Two-Dimensional Boundary Layer Flow of Chemical Reaction MHD Fluid over a Shrinking Sheet with Suction and Injection
Publication: Journal of Aerospace Engineering
Volume 27, Issue 5
Abstract
In this paper, the steady two-dimensional boundary layer flow of chemical reaction magnetohydrodynamics (MHD) viscous fluid over a shrinking sheet with suction/injection is studied. The governing equations for the problem are changed to dimensionless ordinary differential equations by similarity transformation. The resulting nonlinear differential equations are solved for velocity and concentration profiles using the homotopy perturbation and the finite difference methods. Graphical results have been presented for velocity and concentration profiles for various physical parameters of interest. To the best of our knowledge, this type of analytical solution for chemical reaction MHD viscous fluid over a shrinking sheet with suction/injection is presented for the first time in the literature.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abo-Eldahab, E., and Salem, A. M. (2005). “MHD flow and heat transfer of nonnewtonian power-law fluid with diffusion and chemical reaction on a moving cylinder.” Heat Mass Transfer, 41(8), 703–708.
Afify, A. (2004). “MHD free convective flow and mass transfer over a stretching sheet with chemical reaction.” Heat Mass Transfer, 40(6–7), 495–500.
Andersson, H. I., Hansen, O. R., and Holmedal, B. (1994). “Diffusion of a chemically reactive species from a stretching sheet.” Int. J. Heat Mass Transfer, 37(4), 659–664.
Anjalidavi, S. P., and Kandasamy, R. (1999). “Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate.” Heat Mass Transfer, 35(6), 465–467.
Anjalidavi, S. P., and Kandasamy, R. (2000). “Effects of chemical reaction, heat and mass transfer on MHD flow past a semi infinite plate.” Z. Angew. Math. Mech., 80(10), 697–700.
Ariel, P. D. (2007). “The three-dimensional flow past a stretching sheet and the homotopy perturbation method.” Comput. Math. Appl., 54(7–8), 920–925.
Ariel, P. D. (2009). “Extended homotopy perturbation method and computation of flow past a stretching sheet.” Comput. Math. Appl., 58(11–12), 2402–2409.
Berezansky, L., Diblík, J., and Šmarda, Z. (2010). “Positive solutions of a second-order delay differential equations with a damping term.” Comput. Math. Appl., 60(5), 1332–1342.
Bhattacharyya, K., and Layek, G. C. (2010). “Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction and blowing.” Chem. Eng. Commun., 197(12), 1527–1540.
Cortell, R. (2007a). “MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species.” Chem. Eng. Process., 46(8), 721–728.
Cortell, R. (2007b). “Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet.” Chem. Eng. Process., 46(10), 982–989.
Crane, L. J. (1970). “Flow past a stretching plate.” Z. Angew Math. Phys., 21(4), 645–647.
Cussler, E. L. (1988). Diffusion: Mass transfer in fluid systems, Cambridge University Press, London.
Das, U. N., Deka, R., and Soundalgekar, V. M. (1994). “Effect of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction.” Forsch. Ingenieurwes., 60(10), 284–287.
Erickson, L. E., Fan, L. T., and Fox, V. G. (1966). “Heat and mass transfer problem on a moving continuous plate with suction or injection.” Ind. Eng. Chem. Fundam., 5(1), 19–25.
He, J. H. (1999). “Homotopy perturbation technique.” Comput. Meth. Appl. Mech. Eng., 178(3–4), 257–262.
He, J. H., Wu, G. C., and Austin, F. (2010). “The variational iteration method which should be followed.” Nonlinear Sci. Lett. A - Math. Phys. Mech., 1(1), 1–30.
Hetmaniok, E., Nowak, I., Slota, D., and Wituła, R. (2012). “Application of the homotopy perturbation method for the solution of inverse heat conduction problem.” Int. Commun. Heat Mass Tranfer, 39(1), 30–35.
Hetmaniok, E., Slota, D., Wituła, R., and Zielonka, A. (2011). “Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem.” Comput. Math. Appl., 61(8), 1931–1934.
Khan, R. A., and Usman, M. (2012). “Eventual periodicity of forced oscillations of the Korteweg-de Vries type equation.” Appl. Math. Modell., 36(2), 736–742.
