Effect of Magnetic Field on Mixed Convection Boundary Layer Flow over an Exponentially Shrinking Vertical Sheet with Suction

Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

Abstract:

A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: Exponentially shrinking sheet, magnetic field, mixed convection, suction.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1094733

References:

[1] B. C. Sakiadis, "Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE J., vol. 7, pp. 26–28, March 1961.
[2] B. C. Sakiadis, "Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface,” AIChE J., vol. 7, pp. 221–225, June 1961.
[3] F. K.Tsou, E. M. Sparrow, and R.J. Goldstein, "Flow and heat transfer in the boundary layer on a continuous moving surface,” Int J Heat Mass Transfer, vol. 10, pp. 219–235, February 1967.
[4] L. J. Crane, "Flow past a stretching plate,” ZAMP, vol. 21, pp. 645–647, July 1970.
[5] L. G. Grubka and K. M. Bobba, "Heat transfer characteristics of a continuous stretching surface with variable temperature,” Trans ASME J Heat Transfer, vol. 107, pp. 248–250, Feb 1985.
[6] V.G. Fox, L.E. Erickson, and L.T. Fan, "Methods for solving the boundary layer equations for moving continuous flat surfaces with suction and injection,” AIChE J., vol. 14, 726–736, September 1968.
[7] C. K. Chen and M. Char, "Heat Transfer over a Continuous Stretching Surface with Suction and Blowing,” J. Math. Anal. Appl., vol. 135, pp. 568–580, November 1988.
[8] P. S. Gupta and A. S. Gupta, "Heat and mass transfer on a stretching sheet with suction or blowing,” Canad. J. Chem. Eng., vol. 55, pp. 744–746, December 1977.
[9] E. Magyari and B. Keller, "Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” J. Phys. D Appl. Phys., vol. 32, pp. 577–585, March 1999.
[10] E. M. A Elbashbeshy, "Heat transfer over an exponentially stretching continuous surface with suction,” Arch. Mech., vol. 53, pp. 643–651, May 2001.
[11] S. K. Khan and E. Sanjayanand, "Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet,” Int. J. Heat Mass Transfer, vol. 48, pp. 1534–1542, April 2005.
[12] E. Sanjayanand and S. K. Khan, "On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet,” Int. J. Therm. Sci., vol. 45, pp. 819–828, August 2006.
[13] M. Sajid and T. Hayat, "Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet,” Int. Comm. Heat Mass Transfer, vol. 35, pp. 347–356, March 2008.
[14] M. K. Partha, P. V. S. N. Murthy, and G.P. Rajasekhar, "Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface,” Heat Mass Transfer, vol. 41, pp. 360–366, February 2005.
[15] T. R. Mahapatra and S. K. Nandy, "Slip effets on unsteady stagnation-point flow and heat transfer over a shrinking sheet,” Meccanica, vol. 48, pp. 1599–1606, September 2013.
[16] M. Miklavčič and C. Y. Wang, "Viscous flow due to a shrinking sheet,” Q. Appl Math., vol. 64, pp. 283–290, April 2006.
[17] T. Hayat, Z. Abbas, and M. Sajid, "On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet,” J. Appl. Mech. Trans. ASME, vol. 74, pp. 1165–1171, Jan 2007.
[18] T. Hayat, T. Javed, and M. Sajid, "Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface,” Phys. Lett. A, vol. 372, pp. 3264–3273, April 2008.
[19] T. Hayat, Z. Abbas, and N. Ali, "MHD flow and mass transfer of an upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species,” Phys. Lett. A, vol. 372, pp. 4698–4704, June 2008.
[20] T. Fang and J. Zhang, "Closed-form exact solutions of MHD viscous flow over a shrinking sheet,” Commun. Nonlinear Sci. Numer.Simulat., vol. 14, pp. 2853–2857, July 2009.
[21] N. F. M. Noor, S. A. Kechil, and I. Hashim, "Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet,” Commun. Nonlin.Sci. Numer. Simulat., vol. 15, pp. 144–148, February 2010.
[22] R. Cortell, "On a certain boundary value problem arising in shrinking sheet flows,” Appl. Math. Comput., vol. 217, pp. 4086–4093, December 2010.
[23] J. H. Merkin and V. Kumaran, "The unsteady MHD boundary-layer flow on a shrinking sheet,” Eur. J. Mech. B Fluids, vol. 29, pp. 357–363, September–October 2010.
[24] K. Bhattacharyya, "Boundary layer flow and heat transfer over an exponentially shrinking sheet,” Chin Phys. Lett., vol. 28, pp. 074701-1–074701-4, April 2011.
[25] A. M. Rohni, S. Ahmad, A. I. M. Ismail and I. Pop, "Boundary layer flow and heat transfer over an exponentially shrinking vertical sheet with suction,” Int. J. Therm. Sci., vol. 64, pp. 264–272, February 2013.