On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows
The nonlinear boundary value problem describing the nanoboundary-layer flow with linear Navier boundary condition is investigated theoretically and numerically in this paper. The G′/G-expansion method is applied to search for the all possible exact solutions, and its results are then validated by th...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/415431 |
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| author | Emad H. Aly Abdelhalim Ebaid |
| author_facet | Emad H. Aly Abdelhalim Ebaid |
| author_sort | Emad H. Aly |
| collection | DOAJ |
| description | The nonlinear boundary value problem describing the nanoboundary-layer flow with linear
Navier boundary condition is investigated theoretically and numerically in this paper. The
G′/G-expansion method is applied to search for the all possible exact solutions, and its results are
then validated by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach which
has been recently introduced and successfully used. This numerical technique is firstly
applied and, on comparing with the other recent work, it is found that the results are very accurate
and effective to deal with the current problem. It is then used to examine and validate the present
analytical analysis. Although the G′/G-expansion method has been used widely to solve nonlinear wave equations, its application for nonlinear boundary value problems has not been discussed yet, and the present paper may be the first to address this point. It is clarified that the exact solutions obtained via the G′/G-expansion method cannot be obtained by using some of the other methods. In addition, the domain of the physical parameters involved in the current boundary value problem is also discussed. Furthermore, the convex, vicinity of zero, and asymptotic solutions are deduced. |
| format | Article |
| id | doaj-art-c1f9bf3bc4f04be6bbc45df889f659e9 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c1f9bf3bc4f04be6bbc45df889f659e92025-08-20T03:23:30ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/415431415431On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid FlowsEmad H. Aly0Abdelhalim Ebaid1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Tabuk University, Tabuk 71491, Saudi ArabiaThe nonlinear boundary value problem describing the nanoboundary-layer flow with linear Navier boundary condition is investigated theoretically and numerically in this paper. The G′/G-expansion method is applied to search for the all possible exact solutions, and its results are then validated by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach which has been recently introduced and successfully used. This numerical technique is firstly applied and, on comparing with the other recent work, it is found that the results are very accurate and effective to deal with the current problem. It is then used to examine and validate the present analytical analysis. Although the G′/G-expansion method has been used widely to solve nonlinear wave equations, its application for nonlinear boundary value problems has not been discussed yet, and the present paper may be the first to address this point. It is clarified that the exact solutions obtained via the G′/G-expansion method cannot be obtained by using some of the other methods. In addition, the domain of the physical parameters involved in the current boundary value problem is also discussed. Furthermore, the convex, vicinity of zero, and asymptotic solutions are deduced.http://dx.doi.org/10.1155/2012/415431 |
| spellingShingle | Emad H. Aly Abdelhalim Ebaid On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows Abstract and Applied Analysis |
| title | On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows |
| title_full | On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows |
| title_fullStr | On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows |
| title_full_unstemmed | On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows |
| title_short | On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows |
| title_sort | on the exact analytical and numerical solutions of nano boundary layer fluid flows |
| url | http://dx.doi.org/10.1155/2012/415431 |
| work_keys_str_mv | AT emadhaly ontheexactanalyticalandnumericalsolutionsofnanoboundarylayerfluidflows AT abdelhalimebaid ontheexactanalyticalandnumericalsolutionsofnanoboundarylayerfluidflows |