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# International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 2

# Numerical Exploration of Heat Transfer and Lorentz Force Effects on the Flow of MHD Casson Fluid over an Upper Horizontal Surface of a Thermally Stratified Melting Surface of a Paraboloid of Revolution

O. D. Makinde
• Corresponding author
• Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
• Email
• Other articles by this author:
/ N. Sandeep
/ T. M. Ajayi
/ I. L. Animasaun
Published Online: 2018-03-07 | DOI: https://doi.org/10.1515/ijnsns-2016-0087

## Abstract

Considering the recent aspiration of experts dealing with the painting of aircraft and bonnet of cars to further understand the relevance of skin friction and heat transfer while painting all these objects that are neither horizontal nor vertical, neither a cone/wedge or cylinder but upper horizontal surface of a paraboloid of revolution; a two-dimensional electrically conducting Casson fluid flow on an upper horizontal thermally stratified surface of a paraboloid of revolution is analyzed. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying classical boundary condition of temperature. Plastic dynamic viscosity and thermal conductivity of the fluid are assumed to vary linearly with temperature. In view of this, all necessary models were modified to suit the case ${T}_{m}<{T}_{\mathrm{\infty }}$. It is assumed that natural convection is driven by buoyancy; hence the suitable model of Boussinesq approximation is adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge–Kutta technique along with shooting method. Effects of the magnetic field, temperature-dependent plastic dynamic viscosity and buoyancy parameters on the velocity and temperature are showed graphically and discussed. Normal influence of Lorentz force exists on Casson fluid flow when the thickness of the surface is small. Scientists and experts are urge to note an adverse effect of this force occurs on the fluid flow when the thickness of the surface is large.

MSC 2010: 76D10

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Accepted: 2018-02-02

Published Online: 2018-03-07

Published in Print: 2018-04-25

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 2, Pages 93–106, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339,

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