0
Research Papers: Radiative Heat Transfer

Effect of Induced Magnetic Field on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer on a Stretching Sheet

[+] Author and Article Information
A. Sinha

School of Medical Science and Technology,
Indian Institute of Technology,
Kharagpur 721302, India

J. C. Misra

Department of Mathematics,
Institute of Technical Education and Research,
Siksha O Anusandhan University,
Bhubaneswar 751030, India
e-mail: misrajc@rediffmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received December 5, 2011; final manuscript received April 22, 2013; published online August 18, 2014. Assoc. Editor: Alfonso Ortega.

J. Heat Transfer 136(11), 112701 (Aug 18, 2014) (11 pages) Paper No: HT-11-1549; doi: 10.1115/1.4024666 History: Received December 05, 2011; Revised April 22, 2013

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sakiadis, B. C., 1961, “Boundary Layer Behavior on Continuous Solid Surfaces: I. Boundary Layer Equations for Two Dimensional and Axisymmetric Flow,” AICHE J., 7, pp. 26–28. [CrossRef]
Sakiadis, B. C., 1961, “Boundary Layer Behavior on Continuous Solid Surfaces: II. Boundary Layer on a Continuous Flat Surface,” AICHE J., 7, pp. 221–225. [CrossRef]
Tsou, F. K., Sparrow, E. M., and Goldstein, R. J., 1967, “Flow and Heat Transfer in the Boundary Layer on a Continuous Moving Surface,” Int. J. Heat Mass Transfer, 10, pp. 219–223. [CrossRef]
Crane, L. J., 1970, “Flow Past a Stretching Plate,” Z. Angew. Math. Phys., 21, pp. 645–647. [CrossRef]
Tzirtzilakis, E. E., and Kafoussias, N. G., 2003, “Biomagnetic Fluid Flow Over a Stretching Sheet With Nonlinear Temperature Dependent Magnetization,” J. Appl. Math. Mech., 54, pp. 551–565. [CrossRef]
Tzirtzilakis, E. E., and Kafoussias, N. G., 2010, “Three-Dimensional Magnetic Fluid Boundary Layer Flow Over a Linearly Stretching Sheet,” ASME J. Heat Transfer, 132, p. 011702. [CrossRef]
Tzirtzilakis, E. E., and Tanoudis, G. B., 2003, “Numerical Study of Biomagnetic Fluid Flow Over a Stretching Sheet With Heat Transfer,” Int. J. Numer. Methods Heat Fluid Flow, 13, pp. 830–848. [CrossRef]
Beavers, G. S., and Joseph, D. D., 1967, “Boundary Conditions at a Natural Permeable Wall,” J. Fluid Mech., 30, pp. 197–207. [CrossRef]
Misra, J. C., Patra, M. K., and Misra, S. C., 1993, “A Non-Newtonian Fluid Model for Blood Flow Through Arteries Under the Stenotic Conditions,” J. Biomech., 26, pp. 1129–1141. [CrossRef] [PubMed]
Misra, J. C., and Shit, G. C., 2007, “Role of Slip Velocity in Blood Flow Through Stenosed Arteries: A Non-Newtonian Model,” J. Mech. Med. Biol., 7, pp. 337–353. [CrossRef]
Misra, J. C., and Kar, B. K., 1989, “Momentum Integral Method for Studying Flow Characteristics of Blood Through a Stenosed Vessel,” Biorheology, 26, pp. 23–25. [PubMed]
Vand, V., 1948, “Viscosity of Solutions and Suspensions,” J. Phys. Colloid chem.52, pp. 277–321. [CrossRef] [PubMed]
Nubar, Y., 1971, “Blood Flow, Slip, and Viscometry,” J. Biophys., 11, pp. 252–264. [CrossRef]
Brunn, P., 1975, “The Velocity Slip of Polar Fluids,” Rheol. Acta, 14, pp. 1039–1054. [CrossRef]
Ebart, W. A., and Sparrow, E. M., 1965, “Slip Flow in Rectangular and Annular Ducts,” J. Basic Eng., 87, pp. 1018–1024. [CrossRef]
Sparrow, E. M., Beavers, G. S., and Hung, L. Y., 1971, “Flow About a Porous-Surfaced Rotating Disk,” Int. J. Heat Mass Transfer, 14, pp. 993–996. [CrossRef]
Sparrow, E. M., Beavers, G. S., and Hung, L. Y., 1971, “Channel and Tube Flows With Surface Mass Transfer and Velocity Slip,” Phys. Fluids, 14, pp. 1312–1319. [CrossRef]
Wang, C. Y., 2002, “Stagnation Flow With Slip: Exact Solution of Navier-Stokes Equations,” Chem. Eng. Sci., 57, pp. 3745–3747. [CrossRef]
Ramachandran, N., Chen, T. S., and Armaly, B. F., 1988, “Mixed Convection in Stagnation Flows Adjacent to a Vertical Surfaces,” ASME J. Heat Transfer, 110, pp. 373–377. [CrossRef]
Chiam, T. C., 1994, “Stagnation-Point Flow Towards a Stretching Plate,” J. Phys. Soc. Jpn., 63, pp. 2443–2444. [CrossRef]
Chen, C. H., 2010, “Combined Effects of Joule Heating and Viscous Dissipation on Magnetohydrodynamic Flow Past a Permeable, Stretching Surface With Free Convection and Radiative Heat Transfer,” ASME J. Heat Transfer, 132, p. 064503. [CrossRef]
Lok, Y. Y., Amin, N., Campean, D., and Pop, I., 2005, “Steady Mixed Convection Flow of a Micropolar Fluid Near the Stagnation Point on a Vertical Surface,” Int. J. Numer. Methods Heat Fluid Flow, 15, pp. 654–670. [CrossRef]
Ishak, A., Nazar, R., and Pop, I., 2008, “Magnetohydrodynamic (MHD) Flow of a Micropolar Fluid Towards a Stagnation Point on a Vertical Surface,” Comput. Math. Appl., 56, pp. 3188–3194. [CrossRef]
Ishak, A., Nazar, R., and Pop, I., 2007, “Mixed Convection on the Stagnation Point Flow Toward a Vertical, Continuously Stretching Sheet,” ASME J. Heat Transfer, 129, pp. 1087–1090. [CrossRef]
Takhar, H. S., Kumari, M., and Nath, G., 1993, “Unsteady Free Convection Flow Under the Influence of a Magnetic Field,” Arch. Appl. Mech., 63, pp. 313–321. [CrossRef]
Kumari, M., and Nath, G., 2009, “Steady Mixed Convection Stagnation-Point Flow of Upper Convected Maxwell Fluids With Magnetic Field,” Int. J. Non-Linear Mech., 44, pp. 1048–1055. [CrossRef]
Cobble, M. H., 1979, “Free Convection With Mass Transfer Under the Influence of a Magnetic Field,” Nonlinear Anal. Theory, Methods Appl., 3, pp. 135–143. [CrossRef]
Davies, T. V., 1962, “The Magneto-Hydrodynamic Boundary Layer in the Two-Dimensional Steady Flow Past a Semi-Infinite Flat Plate I, Uniform Conditions at Infinity,” Proc. R. Soc. London, 273, pp. 496–508. [CrossRef]
Datti, P. S., Prasad, K. V., Abel, M. S., and Joshi, A., 2004, “MHD Visco-Elastic Fluid Flow Over a Non-Isothermal Stretching Sheet,” Int. J. Eng. Sci., 42, pp. 935–946. [CrossRef]
Hartmann, J., 1937, “Hg-Dynamics I, Theory of the Laminar Flow of an Electrically Conducting Liquid in a Homogenous Magnetic Field,” Mat. Fys. Medd. K. Dan. Vidensk. Selsk., 15, pp. 1–28.
Kafoussias, N. G., and Williams, E. M., 1993, “Improved Approximation Technique to Obtain Numerical Solution of a Class of Two-Point Boundary Value Similarity Problems in Fluid Mechanics,” Int. J. Numer. Methods Fluids, 17(2), pp. 145–162. [CrossRef]
Hayat, T., Qasim, M., and Mesloub, S., 2011, “MHD Flow and Heat Transfer Over Permeable Stretching Sheet With Induced Magnetic Field,” Int. J. Numer. Methods Fluids, 66, pp. 963–975. [CrossRef]
Ali, F. M., Nazar, R., Arifin, N. M., and Pop, I., 2011, “MHD Stagnation-Point Flow and Heat Transfer Towards Stretching Sheet With Induced Magnetic Field,” Appl. Math. Mech., 32(4), pp. 409–418. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Physical sketch of the problem

