MHD Three-Dimensional Flow by an Exponentially Stretching Surface with Convective Boundary Condition
Publication: Journal of Aerospace Engineering
Volume 27, Issue 4
Abstract
Magnetohydrodynamic (MHD) three-dimensional flow of an incompressible fluid induced by an exponentially stretching surface is investigated. Analysis is carried out when the surface exhibits convective condition. Mathematical formulation is completed by employing continuity, momentum, and energy equations. The governing nonlinear partial differential equations are reduced into the ordinary differential equations. Series solutions are constructed for the velocity components and temperature. Results are discussed by plotting graphs. A comparative study between the present solutions is made with the previous available results.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This paper was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Saudi Arabia, under the grant no. (26-130-35-HiCi). The authors therefore, acknowledge with thanks DSR technical and financial support.
References
Abbas, Z., and Hayat, T. (2011). “Stagnation slip flow and heat transfer over a nonlinear stretching sheet.” Numer. Methods Partial Diff. Equ., 27(2), 302–314.
Abbasbandy, S., and Ghehsareh, H. R. (2012). “Solutions of the magnetohydrodynamic flow over a nonlinear stretching sheet and nano boundary layers over stretching surfaces.” Int. J. Numer. Methods Fluids, 70(10), 1324–1340.
Abbasbandy, S., and Shivanian, E. (2011). “Predictor homotopy analysis method and its application to some nonlinear problems.” Commun. Nonlinear Sci. Numer. Simul., 16(6), 2456–2468.
Bhattacharyya, K. (2011). “Boundary layer flow and heat transfer over an exponentially shrinking sheet.” Chin. Phys. Lett., 28(7), 074701.
Bhattacharyya, K., and Layek, G. C. (2011). “MHD boundary layer flow of dilatant fluid in a divergent channel with suction or blowing.” Chin. Phys. Lett., 28(8), 084705.
Bidin, B., and Nazar, R. (2009). “Numerical solution of the boundary layer flow over an exponentially stretching sheet with thermal radiation.” Eur. J. Sci. Res., 33(4), 710–717.
Crane, L. J. (1970). “Flow past a stretching plate.” ZAMP, 21(4), 645–647.
Elbashbeshy, E. M. A. (2001). “Heat transfer over an exponentially stretching continuous surface with suction.” Arch. Mech., 53(6), 643–651.
Hayat, T., Abbasi, F. M., and Obaidat, S. (2011a). “Peristaltic motion with Soret and Dufour effects.” Magnetohydrodynamics, 47(3), 295–302.
Hayat, T., Farooq, M., Iqbal, Z., and Alsaedi, A. (2012a). “Mixed convection Falkner-Skan flow of a Maxwell fluid.” J. Heat Transfer-Trans. ASME, 134(11), 114504-1–114504-6.
Hayat, T., Qasim, M., and Mesloub, S. (2011b). “MHD flow and heat transfer over permeable stretching sheet with slip condition.” Int. J. Num. Methods Fluids, 66(8), 963–975.
Hayat, T., Shehzad, S. A., and Alsaedi, A. (2012b). “Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid.” Appl. Math. Mech., 33(10), 1301–1312.
Hayat, T., Shehzad, S. A., Alsaedi, A., and Alhothuali, M. S. (2012c). “Mixed convection stagnation point flow of Casson fluid with convective boundary conditions.” Chin. Phys. Lett., 29(11), 114704.
Hayat, T., Shehzad, S. A., Mustafa, M., and Hendi, A. A. (2012d). “MHD flow of an Oldroyd-B fluid through a porous channel.” Int. J. Chem. React. Eng., 10(1), 1542–6580.
Hayat, T., Shehzad, S. A., Qasim, M., and Alsaedi, A. (2012e). “Radiative flow with variable thermal conductivity in porous medium.” ZNA, 67a, 153–159.
Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. (2011c). “Flow of a second grade fluid with convective boundary conditions.” Therm. Sci., 15(2), S253–S261.
Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. (2012f). “Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source.” Nucl. Eng. Des., 243, 15–19.
Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. (2011d). “Steady flow of Maxwell fluid with convective boundary conditions.” Z. Naturforsch., 66a, 417–422.
Javed, T., Sajid, M., Abbas, Z., and Ali, N. (2011). “Nonsimilar solution for rotating flow over an exponentially stretching surface.” Int. J. Num. Methods Heat Fluid Flow, 21(7), 903–908.
