Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata)
Although several studies have been carried out on mathematical modeling of the spaghetti drying kinetics, they have not been developed for spaghetti with an incorporation of Triticum durumwheat semolina by dehydrated squash pulp (DSP). Therefore, the objective of this investigation was to model the...
- Autores:
-
López Mejía, Natali
Andrade Mahecha, Margarita María
Martínez Correa, Hugo Alexander
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Universidad de Ciencias Aplicadas y Ambientales U.D.C.A
- Repositorio:
- Repositorio Institucional UDCA
- Idioma:
- spa
- OAI Identifier:
- oai:repository.udca.edu.co:11158/2031
- Acceso en línea:
- https://revistas.udca.edu.co/index.php/ruadc/article/view/1151
https://doi.org/10.31910/rudca.v22.n1.2019.1151
- Palabra clave:
- Modelos matemáticos
Transferencia de masa
Difusividad
Sustitución
Cucurbita
Triticum durum
Cucurbita moschata
Triticum durum
Secado
- Rights
- openAccess
- License
- Derechos Reservados - Universidad de Ciencias Aplicadas y Ambientales
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Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| dc.title.alternative.spa.fl_str_mv |
Mathematical modeling of spaghetti drying kinetics enriched with dehydrated squash pulp (Cucurbita moschata) |
| title |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| spellingShingle |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) Modelos matemáticos Transferencia de masa Difusividad Sustitución Cucurbita Triticum durum Cucurbita moschata Triticum durum Secado |
| title_short |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| title_full |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| title_fullStr |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| title_full_unstemmed |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| title_sort |
Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata) |
| dc.creator.fl_str_mv |
López Mejía, Natali Andrade Mahecha, Margarita María Martínez Correa, Hugo Alexander |
| dc.contributor.author.spa.fl_str_mv |
López Mejía, Natali Andrade Mahecha, Margarita María Martínez Correa, Hugo Alexander |
| dc.subject.proposal.spa.fl_str_mv |
Modelos matemáticos Transferencia de masa Difusividad Sustitución Cucurbita Triticum durum |
| topic |
Modelos matemáticos Transferencia de masa Difusividad Sustitución Cucurbita Triticum durum Cucurbita moschata Triticum durum Secado |
| dc.subject.agrovoc.spa.fl_str_mv |
Cucurbita moschata Triticum durum Secado |
| description |
Although several studies have been carried out on mathematical modeling of the spaghetti drying kinetics, they have not been developed for spaghetti with an incorporation of Triticum durumwheat semolina by dehydrated squash pulp (DSP). Therefore, the objective of this investigation was to model the kinetics of spaghetti drying partially substituted with DSP (5 and 10g/100g flour), to evaluate the effect of substitution and temperature (50 and 60°C), on the time of drying (final moisture content = 0.13g/g d.b.), the effective diffusivity (De) and some characteristics that define the quality of the product (moisture content, cooking quality and total carotenoid content). For this, mathematical models reported in the literature were used, as well as the second law of Fick for an infinite cylinder. The results showed that the Henderson & Pabis and the Logarithmic models presented greater adjustment (R2 ≥ 0.90) to the experimental drying kinetics. On the contrary, the Lewis model presented the smallest adjustment. Drying times of 5.00-4.10h were obtained for the kinetics carried out at 50°C and drying times of 3.40-2.80h (approximately) for the kinetics at 60°C. It varied from 1.50 to 2.50 x 10-7cm2s-1, which increased with temperature. Finally, the spaghetti quality was negatively affected with the increase in PZD and positively with the increase in the drying temperature. |
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2019 |
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2019-08-26T22:17:27Z |
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2019-08-26T22:17:27Z |
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2019-01 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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http://purl.org/coar/resource_type/c_6501 |
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info:eu-repo/semantics/article |
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Text |
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https://revistas.udca.edu.co/index.php/ruadc/article/view/1151 |
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https://doi.org/10.31910/rudca.v22.n1.2019.1151 |
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307567 |
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https://revistas.udca.edu.co/index.php/ruadc/article/view/1151 https://doi.org/10.31910/rudca.v22.n1.2019.1151 |
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spa |
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Revista UDCA : Actualidad & Divulgación Científica (Bogotá). -- Vol. 22, No. 1 (Ene.-Jun. 2019). -- páginas 61-71 |
