A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method
This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method (...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2012/634925 |
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| author | R. Ellahi |
| author_facet | R. Ellahi |
| author_sort | R. Ellahi |
| collection | DOAJ |
| description | This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method (HAM) is employed for the presentation of series solutions. The HAM is accepted as an elegant tool for effective solutions for complicated nonlinear problems. The solutions of (Hayat et al., 2007) are developed, and their convergence has been discussed explicitly for two different models, namely, constant and variable viscosity. An error analysis is also described. In addition, the obtained results are illustrated graphically to depict the convergence region. The physical features of the pertinent parameters are presented in the form of numerical tables. |
| format | Article |
| id | doaj-art-cf5b762dcc7f43e9a5966f6c8d141137 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-cf5b762dcc7f43e9a5966f6c8d1411372025-02-03T01:28:11ZengWileyAdvances in Mathematical Physics1687-91201687-91392012-01-01201210.1155/2012/634925634925A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis MethodR. Ellahi0Department of Mechanical Engineering, University of California Riverside, Bourns Hall, A373, Riverside, CA 92521, USAThis work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method (HAM) is employed for the presentation of series solutions. The HAM is accepted as an elegant tool for effective solutions for complicated nonlinear problems. The solutions of (Hayat et al., 2007) are developed, and their convergence has been discussed explicitly for two different models, namely, constant and variable viscosity. An error analysis is also described. In addition, the obtained results are illustrated graphically to depict the convergence region. The physical features of the pertinent parameters are presented in the form of numerical tables.http://dx.doi.org/10.1155/2012/634925 |
| spellingShingle | R. Ellahi A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method Advances in Mathematical Physics |
| title | A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method |
| title_full | A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method |
| title_fullStr | A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method |
| title_full_unstemmed | A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method |
| title_short | A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method |
| title_sort | study on the convergence of series solution of non newtonian third grade fluid with variable viscosity by means of homotopy analysis method |
| url | http://dx.doi.org/10.1155/2012/634925 |
| work_keys_str_mv | AT rellahi astudyontheconvergenceofseriessolutionofnonnewtonianthirdgradefluidwithvariableviscositybymeansofhomotopyanalysismethod AT rellahi studyontheconvergenceofseriessolutionofnonnewtonianthirdgradefluidwithvariableviscositybymeansofhomotopyanalysismethod |