Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm
A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot...
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MDPI AG
2020-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/2/260 |
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| author | Radosław Winiczenko Krzysztof Górnicki Agnieszka Kaleta |
| author_facet | Radosław Winiczenko Krzysztof Górnicki Agnieszka Kaleta |
| author_sort | Radosław Winiczenko |
| collection | DOAJ |
| description | A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot number by applying nondominated sorting genetic algorithm (NSGA) II genetic algorithms. The method is used in drying. The maximization of coefficient of correlation (R) and simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) between the model and experimental data were taken into account. The Biot number and moisture diffusion coefficient can be determined using the following equations: <i>Bi</i> = 0.7647141 + 10.1689977<i>s</i> − 0.003400086<i>T</i> + 948.715758<i>s</i><sup>2</sup> + 0.000024316<i>T</i><sup>2</sup> − 0.12478256<i>sT</i>, <i>D</i> = 1.27547936∙10<sup>−7</sup> − 2.3808∙10<sup>−5</sup>s − 5.08365633∙10<sup>−9</sup><i>T</i> + 0.0030005179<i>s</i><sup>2</sup> + 4.266495∙10<sup>−11</sup><i>T</i><sup>2</sup> + 8.33633∙10<sup>−7</sup><i>sT</i> or <i>Bi</i> = 0.764714 + 10.1689091<i>s</i> − 0.003400089<i>T</i> + 948.715738<i>s</i><sup>2</sup> + 0.000024316<i>T</i><sup>2</sup> − 0.12478252<i>sT</i>, <i>D</i> = 1.27547948∙10<sup>−7</sup> − 2.3806∙10<sup>−5</sup><i>s</i> − 5.08365753∙10<sup>−9</sup><i>T</i> + 0.0030005175<i>s</i><sup>2</sup> + 4.266493∙10<sup>−11</sup><i>T</i><sup>2</sup> + 8.336334∙10<sup>−7</sup><i>sT</i>. The results of statistical analysis for the Biot number and moisture diffusion coefficient equations were as follows: R = 0.9905672, MAE = 0.0406375, RMSE = 0.050252 and R = 0.9905611, MAE = 0.0406403 and RMSE = 0.050273, respectively. |
| first_indexed | 2024-04-12T19:57:33Z |
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| spelling | doaj.art-50509dbe76b84df2a2a3577361c4eafd2022-12-22T03:18:37ZengMDPI AGSymmetry2073-89942020-02-0112226010.3390/sym12020260sym12020260Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic AlgorithmRadosław Winiczenko0Krzysztof Górnicki1Agnieszka Kaleta2Institute of Mechanical Engineering, Warsaw University of Life Sciences, Nowoursynowska 164 St., 02-787 Warsaw, PolandInstitute of Mechanical Engineering, Warsaw University of Life Sciences, Nowoursynowska 164 St., 02-787 Warsaw, PolandInstitute of Mechanical Engineering, Warsaw University of Life Sciences, Nowoursynowska 164 St., 02-787 Warsaw, PolandA precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot number by applying nondominated sorting genetic algorithm (NSGA) II genetic algorithms. The method is used in drying. The maximization of coefficient of correlation (R) and simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) between the model and experimental data were taken into account. The Biot number and moisture diffusion coefficient can be determined using the following equations: <i>Bi</i> = 0.7647141 + 10.1689977<i>s</i> − 0.003400086<i>T</i> + 948.715758<i>s</i><sup>2</sup> + 0.000024316<i>T</i><sup>2</sup> − 0.12478256<i>sT</i>, <i>D</i> = 1.27547936∙10<sup>−7</sup> − 2.3808∙10<sup>−5</sup>s − 5.08365633∙10<sup>−9</sup><i>T</i> + 0.0030005179<i>s</i><sup>2</sup> + 4.266495∙10<sup>−11</sup><i>T</i><sup>2</sup> + 8.33633∙10<sup>−7</sup><i>sT</i> or <i>Bi</i> = 0.764714 + 10.1689091<i>s</i> − 0.003400089<i>T</i> + 948.715738<i>s</i><sup>2</sup> + 0.000024316<i>T</i><sup>2</sup> − 0.12478252<i>sT</i>, <i>D</i> = 1.27547948∙10<sup>−7</sup> − 2.3806∙10<sup>−5</sup><i>s</i> − 5.08365753∙10<sup>−9</sup><i>T</i> + 0.0030005175<i>s</i><sup>2</sup> + 4.266493∙10<sup>−11</sup><i>T</i><sup>2</sup> + 8.336334∙10<sup>−7</sup><i>sT</i>. The results of statistical analysis for the Biot number and moisture diffusion coefficient equations were as follows: R = 0.9905672, MAE = 0.0406375, RMSE = 0.050252 and R = 0.9905611, MAE = 0.0406403 and RMSE = 0.050273, respectively.https://www.mdpi.com/2073-8994/12/2/260mass biot numberdiffusion coefficientmulti-objective genetic algorithm |
| spellingShingle | Radosław Winiczenko Krzysztof Górnicki Agnieszka Kaleta Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm Symmetry mass biot number diffusion coefficient multi-objective genetic algorithm |
| title | Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm |
| title_full | Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm |
| title_fullStr | Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm |
| title_full_unstemmed | Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm |
| title_short | Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm |
| title_sort | evaluation of the mass diffusion coefficient and mass biot number using a nondominated sorting genetic algorithm |
| topic | mass biot number diffusion coefficient multi-objective genetic algorithm |
| url | https://www.mdpi.com/2073-8994/12/2/260 |
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