Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo-Fabrizio fractional derivatives: A comparison

. The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-...

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Published in	European physical journal plus Vol. 132; no. 8; p. 340
Main Authors	Asjad, Muhammad Imran, Shah, Nehad Ali, Aleem, Maryam, Khan, Ilyas
Format	Journal Article
Language	English
Published	Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2017 Springer Nature B.V
Subjects	Applied and Technical Physics Atomic Boundary conditions Complex Systems Condensed Matter Physics Heat transfer Heating Laplace transforms Mathematical and Computational Physics Molecular Non-Newtonian fluids Optical and Plasma Physics Parameters Partial differential equations Physics Physics and Astronomy Regular Article Shear strain Temperature distribution Theoretical Unsteady flow Velocity Velocity distribution
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ISSN	2190-5444 2190-5444
DOI	10.1140/epjp/i2017-11606-6

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Abstract	. The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-grade fluids is developed with fractional derivatives. The expressions for temperature and velocity fields in dimensionless form as well as rates of heat transfer are determined by means of the Laplace transform technique. Solutions for ordinary cases corresponding to integer order derivatives are also obtained. Numerical computations for a comparison between the solutions of the problem with the Caputo time-fractional derivative, problem with Caputo-Fabrizio time-fractional derivative and of the ordinary fluid problem were made. The influence of some flow parameters and fractional parameter α on temperature field as well as velocity field was presented graphically and in tabular forms.
AbstractList	. The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-grade fluids is developed with fractional derivatives. The expressions for temperature and velocity fields in dimensionless form as well as rates of heat transfer are determined by means of the Laplace transform technique. Solutions for ordinary cases corresponding to integer order derivatives are also obtained. Numerical computations for a comparison between the solutions of the problem with the Caputo time-fractional derivative, problem with Caputo-Fabrizio time-fractional derivative and of the ordinary fluid problem were made. The influence of some flow parameters and fractional parameter α on temperature field as well as velocity field was presented graphically and in tabular forms. The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the Caputo fractional derivative (singular kernel) and the Caputo-Fabrizio fractional derivative (non-singular kernel). A physical model for second-grade fluids is developed with fractional derivatives. The expressions for temperature and velocity fields in dimensionless form as well as rates of heat transfer are determined by means of the Laplace transform technique. Solutions for ordinary cases corresponding to integer order derivatives are also obtained. Numerical computations for a comparison between the solutions of the problem with the Caputo time-fractional derivative, problem with Caputo-Fabrizio time-fractional derivative and of the ordinary fluid problem were made. The influence of some flow parameters and fractional parameter α on temperature field as well as velocity field was presented graphically and in tabular forms.
ArticleNumber	340
Author	Asjad, Muhammad Imran Khan, Ilyas Shah, Nehad Ali Aleem, Maryam
Author_xml	– sequence: 1 givenname: Muhammad Imran surname: Asjad fullname: Asjad, Muhammad Imran email: imran.asjad@umt.edu.pk organization: Department of Mathematics, University of Management and Technology Lahore – sequence: 2 givenname: Nehad Ali surname: Shah fullname: Shah, Nehad Ali organization: Abdus Salam School of Mathematical Sciences, GC University Lahore – sequence: 3 givenname: Maryam surname: Aleem fullname: Aleem, Maryam organization: Department of Mathematics, University of Management and Technology Lahore – sequence: 4 givenname: Ilyas surname: Khan fullname: Khan, Ilyas organization: Basic Sciences Department, College of Engineering Majmaah University
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Snippet	. The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the... The present study is a comparative analysis of unsteady flows of a second-grade fluid with Newtonian heating and time-fractional derivatives, namely, the...
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SubjectTerms	Applied and Technical Physics Atomic Boundary conditions Complex Systems Condensed Matter Physics Heat transfer Heating Laplace transforms Mathematical and Computational Physics Molecular Non-Newtonian fluids Optical and Plasma Physics Parameters Partial differential equations Physics Physics and Astronomy Regular Article Shear strain Temperature distribution Theoretical Unsteady flow Velocity Velocity distribution
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Title	Heat transfer analysis of fractional second-grade fluid subject to Newtonian heating with Caputo and Caputo-Fabrizio fractional derivatives: A comparison
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