Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity
Abstract Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$ U w = λ x / t . The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical techniqu...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-03-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-30886-4 |
| _version_ | 1797865057787314176 |
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| author | G. P. Vanitha K. C. Shobha B. Patil Mallikarjun U. S. Mahabaleshwar Gabriella Bognár |
| author_facet | G. P. Vanitha K. C. Shobha B. Patil Mallikarjun U. S. Mahabaleshwar Gabriella Bognár |
| author_sort | G. P. Vanitha |
| collection | DOAJ |
| description | Abstract Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$ U w = λ x / t . The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical technique. The problem is analysed for both two-dimensional film flow and axisymmetric film flow. The exact solution is derived which satisfies the governing equation. It is noted that solution exists only for a specified scale of the moving surface parameter $$\lambda$$ λ . ie., $$\lambda \ge -1/2$$ λ ≥ - 1 / 2 for two-dimensional flow and $$\lambda \le -1/4$$ λ ≤ - 1 / 4 for axisymmetric flow. The velocity increases first and reaches the maximum velocity and then decreases to the boundary condition. Streamlines are also analysed for both axisymmetric and two-dimensional flow patterns by considering the stretching ( $$\lambda >0$$ λ > 0 ) and shrinking wall conditions ( $$\lambda <0$$ λ < 0 ). Study has been made for large values of wall moving parameter $$\lambda$$ λ . The aim of this investigation is to analyse the Casson nanoliquid film flow which finds applications in industries like coating of sheet or wire, laboratories, painting, many more. |
| first_indexed | 2024-04-09T23:01:53Z |
| format | Article |
| id | doaj.art-849cabb66f1a4dc49be6f5cd3964bfed |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-09T23:01:53Z |
| publishDate | 2023-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-849cabb66f1a4dc49be6f5cd3964bfed2023-03-22T10:55:06ZengNature PortfolioScientific Reports2045-23222023-03-0113111310.1038/s41598-023-30886-4Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocityG. P. Vanitha0K. C. Shobha1B. Patil Mallikarjun2U. S. Mahabaleshwar3Gabriella Bognár4Department of Mathematics, Siddaganga Institution of TechnologyDepartment of Studies and Research in Mathematics, Tumkur UniversityDepartment of Studies and Research in Mathematics, Tumkur UniversityDepartment of Mathematics, Davanagere UniversityInstitute of Machine and Product Design, University of MiskolcAbstract Present study explains about unsteady Casson nanoliquid film flow over a surface moving with velocity $$U_w=\lambda x/t$$ U w = λ x / t . The governing momentum equation is reduced to ODE by using corresponding similarity transformation, which is then tackled by employing numerical technique. The problem is analysed for both two-dimensional film flow and axisymmetric film flow. The exact solution is derived which satisfies the governing equation. It is noted that solution exists only for a specified scale of the moving surface parameter $$\lambda$$ λ . ie., $$\lambda \ge -1/2$$ λ ≥ - 1 / 2 for two-dimensional flow and $$\lambda \le -1/4$$ λ ≤ - 1 / 4 for axisymmetric flow. The velocity increases first and reaches the maximum velocity and then decreases to the boundary condition. Streamlines are also analysed for both axisymmetric and two-dimensional flow patterns by considering the stretching ( $$\lambda >0$$ λ > 0 ) and shrinking wall conditions ( $$\lambda <0$$ λ < 0 ). Study has been made for large values of wall moving parameter $$\lambda$$ λ . The aim of this investigation is to analyse the Casson nanoliquid film flow which finds applications in industries like coating of sheet or wire, laboratories, painting, many more.https://doi.org/10.1038/s41598-023-30886-4 |
| spellingShingle | G. P. Vanitha K. C. Shobha B. Patil Mallikarjun U. S. Mahabaleshwar Gabriella Bognár Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity Scientific Reports |
| title | Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity |
| title_full | Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity |
| title_fullStr | Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity |
| title_full_unstemmed | Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity |
| title_short | Casson nanoliquid film flow over an unsteady moving surface with time-varying stretching velocity |
| title_sort | casson nanoliquid film flow over an unsteady moving surface with time varying stretching velocity |
| url | https://doi.org/10.1038/s41598-023-30886-4 |
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