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Agricultura |
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Derechos Reservados - Universidad de Ciencias Aplicadas y Ambientales |
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Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0) |
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Bogotá : Universidad de Ciencias Aplicadas y Ambientales, 2019 |
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López Mejía, NataliAndrade Mahecha, Margarita MaríaMartínez Correa, Hugo Alexander2019-08-26T22:17:27Z2019-08-26T22:17:27Z2019-010123-4226https://revistas.udca.edu.co/index.php/ruadc/article/view/1151https://doi.org/10.31910/rudca.v22.n1.2019.1151307567Although several studies have been carried out on mathematical modeling of the spaghetti drying kinetics, they have not been developed for spaghetti with an incorporation of Triticum durumwheat semolina by dehydrated squash pulp (DSP). Therefore, the objective of this investigation was to model the kinetics of spaghetti drying partially substituted with DSP (5 and 10g/100g flour), to evaluate the effect of substitution and temperature (50 and 60°C), on the time of drying (final moisture content = 0.13g/g d.b.), the effective diffusivity (De) and some characteristics that define the quality of the product (moisture content, cooking quality and total carotenoid content). For this, mathematical models reported in the literature were used, as well as the second law of Fick for an infinite cylinder. The results showed that the Henderson & Pabis and the Logarithmic models presented greater adjustment (R2 ≥ 0.90) to the experimental drying kinetics. On the contrary, the Lewis model presented the smallest adjustment. Drying times of 5.00-4.10h were obtained for the kinetics carried out at 50°C and drying times of 3.40-2.80h (approximately) for the kinetics at 60°C. It varied from 1.50 to 2.50 x 10-7cm2s-1, which increased with temperature. Finally, the spaghetti quality was negatively affected with the increase in PZD and positively with the increase in the drying temperature.A pesar que diversos estudios se han llevado a cabo sobre modelamiento matemático de las cinéticas de secado de espagueti, no se han desarrollado para espaguetis con sustitución de sémola de trigo Triticum durum por pulpa de zapallo deshidratada (PZD), por lo tanto, el objetivo de esta investigación fue modelar las cinéticas de secado de espagueti sustituido parcialmente con PZD (5 y 10g/100g harina), evaluar el efecto de la sustitución y la temperatura (50 y 60°C), sobre el tiempo de secado (contenido de humedad final = 0,13g/g b.s.), la difusividad efectiva (De) y algunas características que definen la calidad del producto (contenido de humedad, calidad de cocción y contenido de carotenoides totales). Para ello, se emplearon modelos matemáticos reportados en la literatura, como también la segunda ley de Fick, para un cilindro infinito. Los resultados mostraron que los modelos Henderson & Pabis y el Logarítmico presentaron mayor ajuste (R2 ≥ 0,90) a las cinéticas de secado experimentales; por el contrario, el modelo de Lewis presentó el menor ajuste. Se obtuvieron tiempos de secado de 5,00-4,10h, para las cinéticas realizadas a 50°C y tiempos de secado de 3,40-2,80h (aproximadamente), para las cinéticas a 60°C. De varió desde 1,50 hasta 2,50 x 10-7 cm2s-1, la cual, aumentó con la temperatura. En definitiva, la calidad del espagueti se afectó negativamente con el aumento de PZD y positivamente con el aumento de la temperatura de secado.Incluye referencias bibliográficasapplication/pdfspaBogotá : Universidad de Ciencias Aplicadas y Ambientales, 2019Revista UDCA : Actualidad & Divulgación Científica (Bogotá). -- Vol. 22, No. 1 (Ene.-Jun. 2019). -- páginas 61-71AgriculturaDerechos Reservados - Universidad de Ciencias Aplicadas y Ambientaleshttps://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)http://purl.org/coar/access_right/c_abf2Modelamiento matemático de la cinética de secado de espagueti enriquecido con pulpa de zapallo deshidratada (Cucurbita moschata)Mathematical modeling of spaghetti drying kinetics enriched with dehydrated squash pulp (Cucurbita moschata)Artículo de 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 nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.
d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:
i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.
ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.
e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, Acinpro), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.
5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.
6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.
7. Término.
a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.
b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.
8. Varios.
a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.
b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.
c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.
d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.

 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