Approximate analytical solutions of MHD viscous flow
DOI:
https://doi.org/10.3329/jname.v13i1.24387Keywords:
Magnetohydrodynamics (MHD), Boundary layer flow, Shrinking sheet,Abstract
The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet caused by boundary layer of an incompressible viscous flow. The governing three partial differential equations of momentum equations are reduced into ordinary differential equation (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use fast converging Dirichlet series and Method of stretching of variables for the solution of these nonlinear differential equations. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes.
Downloads
170
133
References
Altan T, Oh S, Gergel H. Mtal forming fundamentals and applications. Metals Park,
OH:American Society of Metals : 1979.
Fisher EG. Extrusion of plastics. New York ; Wiley: 1976.
Tadmor Z, Klein I. Engineering principles of plasticating extrusion polymer science
and engineering series. New York, Van Nostrand Raihold : 1970.
Sakiadis BC. Boundary layer behaviour on continuous solid surfaces. AICHE J, 1961
;7:26-28.
Sakiadis BC. Boundary layer behaviour on continuous solid surfaces : II, the boundary
layer on a continuous flat surface. AICHE J, 1961;17:221-225.
Crane LJ. Flow past a stretching plate. Z Angew Math Mech 1970;21:645-647.
McLeod JB, Rajagopal KR. On the uniqueness of flow of a Navier-Stokes fluid due to
a stretching boundary. Arch Rat Mech Anal 1987; 98:385-393.
Gupta PS, Gupta AS. Heat and mass transfer on a stretching sheet with suction or
injection and blowing. Can J Chem Eng 1977; 55:744-746.
Brady JF, Acrivos A. Steady flow in a channel or tube with accelerating surface
velocity. An exact analytical solution to the Navier-Stokes equations with reverse flow.
J Fluid Mech 1981; 112: 127-150.
Wang CY. Fluid flow due to a stretching cylinder. Phys Fluids 1988 ; 31 :466-468.
Wang CY. The three dimensional flow due to a stretching flat surface. Phys Fluids
;27:1915-1917.
Wang CY. Liquid film on an unsteady stretching sheet. Quart Appl Math 1990 ; 48:
-610.
Usha R, Sridharan R. The axisymmetrical motion of a liquid film on an unsteady
stretching surface. J Fluids Eng 1995; 117 : 81-85.
Miklacic M, Wang CY. Viscous flow due to a shrinking sheet. Quart Appl Math 2006;
: 283-290.
Nadeem S, Hussain A. MHD flow of a viscous fluid on a nonlinear porous shrinking
sheet with HAM. Appl Math Mech Eng 2009 ; 30(12): 1569-1578.
Fang T and Zhang J. Closed-form exact solutions of MHD viscous flow over a
shrinking sheet. Commun Nonlinear Sci Neumer Simulat 2009; 14:2853-2857.
Sajid M, Hayat T. The application of homotopy analysis method for MHD viscous flow
due to shrinking sheet. Chaos Solitons and Fractal 2009; 39:1317-1323.
Ali F, Nazar R, Arifin N. MHD viscous flow and heat transfer induced by permeable
shrinking sheet with prescribed surface heat flux. WSAS Trans Math 2010; 5(9) :
-375.
Noor NFM, Kechil SA, Hashim I. Simple non-perturbative solution for MHD viscous
flow due to a shrinking sheet. CommunNonlinar Sci. NumerSimulat 2010;15:144-148.
Raftari B, Yildirim A. A series solution of nonlinear ODE arising in MHD by
HPM-Pade technique. Comp Math Appl 2011;61:1676-1681.
Bhattacharyya K. Effects of heat source/ sink on MHD flow and heat transfer over a
Shrinking sheet with mass suction. Chem Eng Res Bull 2011; 15 :12-17.
Kravchenko TK and Yablonskii AI. Solution of an infinite boundary value problem for
third order equation, Differentialnye Uraneniya.1965 ; 327:1.
Kravchenko TK and Yablonskii AI, A boundary value problem on a semi-infinite
interval, DifferentialnyeUraneniya. 1972;8(12):2180-2186.
Riesz S. Introduction to Dirichler series, Camb. Univ. Press, 1957.
Sachdev PL, Bujurke NM and Awati VB, Boundary value problems for third order
nonlinear ordinary differential equations, Stud. Appl. Math. 2005;115: 303-318.
Awati VB, Bujurke NM and Kudenatti RB.An exponential series method for the
solution of the free convection boundary layer flow in a saturated porous medium.
AJCM (2011); 1: 104-110.
Awati VB, Bujurke NM and Kudenatti RB. Dirichlet series method for the solution
of MHD flow over a nonlinear stretching sheet. IJAMES, 2011; 5(1):07-12.
Kudenatti RB, Awati VB and Bujurke NM. Exact analytical solutions of class of
boundary layer equations for a stretching surface, Appl Math Comp, 2011;218:
-2959.
Press WHH, Flannery BP, Teulosky SA and Vetterling WT. Numerical Recipes in C,
Camb. Univ. Press, UK, 1987.
Ariel PD. Stagnation point flow with suction ; an approximate solution. Journal of
Applied Mechanics 1994; 61(4): 976-978.
Downloads
Published
How to Cite
Issue
Section
License
Please download the Copyright Transfer Agreement and send it after duly filled in.
Link to FaceBook
