On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning
It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. The present article contains an artificial neural network remedy...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-03-01
|
| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125000063 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841528013180633088 |
|---|---|
| author | Khalil Ur Rehman Wasfi Shatanawi Lok Yian Yian |
| author_facet | Khalil Ur Rehman Wasfi Shatanawi Lok Yian Yian |
| author_sort | Khalil Ur Rehman |
| collection | DOAJ |
| description | It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. The present article contains an artificial neural network remedy to tackle nonlinear differential equations for heat transfer in an enclosure. In detail, we considered Casson fluid equipped in a semi-heated square cavity in the presence of both magnetic field and natural convection. The upper wall of the cavity is taken adiabatic and the lower wall is heated uniformly. The both right and left walls are considered cold. The flow is formulated in terms of coupled non-linear differential equations and solved for two different thermal flow fields namely baffle with heated tip and baffle with cold tip. An artificial intelligence-based neural model is developed to approximate the Nusselt number along the fin for both heated and cold tips of the T-shaped baffle. The low mean square error (MSE) values and perfect Regression values demonstrate the exceptional performance of the neural model being trained using the Levenberg-Marquardt algorithm. We found that the Nusselt number rises significantly with increasing Rayleigh numbers, especially in the vicinity of the heated baffle. This suggests increased buoyancy effects leading to improved convective heat transfer. |
| format | Article |
| id | doaj-art-a88ea69d27cf4d49a896e8461d982c15 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-a88ea69d27cf4d49a896e8461d982c152025-01-15T04:11:58ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101078On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learningKhalil Ur Rehman0Wasfi Shatanawi1Lok Yian Yian2Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Mathematics Section, School of Distance Education, Universiti Sains Malaysia 11800, USM Penang, Malaysia; Corresponding author.Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics, Faculty of Science, The Hashemite University, P.O Box 330127, Zarqa 13133, JordanMathematics Section, School of Distance Education, Universiti Sains Malaysia 11800, USM Penang, MalaysiaIt is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. The present article contains an artificial neural network remedy to tackle nonlinear differential equations for heat transfer in an enclosure. In detail, we considered Casson fluid equipped in a semi-heated square cavity in the presence of both magnetic field and natural convection. The upper wall of the cavity is taken adiabatic and the lower wall is heated uniformly. The both right and left walls are considered cold. The flow is formulated in terms of coupled non-linear differential equations and solved for two different thermal flow fields namely baffle with heated tip and baffle with cold tip. An artificial intelligence-based neural model is developed to approximate the Nusselt number along the fin for both heated and cold tips of the T-shaped baffle. The low mean square error (MSE) values and perfect Regression values demonstrate the exceptional performance of the neural model being trained using the Levenberg-Marquardt algorithm. We found that the Nusselt number rises significantly with increasing Rayleigh numbers, especially in the vicinity of the heated baffle. This suggests increased buoyancy effects leading to improved convective heat transfer.http://www.sciencedirect.com/science/article/pii/S2666818125000063Nonlinear PDEsHeat transferSquare enclosureNatural convectionArtificial neural networking |
| spellingShingle | Khalil Ur Rehman Wasfi Shatanawi Lok Yian Yian On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning Partial Differential Equations in Applied Mathematics Nonlinear PDEs Heat transfer Square enclosure Natural convection Artificial neural networking |
| title | On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning |
| title_full | On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning |
| title_fullStr | On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning |
| title_full_unstemmed | On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning |
| title_short | On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning |
| title_sort | on nonlinear coupled differential system for heat transfer in magnetized enclosure with t shaped baffle by using machine learning |
| topic | Nonlinear PDEs Heat transfer Square enclosure Natural convection Artificial neural networking |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125000063 |
| work_keys_str_mv | AT khalilurrehman onnonlinearcoupleddifferentialsystemforheattransferinmagnetizedenclosurewithtshapedbafflebyusingmachinelearning AT wasfishatanawi onnonlinearcoupleddifferentialsystemforheattransferinmagnetizedenclosurewithtshapedbafflebyusingmachinelearning AT lokyianyian onnonlinearcoupleddifferentialsystemforheattransferinmagnetizedenclosurewithtshapedbafflebyusingmachinelearning |