A Mathematical Study on Non-Linear MHD Boundary Layer Past a Porous Shrinking Sheet with Suction

Authors

  • V. Ananthaswamy The Madura College, India
  • K. Renganathan SSM Institute of Engineering and Technology, India

DOI:

https://doi.org/10.46545/aijser.v2i2.87

Keywords:

Chemical reaction; Suction at the surface; Porous shrinking sheet’ Non-linear ordinary differential equations; Homotopy analysis method.

Abstract

In this paper we discuss with magneto hydrodynamic viscous flow due to a shrinking sheet in the presence of suction. We also discuss two dimensional and axisymmetric shrinking for various cases. Using similarity transformation the governing boundary layer equations are converted into its dimensionless form. The transformed simultaneous ordinary differential equations are solved analytically by using Homotopy analysis method. The approximate analytical expression of the dimensionless velocity, dimensionless temperature and dimensionless concentration are derived using the Homotopy analysis method through the guessing solutions. Our analytical results are compared with the previous work and a good agreement is observed.

Downloads

Download data is not yet available.

Author Biographies

  • V. Ananthaswamy , The Madura College, India

    Assistant Professor

    Department of Mathematics

    The Madura College, Madurai, Tamil Nadu, India

  • K. Renganathan , SSM Institute of Engineering and Technology, India

    Assistant Professor

    Department of Mathematics

    SSM Institute of Engineering and Technology

    Dindigul, Tamil Nadu, India

References

A. Apelblat, Mass transfer with a chemical reaction of the first order effects of axial diffusion, The chemical Engineering Journal, 23(1982), 193 - 201.

S. N. Bhattacharyya and A. S. Gupta, On the stability of viscous Flow over a stretching sheet, Quarterly Applied Mathematics, 43(1985), 359-367.

J. F. Brady and A. Acrivos, Steady flow in a channel or tube with accelerating surface velocity, an exact solution to the Navier-Stokes equations with reverse flow, Journal of Fluid Mechanics, 112(1981), 127-150.

R. Lester Brown, The earth is shrinking: Advancing Deserts and rising seas squeezing civilization, ECO-Economy Updates, November 15(2006), Copyright Earth Policy Institute.

W. T. Cheng and H. T. Lin, Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge, International journal of Engineering Science, 40(2002), 531 - 539.

S. Gill, A process for the Step-by-Step Integration of Differential Equations in an Automatic Digital Computing Machine., Proceedings of the Cambridge Philosophical Society, 47(1)(1951), 96-108.

L. J. Crane, Flow past a stretching plate, Zeitschrift fr Angewandte Mathematik und Physik, 21(1970), 645-647.

P. S. Gupta and A. S. Gupta, Heat and mass transfer on a stretching sheet with suction and blowing, Canadian Journal of Chemical Engineering, 55(1977), 744-746.

M. A. Hakiem, EL, A. A. Mohammadeian, S. M. M. EL. Kaheir, and R. S. R. Gorla, Joule heating effects on MHD free convection On the effect of chemical reaction, heat... 115 flow of a micro polar fluid, International Communications Heat Mass Transfer, 26(1999), 219 - 225.

T. Hayat, Z. Abbas and M. Sajid, On the analytic solution of Magnetohydrodynamic flow of a second grade fluid over a shrinking sheet, Journal of Applied Mechanics, 74(2007), 1165-1170.

K. F. Jensen, E. O. Einset and D.I. Fotiadis, Flow phenomena in chemical vapor deposition of thin films, Annual Review of Fluid Mechanics, 23(1991), 197-232.

Kuo Bor-Lin, Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method, International Journal of Heat Mass Transfer, 48(2005), 5036- 5043.

M. Miklavcic and C. Y. Wang, Viscous flow due to a shrinking sheet, Quarterly Applied Mathematics, 64(2006), 283-290.

Muhaimin, R.Kandasamy, Azme B. Khamis, Effects of heat and mass transfer on nonlinear MHD boundary layer flow over a shrinking sheet in the presence of suction, Applied Mathematics and Mechanics (English Edition), 29(10)(2008), 1309-1317.

M. Sajid, T. Javed and T. Hayat, MHD rotating flow of a viscous fluid over a shrinking surface, Nonlinear Dynamics, 51(2008), 259 - 265.

M. Sajid and T. Hayat, The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet, Chaos, Solutions and Fractals (Article in press), (2007).

H. Schlichting, Boundary Layer Theory, McGraw Hill Inc, New York, (1979), 164.

W. Troy E. A. Overman, G. B. Ermentrout and J. P. Keener, 1987, Uniqueness of flow of a second-order fluid past a stretching sheet, Quarterly Applied Mathematics, 44(1987), 753-755.

S.J. Liao and K.F. Cheung, Homotopy analysis of nonlinear progressive waves in deep water, J. Engng Maths., 45 (2003), 105-116.

W. Kierkus, An analysis of laminar free convection flow and heat transfer about an inclined isothermal plate, Int. J. Heat mass trans., 11 (1968), 241-253.

S.J. Liao, An explicit totally analytic approximation of Blasius viscous flow problems, Int. J. Non-Linear Mech., 34(1999), 759-778.

S.J. Liao and A.T. Chwang, Application of homotopy analysis method in nonlinear oscillations, Trans. ASME: J. Appl. Mech., 65(1998), 914-922.

S.J. Liao, An analytical approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude, Int. J. Non-Linear Mech., 38(2003), 1173-1183.

S.J. Liao, An analytic approximation of the drag coefficient for the viscous flow past a sphere. Int. J. Non-Linear Mech, 37(2002), 1-18.

S.J. Liao, The Homotopy Analysis method in non-linear differential equations. Springer and Higher Education Press. (2012), 45-54.

S.J. Liao,Beyond Perturbation introduction to the Homotopy analysis method, First Edition, Chapman and Hall, CRC press, Boca Raton,(2003), 92-98.

V. Ananthaswamy and S. UmaMaheswari, Analytical expression for the hydrodynamic fluid flow through a porous medium, International Journal of Automation and Control Engineering, 4(2)(2015), 67-76.

V. Ananthaswamy and L. Sahanya Amalraj, Thermal stability analysis of reactive hydromagnetic third-grade fluid using Homotopy analysis method, International Journal of Modern Mathematical Sciences, 14(1) (2016), 25-41.

R. Usha and R. Sridharan, The axisymmetric motion of a liquid film on an unsteady stretching surface, Journal of Fluids Engineering, 117(1995), 81-85.

C. Y. Wang, The three-dimensional flow due to a stretching at surface, Physics of Fluids, 27(1984), 1915-1917.

Downloads

Published

2019-06-07

Issue

Section

Original Articles/Review Articles/Case Reports/Short Communications

How to Cite

A Mathematical Study on Non-Linear MHD Boundary Layer Past a Porous Shrinking Sheet with Suction. (2019). American International Journal of Sciences and Engineering Research , 2(2), 32-48. https://doi.org/10.46545/aijser.v2i2.87

Similar Articles

You may also start an advanced similarity search for this article.