Research Article
Interaction of Magnetic Field and Nonlinear Convection in
the Stagnation Point Flow over a Shrinking Sheet
Rakesh Kumar and Shilpa Sood
Department of Mathematics, Central University of Himachal Pradesh, TAB, Shahpur, Kangra, Himachal Pradesh 176206, India
Correspondence should be addressed to Rakesh Kumar; rakesh.lect@gmail.com
Received 27 November 2015; Revised 26 March 2016; Accepted 28 March 2016
Academic Editor: Yuanxin Zhou
Copyright © 2016 R. Kumar and S. Sood. Tis 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.
Te steady two-dimensional boundary layer stagnation point fow due to a shrinking sheet is analyzed. Te combined efects
of magnetic feld and nonlinear convection are taken into account. Te governing equations for the fow are modeled and then
simplifed using the similarity transformation and boundary layer approach. Te numerical solution of the reduced equations is
obtained by the second-order fnite diference scheme also known as Keller box method. Te infuence of the pertinent parameters
of the problem on velocity and temperature profles, skin friction, and sheet temperature gradient are presented through the graphs
and tables and discussed. Te magnetic feld and nonlinear convection parameters signifcantly enhance the solution range.
1. Introduction
Te analysis of the hydromagnetic fow over stretching or
shrinking surfaces is very demanding due to wide range of
its applications in industry, physics, and engineering sciences
including bioengineering. Te impact of magnetic feld on
the fow of an electrically conducting viscous fuid fnds its
applications in purifcation of crude oil, glass manufacturing,
paper production, polymer sheets, MHD electrical power
generation, magnetic material processing, and so forth [1].
Moreover, the fnal product relies on the rate of cooling,
which is decided by the confguration of the boundary layer
near the stretching/shrinking sheet. Chakrabarti and Gupta
[2] investigated the hydromagnetic fow and heat transfer
over a stretching surface. Zhang and Wang [3] presented a
rigorous mathematical analysis to analyze the MHD fow of
power law fuid over a stretching sheet. Te axially symmetric
stagnation point fow of an electrically conducting fuid
under transverse magnetic feld was examined by Kakutani
[4]. An analysis for three-dimensional stagnation point fow
over a stretching surface was made by Attia [5] considering
magnetic feld and heat generation. Ali et al. [6] extended
the above paper by considering the induced magnetic feld.
Recently, Ali et al. [7] have reported on the efects of mixed
convection parameter and magnetic feld over a vertical
stretching sheet in the neighborhood of the stagnation point.
Mahapatra et al. [8] investigated the MHD stagnation point
fow of power law fuid over a sheet which is stretching in its
own plane with a velocity proportional to the distance from
the stagnation point. Very recently, Khan et al. [9] analyzed
the thermodifusion efects on the MHD stagnation point
fow of nanofuid over a stretching sheet. Hayat et al. [10]
investigated the stagnation point fow on a non-Newtonian
fuid over a stretching sheet. Some signifcant aspects of the
MHD stagnation point fow over stretching surfaces can be
found in Hayat et al. [11], Shateyi and Makinde [12], Ibrahim
et al. [13], Mahapatra and Gupta [14], Ishak et al. [15], and so
forth. In recent times, the researchers are attracted towards
the fow over shrinking surfaces. Tese fows are diferent
from the fow over stretching surfaces in many ways. In
shrinking sheet problems, the surface of the sheet is stretched
towards a slot and hence generating a velocity away from
the sheet. Terefore, the generated vorticity does not remain
within the boundary layer and the fow will be unlikely to
exist [16]. Wang [17] confrmed that the solutions can be
found only for small shrinking rates and multiple solutions
may exist for two-dimensional cases. Mahapatra and Nandy
[18] were the researchers who analyzed that if suitable suction
or stagnation point is added, then the vorticity can be
controlled and the similarity solution will exist. Moreover, the
Hindawi Publishing Corporation
Journal of Engineering
Volume 2016, Article ID 6752520, 8 pages
http://dx.doi.org/10.1155/2016/6752520