Liao, S. J. (2003). Beyond perturbation: Introduction to homotopy analysis method, Chapman and Hall, Boca Raton, FL.
Liu, I. C., Wang, H. H., and Peng, Y. F. (2013). “Flow and heat transfer for three-dimensional flow over an exponentially stretching surface.” Chem. Eng. Commun., 200(2), 253–268.
Mahapatra, T. R., Nandy, S. K., and Gupta, A. S. (2009). “Magnetohydrodynamic stagnation point flow of power-law fluid towards a stretching surface.” Int. J. Non-Linear Mech., 44(2), 124–129.
Makinde, O. D. (2011). “Similarity solution for natural convection from a moving vertical plate with internal heat generation and a convective boundary condition.” Therm. Sci., 15(1), S137–S143.
Makinde, O. D., and Aziz, A. (2011). “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition.” Int. J. Therm. Sci., 50(7), 1326–1332.
Makinde, O. D., and Onyejekwe, O. O. (2011). “A numerical study of MHD generalized Couette flow and heat transfer with variable viscosity and electrical conductivity.” J. Magn. Magn. Mater., 323(22), 2757–2763.
Mebine, P., and Adigiom, E. M. (2011). “Effects of thermal radiation on transient MHD free convection flow over a vertical surface embedded in a porous medium with periodic boundary temperature.” Math. Aeterna, 1(4), 245–261.
Moradi, A., Ahmadikia, H., Hayat, T., and Alsaedi, A. (2013). “On mixed convection radiation interaction about an inclined plate through a porous medium.” Int. J. Therm. Sci., 64, 129–136.
Mushtaq, M., Asghar, S., and Hossain, M. A. (2007). “Mixed convection flow of second grade fluid along a vertical stretching surface with variable surface temperature.” Heat Mass Transfer, 43(10), 1049–1061.
Patil, P. M., Gubbi, S. K., Roy, S., and Chamkha, A. J. (2010). “Mixed convection flow over a vertical power-law stretching sheet.” Int. J. Num. Methods Heat Fluid Flow, 20(4), 445–458.
Qian, S., and Bau, H. H. (2009). “Magnetohydrodynamics based microfluidics.” Mech. Res. Commun., 36(1), 10–21.
Rashidi, M. M., Chamkha, A. J., and Keimanesh, M. (2011). “Application of multi-step differential transform method on flow of a second-grade fluid over a stretching or shrinking sheet.” Am. J. Comput. Math., 1(2), 119–128.
Rashidi, M. M., Pour, S. A. M., and Abbasbandy, S. (2011). “Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation.” Commun. Nonlinear Sci. Numer. Simul., 16(4), 1874–1889.
Sahoo, B., and Poncet, S. (2011). “Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition.” Int. J. Heat Mass Transfer, 54(23–24), 5010–5019.
Sajid, M., and Hayat, T. (2008). “Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet.” Int. Commun. Heat Mass Transfer, 35(3), 347–356.
Sakiadis, B. C. (1961). “Boundary layer behaviour on continuous solid surfaces: I boundary layer equations for two dimensional and axisymmetric flow.” AIChE J., 7(1), 26–28.
Sanjayanand, E., and Khan, S. J. (2006). “On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet.” Int. J. Therm. Sci., 45(8), 819–828.
Turkyilmazoglu, M. (2011a). “Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere.” Int. J. Therm. Sci., 50(5), 831–842.
Turkyilmazoglu, M. (2011b). “Thermal radiation effects on the time-dependent MHD permeable flow having variable viscosity.” Int. J. Therm. Sci., 50(1), 88–96.
Vyas, P., and Ranjan, A. (2010). “Dissipative MHD boundary layer flow in a porous medium over a sheet stretching nonlinearly in the presence of radiation.” Appl. Math. Sci., 4(63), 3133–3142.
Yao, B. (2009). “Approximate analytical solution to the Falkner-Skan wedge flow with the permeable wall of uniform suction.” Commun. Nonlinear Sci. Numer. Simul., 14(8), 3320–3326.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 27 • Issue 4 • July 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jan 5, 2013
Accepted: Jun 4, 2013
Published online: Apr 24, 2014
Published in print: Jul 1, 2014
Discussion open until: Sep 24, 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.