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MHD mixed convection stagnation point flow of a viscous fluid over a lubricated vertical surface

Khalid Mahmood (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
Muhammad Sajid (Theoretical Physics Division, PINSTECH, Islamabad, Pakistan)
Nasir Ali (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)
Tariq Javed (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan)

Industrial Lubrication and Tribology

ISSN: 0036-8792

Article publication date: 10 July 2017

Abstract

Purpose

An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been assumed that the surface temperature varies linearly with the distance from the stagnation point. The problem is governed by system of partial differential equations for both the base fluid and the lubricant. The continuity of velocity and shear stress is assumed at the interface layer between the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions. The influence of various important parameters is presented in the form of graphs and tables. The limiting cases for full and no-slip conditions are deduced from the present solutions. A comparison of the present results with the existing results in the special case validates the obtained numerical solutions. The purpose of this study is to see the behaviour of flow characteristics in the presence of lubrication.

Design/methodology/approach

The authors’ problem is governed by system of partial differential equations for both the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. The obtained ordinary differential equation along with boundary conditions are highly nonlinear and coupled. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions.

Findings

Some findings of this study are that the lubricant increases the velocity of the base fluid inside the boundary layer. In the case of full slip, the effects of viscosity are suppressed by the lubricant. The temperature of the base fluid decreases by increase in lubrication on the surface. By increasing the slip on the surface, the skin friction decreases and local Nusselt number increases, but the rate of increase or decrease is less in magnitude for the case of opposing flow. The similarity solutions only exist for n = 1/2. A non-similar solution is obtained for the other values of the power-law index n.

Originality/value

The study of flow phenomenon over a lubricated surface has important applications in machinery components such as fluid bearings and mechanical seals. Coating is another major application of lubrication including the preparation of thin films, printing, painting, etc. The authors hope that the current study will provide the roadmap for the future studies in this direction.

Keywords

Citation

Mahmood, K., Sajid, M., Ali, N. and Javed, T. (2017), "MHD mixed convection stagnation point flow of a viscous fluid over a lubricated vertical surface", Industrial Lubrication and Tribology, Vol. 69 No. 4, pp. 527-535. https://doi.org/10.1108/ILT-02-2016-0025

Publisher

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Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited