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Thermally Charged MHD Bi-phase Flow Coatings with non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls

1
Center for Modeling & Computer Simulation, Research Institute, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
2
Department of Mathematics & Statistics, Faculty of Basic and Applied Sciences (FBAS), International Islamic University (IIUI), Islamabad 44000, Pakistan
3
Department of Mathematics, Faculty of Arts and Basic Sciences (FABS), Balochistan University of Information Technology, Engineering, and Management Sciences (BUITEMS), Quetta 87300, Pakistan
4
Department of Mathematics, University of Education Lahore, Faisalabad Campus, Faisalabad 38000, Pakistan
*
Author to whom correspondence should be addressed.
Coatings 2019, 9(5), 300; https://doi.org/10.3390/coatings9050300
Received: 19 March 2019 / Revised: 13 April 2019 / Accepted: 29 April 2019 / Published: 2 May 2019
PDF [924 KB, uploaded 2 May 2019]

Abstract

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge–Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.
Keywords: heated bi-phase flow; couple stress fluid; lubrication effects; slippery walls; magnetohydrodynamics heated bi-phase flow; couple stress fluid; lubrication effects; slippery walls; magnetohydrodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ellahi, R.; Zeeshan, A.; Hussain, F.; Abbas, T. Thermally Charged MHD Bi-phase Flow Coatings with non-Newtonian Nanofluid and Hafnium Particles along Slippery Walls. Coatings 2019, 9, 300.

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