Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution
Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824014108 |
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| author | Ghani Khan Muhammad Safdar Safia Taj Adnan Munir Muhammad Tauseef Nasir |
| author_facet | Ghani Khan Muhammad Safdar Safia Taj Adnan Munir Muhammad Tauseef Nasir |
| author_sort | Ghani Khan |
| collection | DOAJ |
| description | Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. Invariants for these Lie symmetries are obtained to construct a new class of similarity transformations. With the deduced similarity transformations, the flow equations are converted to ordinary differential equations which are solved using the Homotopy analysis method. The deduced analytic solution enables an exploration of the effects of various parameters on the flow and heat transfer, which have not been revealed previously using the Lie method as per the authors’ knowledge. The influences of the stretching rate, parameters that maintain the non-uniformity and unsteadiness of sheet temperature, and the Prandtl number, are demonstrated with the help of graphs and tables. These results show that for certain values of the system parameters, heat transfer reverses its direction and occurs from the fluid to the sheet. At these values, maximum heat transfer does not occur at the sheet but rather slightly above it. |
| format | Article |
| id | doaj-art-a302d02a087d443eb9ae5f240cfab815 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-a302d02a087d443eb9ae5f240cfab8152025-01-29T05:00:16ZengElsevierAlexandria Engineering Journal1110-01682025-01-01112424435Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distributionGhani Khan0Muhammad Safdar1Safia Taj2Adnan Munir3Muhammad Tauseef Nasir4School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, PakistanSchool of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, PakistanCollege of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), Islamabad 44000, PakistanSchool of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan; School of Engineering, Design and Built Environment, Western Sydney University, Locked Bay 1797, Penrith, NSW 2751, AustraliaSchool of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan; Corresponding author.Various mathematical frameworks have been developed to study dynamics of the fluid flow in stretching films. In this work, a three–dimensional flow induced by an unsteady stretching of an infinite flat sheet is analyzed through the Lie symmetry approach. Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. Invariants for these Lie symmetries are obtained to construct a new class of similarity transformations. With the deduced similarity transformations, the flow equations are converted to ordinary differential equations which are solved using the Homotopy analysis method. The deduced analytic solution enables an exploration of the effects of various parameters on the flow and heat transfer, which have not been revealed previously using the Lie method as per the authors’ knowledge. The influences of the stretching rate, parameters that maintain the non-uniformity and unsteadiness of sheet temperature, and the Prandtl number, are demonstrated with the help of graphs and tables. These results show that for certain values of the system parameters, heat transfer reverses its direction and occurs from the fluid to the sheet. At these values, maximum heat transfer does not occur at the sheet but rather slightly above it.http://www.sciencedirect.com/science/article/pii/S1110016824014108Thin filmsThree-dimensional flowLie transformationsInvariantsSimilarity transformationsHomotopy analysis method |
| spellingShingle | Ghani Khan Muhammad Safdar Safia Taj Adnan Munir Muhammad Tauseef Nasir Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution Alexandria Engineering Journal Thin films Three-dimensional flow Lie transformations Invariants Similarity transformations Homotopy analysis method |
| title | Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution |
| title_full | Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution |
| title_fullStr | Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution |
| title_full_unstemmed | Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution |
| title_short | Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution |
| title_sort | lie symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non uniform temperature distribution |
| topic | Thin films Three-dimensional flow Lie transformations Invariants Similarity transformations Homotopy analysis method |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824014108 |
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