Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T13:32:46.196Z Has data issue: false hasContentIssue false
  • English
  • Français

MHD Mixed Convection of Viscoelastic Fluid Over a Stretching Sheet with Ohmic Dissipation

Published online by Cambridge University Press:  05 May 2011

K.-L. Hsiao
K.-L. Hsiao*
Affiliation:
Department of the Computer & Communication, Diwan College of Management, Tainan, Taiwan 72153, R.O.C.
*
*Assitant Professor
Get access

Abstract

A magnetic hydrodynamic (MHD) mixed convection of an incompressible viscoelastic fluid over a stretching sheet with ohmic dissipation is studied. The buoyant effect and the electric number E1 couple with magnetic parameter M to represent the dominance of the ohmic effect are presented in governing equations which is the main contribution by this study. The similarity transformation, the finitedifference method have been used to analyze the present problem. The numerical solutions of the flow velocity distributions, temperature profiles and the important wall unknown values of f″(0) and θ′(0) are carried out.

Keywords

Viscoelastic fluidStretching sheetMagnetic fieldMixed convectiveOhmic dissipationFinite-difference.
Type
Technical Note
Information
Journal of Mechanics , Volume 24 , Issue 3 , September 2008 , pp. N29 - N34
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Hartnett, J. P., “Viscoelastic Fluids: A New Challenge in Heat Transfer,” Transactions of ASME, pp. 296–303 (1992).Google Scholar
2.Srivatsava, A. C., “The Flow of a Non-Newtonian Liquid Near a Stagnation Point,” Z. Angew. Math. Phys., pp. 80–84 (1958).CrossRefGoogle Scholar
3.Rajeswari, G. and Rathna, S. L., “Flow of a Particular Class of Non-Newtonian Visco-Elastic and Visco-Inelastic Fluids Near a Stagnation Point,” Z. Angew. Math. Phys., pp. 43–57 (1962).CrossRefGoogle Scholar
4.Mishra, S. P. and Panda, T. C., “Effect of Injection on the Flow of Second Order Fluid in the Inlet Region of a Channel,” Acta Mech., pp, 11–17 (1979).CrossRefGoogle Scholar
5.Rajagopal, K. R., Gupta, A. S. and Na, T. Y., “A Note on the Falkner-Skan Flows of a Non-Newtonian Fluid,” Int. J. Non-linear Mech., pp. 313–320 (1983).CrossRefGoogle Scholar
6.Massoudi, M. and Ramezan, M., “Effect of Injection or Suction on the Falkner-Skan Flows of Second Grade Fluids,” Int. J. Non-linear Mech., pp. 221–227 (1989).CrossRefGoogle Scholar
7.Rajagopal, K. R., “Boundary Layers in Non-linear Fluids, Pitman Monographs and Surveys in Pure and Applied Mathematics,” pp. 209–218 (1995).Google Scholar
8.Vajravelu, K. and Soewono, E., “Fourth Order Non-Linear Systems Arising in Combined Free and Forced Convection Flow of a Second Order Fluid,” Int. J. Non-Linear Mech., 29, pp. 861–869 (1994).CrossRefGoogle Scholar
9.Garg, V. K. and Rajagopal, K. R., “Stagnation Point Flow of a Non-Newtonian Fluid,” Mechanics Research Communications, 17, pp. 415–421 (1990).CrossRefGoogle Scholar
10.Raptis, A. A., “Heat Transfer From Flow of an Elastico Viscous Fluid,” Int. Comm. Heat Mass Transfer, 16, pp. 193–197 (1989).CrossRefGoogle Scholar
11.Mahmoud, E.M. Ouaf, “Exact Solution of Thermal Radiation on MHD Flow Over a Stretching Porous Sheet,” Applied Mathematics and Computation, 170, pp. 1117–1125 (2005).Google Scholar
12.Datti, P. S., Prasad, K. V., Subhas, Abel, M. and Ambuja, Joshi., “MHD Visco-Elastic Fluid Flow Over a Non- Isothermal Stretching Sheet,” International Journal of Engineering Science, 42, pp. 935–946 (2004).CrossRefGoogle Scholar
13.Sanjayanand, Emmanuel and Sujit Kumar, Khan., “On Heat and Mass Transfer in a Viscoelastic Boundary Layer Flow Over an Exponentially Stretching Sheet,” International Journal of Thermal Sciences, 45, pp. 819–828 (2006).CrossRefGoogle Scholar
14.Rafael, Cortell., “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,” Chemical Engineering and Processing, 46, pp. 721–728 (2007).Google Scholar
15.Seddeek, M. A., “Heat and Mass Transfer on a Stretching Sheet with a Magnetic Field in a Visco-Elastic Fluid Flow Through a Porous Medium with Heat Source or Sink,” Computational Materials Science, 38, pp. 781–787 (2007).CrossRefGoogle Scholar
16.Liu, C. and Kong, C. H., “Heat Transfer of an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet,” Journal of Mechanics, 21, pp. 5–13 (2005).CrossRefGoogle Scholar
17.Liu, C., “Exact Solutions for a Fluid-Saturated Porous Medium with Heat and Mass Transfer,” Journal of Mechanics, 21, pp. 57–62 (2005).CrossRefGoogle Scholar
18.Liu, Chi-Min. and Liu, I-Chung., “A Note on the Transient Solution of Stokes' Second Problem with Arbitrary Initial Phase,” Journal of Mechanics, 22, pp. 349–354 (2006).CrossRefGoogle Scholar
19.Cheng, P. J. and Liu, K. C., “Stability Analysis on Viscous Magnetic Fluid Film Flowing Down Along a Vertical Cylinder,” Journal of Mechanics, 23, pp. 127–134 (2007).CrossRefGoogle Scholar
20.Rivlin, R. S. and Ericksen, J. L., “Stress Deformation Relation for Isotropic Materials,” J. Rat. Mech. Analysis, pp. 323–425 (1955).CrossRefGoogle Scholar
21.Markovitz, H. and Coleman, B. D., Advances in Applied Mechanics, 8, Academic Press, New York (1964).Google Scholar
22.Acrivos, A., “A Theoretical Analysis of Laminar Natural Convection Heat Transfer to Non-Newtonian Fluids,” Am. Inst. Chem. Eng. J., pp. 584–590 (1960).CrossRefGoogle Scholar
23.Beard, D. W. and Walters, K., “Elastico viscous boundary layer flows,” Proc. Camb. Phil. Soc., pp. 661–614 (1964).Google Scholar
24.Cebeci, T. and Bradshaw, P., Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag (1984).CrossRefGoogle Scholar
25.Hsiao, Kai-Long. and Chen, Guan-Bang, “Conjugate Heat Transfer of Mixed Convection for Viscoelastic Fluid Past a Stretching Sheet,” Mathematical Problems in Engineering, Article ID 17058, 21, pp. doi: 10.1155/2007/17058 (2007).CrossRefGoogle Scholar
26.Hsiao, Kai-Long., “Conjugate Heat Transfer of Magnetic Mixed Convection with Radiative and Viscous Dissipation Effects for Second Grade Viscoelastic Fluid past a Stretching Sheet,” Applied Thermal Engineering, 27/11–12, pp. 1895–1903 (2007).CrossRefGoogle Scholar
27.Chapra, and Canale, , Numerical Methods for Engineers, McGraw-Hill, 2ed (1990)Google Scholar