The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer
Heat transfer problems are of critical importance in almost all areas of engineering and technology, especially in mechanical engineering. Over several decades, engineers and scientists have been working on solving these problems by designing and optimizing components and systems needed to transfer,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-02-01
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| Series: | International Journal of Thermofluids |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666202721000045 |
| _version_ | 1818928210848514048 |
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| author | S. Kumbinarasaiah K.R. Raghunatha |
| author_facet | S. Kumbinarasaiah K.R. Raghunatha |
| author_sort | S. Kumbinarasaiah |
| collection | DOAJ |
| description | Heat transfer problems are of critical importance in almost all areas of engineering and technology, especially in mechanical engineering. Over several decades, engineers and scientists have been working on solving these problems by designing and optimizing components and systems needed to transfer, handle, and store thermal energy. Heat can be transmitted via different mechanisms, like conduction and convection. In this article, two nonlinear heat transfer problems are solved by allowing for the changeable specific heat coefficient. The mathematical calculations are permitted out via a Hermite wavelet method (HWM). By using HWM, the nonlinear unnatural governing equations are abridged to an interconnected system of algebraic equations. The current outcomes are compared with the Homotopy perturbation method (HPM), variational iteration method (VIM), differential transformation method (DTM), and the accurate solutions to confirm the exactness of the future method. The HWM method is helpful and practical for solving the nonlinear heat diffusion equations linked through variable thermal conductivity conditions. Moreover, the equation outcomes in boundary points, and scheming the inaccuracy differences with the accurate amount, the advantages and disadvantages of this technique are considered. The results reveal that the HWM can attain more appropriate consequences in predicting the solution of such problems. |
| first_indexed | 2024-12-20T03:25:18Z |
| format | Article |
| id | doaj.art-2e9314e7d4374682b8003372b776f783 |
| institution | Directory Open Access Journal |
| issn | 2666-2027 |
| language | English |
| last_indexed | 2024-12-20T03:25:18Z |
| publishDate | 2021-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | International Journal of Thermofluids |
| spelling | doaj.art-2e9314e7d4374682b8003372b776f7832022-12-21T19:55:07ZengElsevierInternational Journal of Thermofluids2666-20272021-02-019100066The applications of Hermite wavelet method to nonlinear differential equations arising in heat transferS. Kumbinarasaiah0K.R. Raghunatha1Department of Mathematics, Bangalore University, Bengaluru, 560056, IndiaDepartment of Mathematics, Davangere University, Davangere, 577002, India; Corresponding author.Heat transfer problems are of critical importance in almost all areas of engineering and technology, especially in mechanical engineering. Over several decades, engineers and scientists have been working on solving these problems by designing and optimizing components and systems needed to transfer, handle, and store thermal energy. Heat can be transmitted via different mechanisms, like conduction and convection. In this article, two nonlinear heat transfer problems are solved by allowing for the changeable specific heat coefficient. The mathematical calculations are permitted out via a Hermite wavelet method (HWM). By using HWM, the nonlinear unnatural governing equations are abridged to an interconnected system of algebraic equations. The current outcomes are compared with the Homotopy perturbation method (HPM), variational iteration method (VIM), differential transformation method (DTM), and the accurate solutions to confirm the exactness of the future method. The HWM method is helpful and practical for solving the nonlinear heat diffusion equations linked through variable thermal conductivity conditions. Moreover, the equation outcomes in boundary points, and scheming the inaccuracy differences with the accurate amount, the advantages and disadvantages of this technique are considered. The results reveal that the HWM can attain more appropriate consequences in predicting the solution of such problems.http://www.sciencedirect.com/science/article/pii/S2666202721000045Operational matrix of integrationHermite waveletsCollocation methodHeat transfer problems: nonlinear differential equations |
| spellingShingle | S. Kumbinarasaiah K.R. Raghunatha The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer International Journal of Thermofluids Operational matrix of integration Hermite wavelets Collocation method Heat transfer problems: nonlinear differential equations |
| title | The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer |
| title_full | The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer |
| title_fullStr | The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer |
| title_full_unstemmed | The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer |
| title_short | The applications of Hermite wavelet method to nonlinear differential equations arising in heat transfer |
| title_sort | applications of hermite wavelet method to nonlinear differential equations arising in heat transfer |
| topic | Operational matrix of integration Hermite wavelets Collocation method Heat transfer problems: nonlinear differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S2666202721000045 |
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