On the exact analytical and numerical solutions of nano boundary-layer fluid flows
type: Item
instance of: scholarly article
title: On the exact analytical and numerical solutions of nano boundary-layer fluid flows
zbMATH Open document ID: 1253.76089
DOI: 10.1155/2012/415431
author: Emad Aly
author: Abdelhalim Ebaid
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 6116393
zbMATH Keywords: nanoboundary-layer flow
zbMATH Keywords: \(G'/G\)-expansion method
zbMATH Keywords: Chebyshev pseudospectral differentiation matrix
Wikidata QID: Q58696578
describes a project that uses: ATFM
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/415431
OpenAlex ID: W2153477559
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description: scientific article; zbMATH DE number 6116393