Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-05T04:30:02.720Z Has data issue: false hasContentIssue false
  • English
  • Français

Effect of Non-Uniform Heat Generation on Unsteady MHD Flow Over a Vertical Stretching Surface with Variable Thermal Conductivity

Published online by Cambridge University Press:  14 November 2013

M. Muthtamilselvan ,
D. Prakash  and
D.-H. Doh
M. Muthtamilselvan*
Affiliation:
Department of Applied Mathematics, Bharathiar University, Coimbatore-641 046, India
D. Prakash
Affiliation:
Department of Applied Mathematics, Bharathiar University, Coimbatore-641 046, India
D.-H. Doh
Affiliation:
Division of Mechanical and Energy Systems Engineering, College of Engineering, Korea Maritime University, Busan 606-791, South Korea
*
[email protected]
Get access

Abstract

The effect of space and temperature dependent heat generation/absorption on an unsteady laminar boundary layer flow of viscous, incompressible, radiating and electrically conducting fluid over a vertical stretching permeable surface is investigated numerically in the presence of applied magnetic field and buoyancy force. By applying similarity analysis, the governing partial differential equations are transformed into a set of non-linear coupled ordinary differential equations and they are solved by Runge-Kutta-Fehlberg method along with shooting technique. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and heat transfer rate are presented through graphs and tables for several set of values of governing parameters.

Keywords

MHDBuoyancy forceNon-uniform heat source/sinkVariable fluid propertyStretching permeable surface
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 2 , April 2014 , pp. 199 - 208
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013 