Grahic Jump Location
Fig. 2

Nature of velocity distribution for different values of β with λ = 1.0,Sf = 0.25, and a/c = 2.5

Grahic Jump Location
Fig. 3

Variation of induced magnetic field in x-direction for different values of β with λ = 1.0,Sf = 0.25, and a/c = 2.5

Grahic Jump Location
Fig. 4

Temperature distribution for different values of β, when λ = 1.0,Sf = 0.25, a/c = 2.5, Pr = 0.72, Nr = 2.0, and St = 1.0

Grahic Jump Location
Fig. 5

Velocity distribution for different values of a/c, if λ = 1.0,Sf = 0.25, and β = 0.5

Grahic Jump Location
Fig. 6

Variation of the induced magnetic field in x-direction for different values of a/c, when λ = 1.0,Sf = 0.25, and β = 0.5

Grahic Jump Location
Fig. 7

Temperature distribution for different values of a/c, if λ = 1.0,Sf = 0.25,β = 0.5, Pr = 0.72, Nr = 2.0, and St = 1.0

Grahic Jump Location
Fig. 8

Velocity distribution for different values of Sf when λ = 1.0, a/c = 2.5, and β = 0.5

Grahic Jump Location
Fig. 9

Variation of induced magnetic field in x-direction for different values of Sf if λ = 1.0, a/c = 2.5, and β = 0.5

Grahic Jump Location
Fig. 10

Temperature distribution for different values of Pr, when λ = 1.0,Sf = 0.25,β = 0.5, a/c = 2.5, Nr = 2.0, and St = 1.0

Grahic Jump Location
Fig. 11

Temperature distribution for different values of Nr, if λ = 1.0,Sf = 0.25,β = 0.5, a/c = 2.5, Pr = 0.72, and St = 1.0

Grahic Jump Location
Fig. 12

Temperature distribution for different values of St, when λ = 1.0,Sf = 0.25,β = 0.5, a/c = 2.5, Pr = 0.72, and Nr = 2.0

Grahic Jump Location
Fig. 13

Variation of skin-friction with β for different values of λ, when a/c = 2.5 and Sf = 0.25

Grahic Jump Location
Fig. 14

Axial velocity distribution in the absence of induced magnetic field and velocity slip (when a/c = 0). (Comparison of the results of the present study with the analytical solution of Crane [4].)

Grahic Jump Location
Fig. 15

Comparison of velocity distribution between the results of the present study with those of Ali et al. [33]

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In