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...

Full description

Saved in:
Bibliographic Details
Main Authors: Emad H. Aly, Abdelhalim Ebaid
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/415431
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849684315630206976
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