Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface
This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. S...
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| Published in | PloS one Vol. 10; no. 9; p. e0137363 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Public Library of Science
01.09.2015
Public Library of Science (PLoS) |
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| Abstract | This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. Similarity approach is utilized to normalize the governing boundary layer equations. Local similarity solutions are achieved by shooting approach together with fourth-fifth-order Runge-Kutta integration technique and Newton's method. Our computations reveal that fluid temperature has inverse relationship with the thermal relaxation time. Further the fluid velocity is a decreasing function of the fluid relaxation time. A comparison of Fourier's law and the Cattaneo-Christov's law is also presented. Present attempt even in the case of Newtonian fluid is not yet available in the literature. |
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| AbstractList | This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. Similarity approach is utilized to normalize the governing boundary layer equations. Local similarity solutions are achieved by shooting approach together with fourth-fifth-order Runge-Kutta integration technique and Newton’s method. Our computations reveal that fluid temperature has inverse relationship with the thermal relaxation time. Further the fluid velocity is a decreasing function of the fluid relaxation time. A comparison of Fourier’s law and the Cattaneo-Christov’s law is also presented. Present attempt even in the case of Newtonian fluid is not yet available in the literature. |
| Audience | Academic |
| Author | Mustafa, M Ahmad Khan, Junaid Hayat, T Alsaedi, A |
| AuthorAffiliation | 3 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan 4 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia Tsinghua University, CHINA 1 Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan 2 School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan |
| AuthorAffiliation_xml | – name: 2 School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan – name: Tsinghua University, CHINA – name: 1 Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan – name: 4 Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia – name: 3 Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan |
| Author_xml | – sequence: 1 givenname: Junaid surname: Ahmad Khan fullname: Ahmad Khan, Junaid organization: Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan – sequence: 2 givenname: M surname: Mustafa fullname: Mustafa, M organization: School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan – sequence: 3 givenname: T surname: Hayat fullname: Hayat, T organization: Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia – sequence: 4 givenname: A surname: Alsaedi fullname: Alsaedi, A organization: Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80257, Jeddah, 21589, Saudi Arabia |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/26325426$$D View this record in MEDLINE/PubMed |
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| Copyright | COPYRIGHT 2015 Public Library of Science 2015 Ahmad Khan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2015 Ahmad Khan et al 2015 Ahmad Khan et al |
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| SubjectTerms | Applied mathematics Boundary conditions Boundary layer equations Boundary layers Boundary layers (Fluid dynamics) Chemical reactions Continuous casting Cooling Elasticity Energy equation Fluid Fluids Fourier law Heat conductivity Heat flux Heat transfer Mathematical models Maxwell fluids Measurement Methods Models, Theoretical Newtonian fluids Numerical analysis Relaxation time Runge-Kutta method Shooting Similarity Similarity solutions Stretching Surface Properties Thermal relaxation Viscoelasticity Viscosity |
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| Title | Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface |
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