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

REFERENCES

1.Sakiadis, B. C., “Boundary Layer Behavior on Continuous Solid Surfaces,” Journal of American Institute of Chemical Engineering, 7, pp. 26–28 (1961).Google Scholar
2.Sparrow, M. E. and Cess, R. D., “Effect of Magnetic Field on Free Convection Heat Transfer,” International Journal of Heat and Mass Transfer, 3, pp. 267–274 (1961).CrossRefGoogle Scholar
3.Singh, K. R. and Cowling, T. G., “Thermal Conduction in Magneto Hydrodynamics,” Journal of Mechanics and Applied Mathematics, 16, pp. 1–5 (1963).Google Scholar
4.Riley, N., “Magneto Hydrodynamic Free Convection,” Journal of Fluid Mechanics, 18, pp. 577–586 (1964).CrossRefGoogle Scholar
5.Crane, L., “Flow Past a Stretching Plate,” Zeitschrift für angewandte Mathematik und Physik, 21, pp. 645–647 (1970).CrossRefGoogle Scholar
6.Gupta, P. S. and Gupta, A. S., “Heat and Mass Transfer on a Stretching Sheet with Suction or Blowing,” Canadian Journal of Chemical Engineers, 55, pp. 744–746 (1977).Google Scholar
7.Hayat, T., Waqas, M., Shehzad, S. A. and Alsaedi, A., “Mixed Convection Radiative Flow of Maxwell Fluid Near a Stagnation Point with Convective Condition,” Journal of Mechanics, 29, pp. 403–409 (2013).Google Scholar
8.Wang, C. Y., “Liquid Film on an Unsteady Stretching Surface,” Quarterly of Applied Mathematics, 48, pp. 601–10 (1990).Google Scholar
9.Andersson, H. I., Aarseth, J. B., Braud, N. and Dandapat, B. S., “Flow of a Power Law Fluid Film on an Unsteady Stretching Surface,” Journal of Non-Newtonian Fluid Mechanics, 62, pp. 1–8 (1996).Google Scholar
10.Andersson, H. I., Aarseth, J. B. and Dandapat, B. S., “Heat Transfer in a Liquid Film on an Unsteady Stretching Surface,” International Journal of Heat and Mass Transfer, 43, pp. 69–74 (2000).Google Scholar
11.Ishak, A., Nazar, R. and Pop, I., “Boundary Layer Flow and Heat Transfer over an Unsteady Stretching Vertical Surface,” Meccanica, 44, pp. 369–375 (2009).CrossRefGoogle Scholar
12.Mustafa, M., Hayat, T. and Alsaedi, A., “Unsteady Boundary Layer Flow of Nanofluid Past an Impulsively Stretching Sheet,” Journal of Mechanics, 29, pp. 423–432 (2013).CrossRefGoogle Scholar
13.Hossain, M. A. and Takhar, H. S., “Radiation Effect on Mixed Convection Along a Vertical Plate with Uniform Surface Temperature,” International Journal Heat and Mass Transfer, 31, pp. 243–248 (1996).CrossRefGoogle Scholar
14.Takhar, H. S., Gorla, R. S. R. and Soundalgekar, V. M., “Radiation Effects on MHD Free Convection Flow of a Gas Past a Semi-Infinite Vertical Plate,” International Journal of Numerical Methods for Heat and Fluid Flow, 6, pp. 77–83 (1996).Google Scholar
15.Seddeek, M. A., “Effects of Radiation and Variable Viscosity on a MHD Free Convection Past a SemiInfinite Flat Plate with an Aligned Magnetic Field in the Case of Unsteady Flow,” International Journal of Heat and Mass Transfer, 45, pp. 931–935 (2002).Google Scholar
16.Pal, D., “Heat and Mass Transfer in StagnationPoint Flow Towards a Stretching Surface in the Presence of Buoyancy Force and Thermal Radiation,” Meccanica, 44, pp. 145–58 (2009).Google Scholar
17.Abo-Eldahab, E. M. and EI-Aziz, M. A., “Blowing/Suction on Hydro Magnetic Heat Transfer by Mixed Convection from an Inclined Continuously Stretching Surface with Internal Heat Generation/Absorption,” International Journal of Thermal Sciences, 43, pp. 709–719 (2004).CrossRefGoogle Scholar
18.Abel, M. S., Siddheshwar, P. G. and Nandeppanavar, M. M., “Heat Transfer in a Viscoelastic Boundary Layer Flow over a Stretching Sheet with Viscous Dissipation and Non-Uniform Heat Source,” International Journal of Heat and Mass Transfer, 50, pp. 960–966 (2007).Google Scholar
19.Bataller, R. C., “Viscoelastic Fluid Flow and Heat Transfer over a Stretching Sheet Under the Effects of a Non-Uniform Heat Source, Viscous Dissipation and Thermal Radiation,” International Journal of Heat and Mass Transfer, 50, pp. 3152–3162 (2007).CrossRefGoogle Scholar
20.Pal, D. and Mondal, H., “Effect of Variable Viscosity on MHD Non-Darcy Mixed Convection Heat Transfer over a Stretching Sheet Embedded in a Porous Medium with Non-Uniform Heat Source/Sink,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 1533–1564 (2010).Google Scholar
21.Pal, D., “Combined Effects of Non-Uniform Heat Source/Sink and Thermal Radiation on Heat Transfer over an Unsteady Stretching Permeable Surface,” Communications in Nonlinear Science and Numerical Simulation, 16, pp. 1890–1904 (2011).Google Scholar
22.Chiam, T. C., “Heat Transfer with Variable Conductivity in a Stagnation Point Flow Towards a Stretching Sheet,” International Communications Heat and Mass Transfer, 23, pp. 239–248 (1996).Google Scholar
23.Chiam, T. C., “Heat Transfer in a Fluid with Variable Thermal Conductivity over a Linearly Stretching Sheet,” Acta Mechanica, 129, pp. 63–72 (1998).Google Scholar
24.Mahmoud, M. A. A., “Thermal Radiation Effects on MHD Flow of a Micro Polar Fluid over a Stretching Surface with Variable Thermal Conductivity,” Physica A, 375, pp. 401–410 (2007).Google Scholar
25.Rahman, M. M., Uddin, M. J. and Aziz, A., “Effects of Variable Electric Conductivity and Non-Uniform Heat Source (or Sink) on Convective Micro Polar Fluid Flow Along an Inclined Flat Plate with Surface,” International Journal of Thermal Sciences, 48, pp. 2331–2340 (2009).CrossRefGoogle Scholar
26.Liu, I. C. and Megahed, A. M., “Numerical Study for the Flow and Heat Transfer in a Thin Liquid Film over an Unsteady Stretching Sheet with Variable Fluid Properties in the Presence of Thermal Radiation,” Journal of Mechanics, 28, pp. 291–297 (2012).Google Scholar
27.Vajravelu, K. and Prasad, K. V., “Heat Transfer Phenomena in a Moving Nanofluid over a Horizontal Surface,” Journal of Mechanics, 28, pp. 579–588 (2012).Google Scholar
28.Savvas, T. A., Markatos, N. C. and Papaspyrides, C. D., “On the Flow of Non-Newtonian Polymer Solutions,” Applied Mathematical Modelling, 18, pp. 14–21 (1994).CrossRefGoogle Scholar
29.Brewster, M. Q., Thermal Radiation Transfer Properties, Wiley, New York (1972).Google Scholar
30.Das, K., “Impact of Thermal Radiation on MHD Slip Flow over a Flat Plate with Variable Fluid Properties,” Heat Mass Transfer, 48, pp. 767–778 (2012).Google Scholar
31.Ishak, A., Nazar, R. and Pop, I., “Heat Transfer over an Unsteady Stretching Permeable Surface with Prescribed Wall Temperature,” Nonlinear Analysis: Real World Applications, 10, pp. 2909–2913 (2009).Google Scholar
32.Vajravelu, K., Prasad, K. V. and Chiu-On, Ng., “Unsteady Convective Boundary Layer Flow of a Viscous Fluid at a Vertical Surface with Variable Fluid Properties,” Nonlinear Analysis: Real World Applications, 14, pp. 455–464 (2013).Google Scholar
33.Mohamed, R. A. and Abo-Dahab, S. M., “Influence of Chemical Reaction and Thermal Radiation on the Heat and Mass Transfer in MHD Micro Polar Flow over a Vertical Moving Porous Plate in a Porous Medium with Heat Generation,” International Journal of Thermal Sciences, 48, pp. 1800–1813 (2009).CrossRefGoogle Scholar
34.Burmeister, L. C., Convective Heat Transfer, Wiley, New York (1983).Google Scholar
35.Kays, W. M. and Crawford, M. E., Convective Heat and Mass Transfer, 2nd Edition, McGraw-Hill, New York (1987)Google Scholar