Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks
In this study, two empirical correlations of the Nusselt number, based on two artificial neural networks (ANN), were developed to determine the heat transfer coefficients for each section of a vertical helical double-pipe evaporator with water as the working fluid. Each ANN was obtained using an exp...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/21/7/689 |
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| author | Arianna Parrales José Alfredo Hernández-Pérez Oliver Flores Horacio Hernandez José Francisco Gómez-Aguilar Ricardo Escobar-Jiménez Armando Huicochea |
| author_facet | Arianna Parrales José Alfredo Hernández-Pérez Oliver Flores Horacio Hernandez José Francisco Gómez-Aguilar Ricardo Escobar-Jiménez Armando Huicochea |
| author_sort | Arianna Parrales |
| collection | DOAJ |
| description | In this study, two empirical correlations of the Nusselt number, based on two artificial neural networks (ANN), were developed to determine the heat transfer coefficients for each section of a vertical helical double-pipe evaporator with water as the working fluid. Each ANN was obtained using an experimental database of 1109 values obtained from an evaporator coupled to an absorption heat transformer with energy recycling. The Nusselt number in the annular section was estimated based on the modified Wilson plot method solved by an ANN. This model included the Reynolds and Prandtl numbers as input variables and three neurons in their hidden layer. The Nusselt number in the inner section was estimated based on the Rohsenow equation, solved by an ANN. This ANN model included the numbers of the Prandtl and Jackob liquids as input variables and one neuron in their hidden layer. The coefficients of determination were <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>></mo> <mn>0.99</mn> </mrow> </semantics> </math> </inline-formula> for both models. Both ANN models satisfied the dimensionless condition of the Nusselt number. The Levenberg–Marquardt algorithm was chosen to determine the optimum values of the weights and biases. The transfer functions used for the learning process were the hyperbolic tangent sigmoid in the hidden layer and the linear function in the output layer. The Nusselt numbers, determined by the ANNs, proved adequate to predict the values of the heat transfer coefficients of a vertical helical double-pipe evaporator that considered biphasic flow with an accuracy of ±0.2 for the annular Nusselt and ±4 for the inner Nusselt. |
| first_indexed | 2024-04-11T22:07:48Z |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:07:48Z |
| publishDate | 2019-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3b3656b84bd541f990827b61601d50912022-12-22T04:00:38ZengMDPI AGEntropy1099-43002019-07-0121768910.3390/e21070689e21070689Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural NetworksArianna Parrales0José Alfredo Hernández-Pérez1Oliver Flores2Horacio Hernandez3José Francisco Gómez-Aguilar4Ricardo Escobar-Jiménez5Armando Huicochea6CONACyT—Centro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos, Cuernavaca C.P. 62209, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos, Cuernavaca C.P. 62209, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos, Cuernavaca C.P. 62209, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos, Cuernavaca C.P. 62209, MexicoCONACyT—Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. Cuernavaca 62490, MexicoTecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. Cuernavaca 62490, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas (CIICAp), Universidad Autónoma del Estado de Morelos, Cuernavaca C.P. 62209, MexicoIn this study, two empirical correlations of the Nusselt number, based on two artificial neural networks (ANN), were developed to determine the heat transfer coefficients for each section of a vertical helical double-pipe evaporator with water as the working fluid. Each ANN was obtained using an experimental database of 1109 values obtained from an evaporator coupled to an absorption heat transformer with energy recycling. The Nusselt number in the annular section was estimated based on the modified Wilson plot method solved by an ANN. This model included the Reynolds and Prandtl numbers as input variables and three neurons in their hidden layer. The Nusselt number in the inner section was estimated based on the Rohsenow equation, solved by an ANN. This ANN model included the numbers of the Prandtl and Jackob liquids as input variables and one neuron in their hidden layer. The coefficients of determination were <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>></mo> <mn>0.99</mn> </mrow> </semantics> </math> </inline-formula> for both models. Both ANN models satisfied the dimensionless condition of the Nusselt number. The Levenberg–Marquardt algorithm was chosen to determine the optimum values of the weights and biases. The transfer functions used for the learning process were the hyperbolic tangent sigmoid in the hidden layer and the linear function in the output layer. The Nusselt numbers, determined by the ANNs, proved adequate to predict the values of the heat transfer coefficients of a vertical helical double-pipe evaporator that considered biphasic flow with an accuracy of ±0.2 for the annular Nusselt and ±4 for the inner Nusselt.https://www.mdpi.com/1099-4300/21/7/689heat transfer coefficientsartificial neural networkNusselt numberhelical heat exchangers |
| spellingShingle | Arianna Parrales José Alfredo Hernández-Pérez Oliver Flores Horacio Hernandez José Francisco Gómez-Aguilar Ricardo Escobar-Jiménez Armando Huicochea Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks Entropy heat transfer coefficients artificial neural network Nusselt number helical heat exchangers |
| title | Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks |
| title_full | Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks |
| title_fullStr | Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks |
| title_full_unstemmed | Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks |
| title_short | Heat Transfer Coefficients Analysis in a Helical Double-Pipe Evaporator: Nusselt Number Correlations through Artificial Neural Networks |
| title_sort | heat transfer coefficients analysis in a helical double pipe evaporator nusselt number correlations through artificial neural networks |
| topic | heat transfer coefficients artificial neural network Nusselt number helical heat exchangers |
| url | https://www.mdpi.com/1099-4300/21/7/689 |
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