Volume 6, Issue 3, September 2018, Page: 69-88
Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation
Gbeminiyi Sobamowo, Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Akinbowale Akinshilo, Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Ahmed Yinusa, Department of Mechanical Engineering, University of Lagos, Yaba, Nigeria
Oluwatoyin Adedibu, Department of Electrical Engineering, the Polytechnic, Ibadan, Nigeria
Received: Jul. 8, 2018;       Accepted: Jul. 19, 2018;       Published: Aug. 21, 2018
DOI: 10.11648/j.se.20180603.11      View  407      Downloads  18
Abstract
The various industrial, biological and engineering applications of third grade fluid have in recent times propel continuous research on the flow dynamics and heat transfer characteristics of the non-Newtonian fluid. In this work, effects of nonlinear hydrodynamic slip and temperature-jump conditions on pipe flow and heat transfer of third grade fluid with nonlinear temperature-dependent viscosities and internal heat generation are presented. The developed nonlinear governing equations are solved using regular perturbation method. In order to verify the accuracy of the solution methodology, the results of the approximate analytical solution are compared with the results of the numerical solutions using Runge-Kutta fourth-order coupled with shooting method. Good agreements are obtained between the analytical and the numerical results. Thereafter, the obtained approximate analytical solutions are used to investigate the effects of variable viscosity, non-Newtonian parameter, viscous dissipation and pressure gradient on the flow and heat transfer characteristics of the third-grade fluid in the pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. The present results can be used to advance the analysis and study of the behaviour of third grade fluid flow and steady state heat transfer processes such as found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, oil recovery applications etc.
Keywords
Third-Grade Fluid, Pipe Flow, Non-Linear Viscosities, Non-Linear Internal Heat Generation, Nonlinear Boundary Conditions
To cite this article
Gbeminiyi Sobamowo, Akinbowale Akinshilo, Ahmed Yinusa, Oluwatoyin Adedibu, Nonlinear Slip Effects on Pipe Flow and Heat Transfer of Third Grade Fluid with Nonlinear Temperature-Dependent Viscosities and Internal Heat Generation, Software Engineering. Vol. 6, No. 3, 2018, pp. 69-88. doi: 10.11648/j.se.20180603.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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