A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis
Thin film flow (TFF) problems received a lot of attention in recent times. Some frequent applications of TFF include polymer and metal extraction, elastic sheet drawing, food striating, heat exchanges, and device fluidization. Further improvement and enhancement of TFF need to be examined due to its...
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| Format: | Article |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1078 |
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| author | Zeeshan Attaullah N. Ameer Ahammad Nehad Ali Shah Jae Dong Chung |
| author_facet | Zeeshan Attaullah N. Ameer Ahammad Nehad Ali Shah Jae Dong Chung |
| author_sort | Zeeshan |
| collection | DOAJ |
| description | Thin film flow (TFF) problems received a lot of attention in recent times. Some frequent applications of TFF include polymer and metal extraction, elastic sheet drawing, food striating, heat exchanges, and device fluidization. Further improvement and enhancement of TFF need to be examined due to its practical applications. In the current analysis, viscoelastic nanofluid thin film flow through the vertical expanding sheet in the presence of a magnetic field with entropy function has been examined. The governing equations are transformed to first-order ODEs through similarity transformation and then solved numerically by using RK4 along with the shooting technique and ND Solve method. The impact of embedded parameters is discussed using graphs and tables. Physical quantities of interest are also discussed in detail. For the numerical solution, the error estimation and the residue error are calculated for the stability and confirmation of the mathematical model. |
| first_indexed | 2024-03-11T07:19:11Z |
| format | Article |
| id | doaj.art-fc28a03bf2034afb9d83591e3595e45a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:19:11Z |
| publishDate | 2023-02-01 |
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| spelling | doaj.art-fc28a03bf2034afb9d83591e3595e45a2023-11-17T08:07:54ZengMDPI AGMathematics2227-73902023-02-01115107810.3390/math11051078A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability AnalysisZeeshan0Attaullah1N. Ameer Ahammad2Nehad Ali Shah3Jae Dong Chung4Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 25000, PakistanDepartment of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, Republic of KoreaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, Republic of KoreaThin film flow (TFF) problems received a lot of attention in recent times. Some frequent applications of TFF include polymer and metal extraction, elastic sheet drawing, food striating, heat exchanges, and device fluidization. Further improvement and enhancement of TFF need to be examined due to its practical applications. In the current analysis, viscoelastic nanofluid thin film flow through the vertical expanding sheet in the presence of a magnetic field with entropy function has been examined. The governing equations are transformed to first-order ODEs through similarity transformation and then solved numerically by using RK4 along with the shooting technique and ND Solve method. The impact of embedded parameters is discussed using graphs and tables. Physical quantities of interest are also discussed in detail. For the numerical solution, the error estimation and the residue error are calculated for the stability and confirmation of the mathematical model.https://www.mdpi.com/2227-7390/11/5/1078RK4ND Solve methodsecond-grade nanofluidstability analysiserror estimationexpanding sheet |
| spellingShingle | Zeeshan Attaullah N. Ameer Ahammad Nehad Ali Shah Jae Dong Chung A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis Mathematics RK4 ND Solve method second-grade nanofluid stability analysis error estimation expanding sheet |
| title | A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis |
| title_full | A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis |
| title_fullStr | A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis |
| title_full_unstemmed | A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis |
| title_short | A Numerical Framework for Entropy Generation Using Second-Order Nanofluid Thin Film Flow over an Expanding Sheet: Error Estimation and Stability Analysis |
| title_sort | numerical framework for entropy generation using second order nanofluid thin film flow over an expanding sheet error estimation and stability analysis |
| topic | RK4 ND Solve method second-grade nanofluid stability analysis error estimation expanding sheet |
| url | https://www.mdpi.com/2227-7390/11/5/1078 |
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