Engineering and Processing, 46, 675-683. doi:10.1016/j.cep.2006.09.002 [10] Mariani, V.C., Lima, A.G.B. and Coelho, L.S. (2008) Apparent thermal diffusivity estimation of the banana during drying using inverse method. Journal of Food Engineering, 85, 569-579. doi:10.1016/j.jfoodeng.2007.08.018 [11] Meeso, N., Nathakaranakule, A. and Madhiyanon, T., Soponronnarit, S. (2008) Different Strategies of Far-Infrared Radiation Application in Paddy Drying. International Journal of Food Engineering, 4, 1267. doi:10.1016/j.biosystemseng.2003.09.004 [12] Wu, B., Yang, W. and Jia, C. (2004) A three-dimensional numerical simulation of transient heat and mass transfer inside a single rice kernel during the drying process. Bio-systems Engineering, 87, 191-200. [13] Brook, R.C. and Foster, G.H. (1981) Drying, cleaning and conditioning. In: CRC Handbook of Transportation, Marketing and Agriculture, v.2, CRC Press, Boca Raton. [14] Brooker, D.B., Bakker-Arkema, F.W. and Hall, C.W. (1992) Drying and storage of grains and oilseeds. The AVI Publishing Company, Westport. [15] Mata, M.E.R.M.C., Dantas, L.A. and Braga, M.E.D. (1999) Programa computacional para simula?ao de secagem de graos. Revista Brasileira de Produtos Agroindustriais, Campina Grande, 1, 33-50. [16] Cavalcanti Mata, M.E.R.M. and Duarte, M.E.M. (2003) Drying simulation theory of the cowpea considering the grains shrinkage. Revista Brasileira de Produtos Agroin-dustriais, Campina Grande, 5, 179-185. [17] Al-Mahasneh, M.A., Rababah, T.M. and Yang, W. (2007) Moisture sorption thermodynamics of defatted sesame meal (DSM). Journal of Food Engineering, 81, 735-740. doi:10.1016/j.jfoodeng.2007.01.010 [18] Prado, M.M. and Sartori, D.J.M. (2008) Simultaneous heat and mass transfer in packed bed drying of seeds having a mucilage coating. Brazilian Journal of Chemical Engineering, 25, 39-50. doi:10.1590/S0104-66322008000100006 [19] Correa, P.C., Christ, D., Martins, J.H. and Mantovani, B.H.M. (1998) Curvas de dessorcao e calor latente de vaporizacao para as sementes de milho pipoca. Revista Brasileira de Engenharia Agrícola e Ambiental, 2, 75-79. [20] Kaleemullah, S. and Kailappan, R. (2005) Latent heat of vaporization of moisture from red chillies. International Journal of Food Properties, 8, 199-205. doi:10.1081/JFP-200060232 [21] Smith, J.M., Van Ness, H.C. and Abbot, M.B. (2004) Introduction to Chemical Engineering Thermodynamics. Mcgraw-Hill, New York. [22] Phoungchandang, S. and Woods, J.L. (2000) Moisture diffusion and desorption isotherms for banana. Food Engineering and Physical Properties, 65, 651-657. [23] Athié, I., Castro, M.F.P.M., Gomes, R.A.R. and Valentini, S.R.T. (1998) Conservacao de Graos. Fundacao Cargill, Campinas. [24] Shore, H., Brauner, N. and Shacham, M. (2002) Modeling Physical and thermodynamic properties via inverse normalizing transformation. Industrial & Engineering Chemistry Research, 41, 651-656. doi:10.1021/ie010039s [25] Bevington, P.R. and Robinson, D.K. (1992) Data Reduction and Error Analysis for the Physical Sciences. 2nd Edition, WCB/McGraw-Hill, Boston. [26] Taylor, J.R. (1997) An introduction to error analysis. 2nd Edition, University Science Books, Sausalito. [27] Silva, W.P., Precker, J.W., Silva, C.M.D.P.S., Silva, C.D. P.S., Silva, D.D.P.S. and Lima, A.G.B. (2007) Calculation of the uncertainty in the determination of the equilibrium moisture content of pumpkin seed flour. International Journal of Food Engineering, 3, 1098.