A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

Taha Aziz; F. M. Mahomed; D. P. Mason

doi:10.1016/j.ijnonlinmec.2015.01.003

A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

Taha Aziz^*
, F. M. Mahomed
, D. P. Mason

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.

Original language	English
Pages (from-to)	142-155
Number of pages	14
Journal	International Journal of Non-Linear Mechanics
Volume	78
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2015.01.003
State	Published - Jan 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Ltd.

Keywords

Compatibility conditions
Conditional symmetry
Exact solvability
Newtonian fluids
Non-Newtonian fluids

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

Access to Document

10.1016/j.ijnonlinmec.2015.01.003

Cite this

@article{e447a69d918842478d364a6122f4cc1f,

title = "A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids",

abstract = "Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.",

keywords = "Compatibility conditions, Conditional symmetry, Exact solvability, Newtonian fluids, Non-Newtonian fluids",

author = "Taha Aziz and Mahomed, \{F. M.\} and Mason, \{D. P.\}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Ltd.",

year = "2016",

month = jan,

doi = "10.1016/j.ijnonlinmec.2015.01.003",

language = "English",

volume = "78",

pages = "142--155",

journal = "International Journal of Non-Linear Mechanics",

issn = "0020-7462",

publisher = "Elsevier Ltd.",

}

TY - JOUR

T1 - A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

AU - Aziz, Taha

AU - Mahomed, F. M.

AU - Mason, D. P.

PY - 2016/1

Y1 - 2016/1

N2 - Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.

AB - Criteria are established for higher order ordinary differential equations to be compatible with lower order ordinary differential equations. Necessary and sufficient compatibility conditions are derived which can be used to construct exact solutions of higher order ordinary differential equations subject to lower order equations. We provide the connection to generalized groups through conditional symmetries. Using this approach of compatibility and generalized groups, new exact solutions of non-linear flow problems arising in the study of Newtonian and non-Newtonian fluids are derived. The ansatz approach for obtaining exact solutions for non-linear flow models of Newtonian and non-Newtonian fluids is unified with the application of the compatibility and generalized group criteria.

KW - Compatibility conditions

KW - Conditional symmetry

KW - Exact solvability

KW - Newtonian fluids

KW - Non-Newtonian fluids

UR - https://www.scopus.com/pages/publications/84948571928

U2 - 10.1016/j.ijnonlinmec.2015.01.003

DO - 10.1016/j.ijnonlinmec.2015.01.003

M3 - Article

AN - SCOPUS:84948571928

SN - 0020-7462

VL - 78

SP - 142

EP - 155

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

ER -

A unified compatibility method for exact solutions of non-linear flow models of Newtonian and non-Newtonian fluids

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this