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Zeitschrift für Naturforschung A

A Journal of Physical Sciences

Editor-in-Chief: Holthaus, Martin

Editorial Board: Fetecau, Corina / Kiefer, Claus


IMPACT FACTOR 2017: 1.414

CiteScore 2018: 1.15

SCImago Journal Rank (SJR) 2018: 0.370
Source Normalized Impact per Paper (SNIP) 2018: 0.431

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1865-7109
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Volume 71, Issue 7

Issues

Exact Solutions for Stokes’ Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach

Taha Aziz
  • Corresponding author
  • DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
  • International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa, Tel.: +27-11-7176132, Fax: +27-11-7176149
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ A. Aziz
  • College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Rawalpindi 46070, Pakistan
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ C.M. Khalique
  • International Institute for Symmetry Analysis and Mathematical Modeling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2016-05-13 | DOI: https://doi.org/10.1515/zna-2016-0031

Abstract

The fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.

Keywords: Conservation Laws; Group Invariant Solutions; Lie Symmetry Analysis; Nanofluid Flow; Third-Grade Fluid

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About the article

Received: 2016-01-30

Accepted: 2016-04-17

Published Online: 2016-05-13

Published in Print: 2016-07-01


Citation Information: Zeitschrift für Naturforschung A, Volume 71, Issue 7, Pages 621–630, ISSN (Online) 1865-7109, ISSN (Print) 0932-0784, DOI: https://doi.org/10.1515/zna-2016-0031.

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