Khan, Y., Faraz, N., Yildirim, A., and Wu, Q. (2011b). “A series solution of the long porous slider.” Tribol. Trans., 54(2), 187–191.
Khan, Y., and Wu, Q. (2011). “Homotopy perturbation transform method for nonlinear equation using He’s polynomials.” Comput. Math. Appl., 61(8), 1963–1967.
Khan, Y., Wu, Q., Faraz, N., and Yildirim, A. (2011a). “The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet.” Comput. Math. Appl., 61(11), 3391–3399.
Koçak, H., Özis, T., and Yildirim, A. (2010). “Homotopy perturbation method for the nonlinear dispersive K(m,n,1) equations with fractional time derivatives.” Int. J. Numer. Methods Heat Fluid Flow, 20(2), 174–185.
Koçak, H., and Yildirim, A. (2011). “An efficient algorithm for solving nonlinear age-structured population models by combining homotopy perturbation and padé techniques.” Int. J. Comput. Math., 88(3), 491–500.
Mahdy, A., and Chamkha, A. J. (2010). “Chemical reaction and viscous dissipation effects on Darcy-Forchheimer mixed convection in a fluid saturated porous media.” Int. J. Numer. Methods Heat Fluid Flow, 20(8), 924–940.
Olga, F., and Zdenek, S. (2010). “Adomian decomposition method for certain singular initial value problems II.” J. Appl. Math., 3(2), 91–98.
Raftari, B., Mohyud-Din, S. T., and Yildirim, A. (2011). “Solution to the MHD flow over a nonlinear stretching sheet by homotopy perturbation method.” Sci. China, Ser. G, 54(2), 342–345.
Raftari, B., and Yildirim, A. (2010). “The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets.” Comput. Math. Appl., 59(10), 3328–3337.
Raftari, B., and Yıldırım, A. (2011). “Series solution of a nonlinear ODE arising in magnetohydrodynamic by HPM-pade technique.” Comput. Math. Appl., 61(6), 1676–1681.
Sakiadis, B. C. (1961a). “Boundary layer behaviour on continuous solid surface. I: The boundary layer equation for two dimensional and asymmetric flow.” AIChE J., 7(2), 26–28.
Sakiadis, B. C. (1961b). “Boundary layer behaviour on continuous solid surface. II: The boundary layer on a continuous flat surface.” AIChE J., 7(2), 221–225.
Shateyi, S., Mosta, S. S., and Sibanda, P. (2010). “Homotopy analysis of heat and mass transfer boundary layer flow through a nonporous channel with chemical reaction and heat generation.” Can. J. Chem. Eng., 88(6), 975–982.
Slota, D. (2009). “Exact solution of the heat equation with boundary condition of the fourth kind by He’s variational iteration method.” Comput. Math. Appl., 58(11–12), 2495–2503.
Slota, D. (2010). “The application of the homotopy perturbation method to one-phase inverse Stefan problem.” Int. Commun. Heat Mass Transfer, 37(6), 587–592.
Slota, D. (2011). “Homotopy perturbation method for solving the two-phase inverse Stefan problem.” Numer. Heat Transfer, Part A, 59(10), 755–768.
Turkyilmazoglu, M. (2011a). “An optimal analytic approximate solution for the limit cycle of Duffing-van der Pol equation.” J. Appl. Mech., Trans. ASME, 78(9–10), 021005.
Turkyilmazoglu, M. (2011b). “An optimal variational iteration method.” Appl. Math. Lett., 24, 762–765(5).
Turkyilmazoglu, M. (2011c). “Convergence of the homotopy perturbation method.” Int. J. Nonlinear Sci. Numer. Simul., 12(1–8), 9–14.
Turkyilmazoglu, M. (2011d). “Some issues on HPM and HAM methods: A convergence scheme.” Math. Comput. Model., 53(2), 1929–1936.
Xu, L. (2007). “He’s homotopy perturbation method for a boundary layer equation in unbounded domain.” Comput. Math. Appl., 54(7–8), 1067–1070.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 27 • Issue 5 • September 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 3, 2012
Accepted: Aug 29, 2012
Published online: May 8, 2014
Published in print: Sep 1, 2014
Discussion open until: Oct 8, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.