Advertisement

Transport in Porous Media

, Volume 104, Issue 2, pp 273–288 | Cite as

Mixed Convection in a Darcy–Brinkman Porous Medium with a Constant Convective Thermal Boundary Condition

  • Asterios PantokratorasEmail author
Article

Abstract

The characteristics of the boundary layer flow past a plane surface adjacent to a saturated Darcy–Brinkman porous medium are investigated in this paper. The flow is driven by an external free stream moving with constant velocity. The surface is heated with a convective boundary condition with constant heat transfer coefficient. The problem is non-similar and is investigated numerically by a finite difference method. The problem is governed by four non-dimensional parameters, that is, the convective Darcy number, the convective Grashof number, the Prandtl number, and the axial distance along the plate. The influence of these parameters on the results is investigated, and the results are presented in tables and figures. The Darcy term and the Grashof term in the momentum equation contradict each other and this contradiction makes the problem complicated. However, the wall shear stress and the wall temperature increase continuously along the plate and the wall temperature always tends to 1.

Keywords

Darcy-Brinkman porous medium Mixed convection Heat transfer Convective parameter Non-similar 

References

  1. Acharya, S., Murthy, J.: Foreword to the special Issue on computational heat transfer. ASME J. Heat Transf. 129, 405–406 (2007)CrossRefGoogle Scholar
  2. Anderson, D., Tannehill, J., Pletcher, R.: Computational Fluid Mechanics and Heat Transfer. McGraw-Hill, New York (1984)Google Scholar
  3. Aziz, A.: A similarity solution for laminar thermal boundary layer over flat plate with convective surface boundary condition. Commun. Nonlinear Sci. Numer. Simul. 14, 1064–1068 (2009)CrossRefGoogle Scholar
  4. Ishak, A.: Similarity solutions for flow and heat transfer over permeable surface with convective boundary conditions. Appl. Math. Comput. 217, 837–842 (2010)CrossRefGoogle Scholar
  5. Magyari, E.: Comment on ‘A similarity solution for laminar thermal boundary layer flow over a flat plate with a convective surface boundary condition’ by A Aziz in Comm Nonlin Sci Numer Sim 14:1064–1068 (2009). Commun. Nonlinear Sci. Numer. Simul. 16, 599–610 (2011)CrossRefGoogle Scholar
  6. Makinde, O.D., Aziz, A.: MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition. Int. J. Therm. Sci. 49, 1813–1820 (2010)CrossRefGoogle Scholar
  7. Merkin, J.H.: Natural convection boundary-layer flow on a vertical surface with Newtonian heating. Int. J. Heat Fluid Flow 15, 392–398 (1994)CrossRefGoogle Scholar
  8. Merkin, J.H., Pop, I.: The forced convection flow of a uniform stream over a flat surface with a convective surface boundary condition. Commun. Nonlinear Sci. Numer. Simul. 16, 3602–3609 (2011)CrossRefGoogle Scholar
  9. Merkin, J.H., Lok, Y.Y., Pop, I.: Mixed convection boundary-layer flow on a vertical surface in a porous medium with constant convective boundary condition. Transp. Porous Med. 99, 413–425 (2013)CrossRefGoogle Scholar
  10. Oosthuizen, P., Naylor, D.: Introduction to Convective Heat Transfer Analysis. Graw-Hill, New York (1999)Google Scholar
  11. Pantokratoras, A.: The nonsimilar laminar wall plume in a constant transverse magnetic field. Int. J. Heat Mass Transf. 52, 3873–3878 (2009a)CrossRefGoogle Scholar
  12. Pantokratoras, A.: The nonsimilar laminar wall jet with uniform blowing or suction: New results. Mech. Res. Commun. 36, 747–753 (2009b)CrossRefGoogle Scholar
  13. Pantokratoras, A.: Nonsimilar aiding mixed convection along a moving cylinder in a free stream. ZAMP 61, 309–315 (2010)CrossRefGoogle Scholar
  14. Pantokratoras, A.: A note on natural convection along a convectively heated vertical plate. Int. J. Therm. Sci. 76, 221–224 (2014)CrossRefGoogle Scholar
  15. Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. McGraw-Hill Book Company, New York (1980)Google Scholar
  16. White, F.: Viscous Fluid Flow, 3rd edn. McGraw-Hill, New York (2006)Google Scholar
  17. Yao, S., Fang, T., Zhong, Y.: Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 16, 752–760 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of EngineeringDemocritus University of ThraceXanthiGreece

Personalised recommendations