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Journal of Applied Mathematics
Volume 2017, Article ID 1697135, 13 pages
https://doi.org/10.1155/2017/1697135
Research Article

Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria

Correspondence should be addressed to T. M. Ajayi; moc.liamg@ednutemllits

Received 30 June 2016; Revised 20 October 2016; Accepted 6 November 2016; Published 4 January 2017

Academic Editor: Igor Andrianov

Copyright © 2017 T. M. Ajayi et al. 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.

Abstract

The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in is guaranteed with when magnitude of is large. decreases with and .