International Journal of Thermophysics

, Volume 32, Issue 10, pp 2079–2091 | Cite as

Mixed Convection of Water at 4 °C Along a Wedge with Variable Surface Temperature in a Porous Medium

  • Waqar A. Khan
  • Rama Subba Reddy GorlaEmail author


In this study, the mixed convection of water at 4 °C along a wedge in a porous medium is investigated numerically using a finite difference method. To explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable walltemperature boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and the Nusselt number are obtained and compared with available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ ranged from 0 to 1 in both regimes, whereas different values of λ are considered for the purpose of comparison of heat transfer results.


Mixed convection Non-similar solutions Nusselt number Skin friction Water Wedge 

List of Symbols


Skin friction


Dimensionless stream function


Acceleration due to gravity, m · s−2


Heat transfer coefficient, W · m−2 · K−1


Permeability of the porous medium, m2


Wedge flow parameter


Nusselt number


Local Peclet number


Local Rayleigh number


Temperature, °C


Free stream velocity, m · s−1

u, v

Velocity components in x- and y-direction

x, y

Coordinates along and normal to wedge surface



Forced convection-dominated regime

Free stream conditions


Free convection-dominated regime



Greek Symbols


Thermal diffusivity of porous medium, m2 · s−1


Thermal expansion coefficient for water at 4 °C, °C−2


Similarity variable


Semi-wedge angle


Temperature variation parameter


Absolute viscosity, Pa · s


Kinematic viscosity, m2 · s−1


Fluid density, kg · m−3


Stream function


Dimensionless temperature


Mixed convection parameter


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  1. 1.
    Weast, R.C. (ed): Handbook of Chemistry and Physics, 65th edn. CRC Press, Boca Raton, FL (1984)Google Scholar
  2. 2.
    Goren S.L.: Chem. Eng. Sci. 21, 515 (1986)Google Scholar
  3. 3.
    Moore D.R., Weiss N.O.: J. Fluid Mech. 61, 553 (1973)ADSCrossRefGoogle Scholar
  4. 4.
    Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1999)zbMATHGoogle Scholar
  5. 5.
    Ingham, D.B., Pop, I. (eds): Transport Phenomena in Porous Media. Pergamon, Oxford (2002)zbMATHGoogle Scholar
  6. 6.
    Pop I., Ingham D.B.: Convective Heat Transfer: Computational and Mathematical Modelling of Viscous Fluids and Porous Media. Pergamon, Oxford (2001)Google Scholar
  7. 7.
    Hassanien I.A., Essawy A.H., Moursy N.M.: Appl. Math. Comput. 145, 667 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Ibrahim F.S., Hassanien I.A.: Transp. Porous Media 39, 5771 (2000)CrossRefGoogle Scholar
  9. 9.
    Gorla R.S.R., Kumari M.: Int. J. Numer. Methods Heat Fluid Flow 9, 601 (1999)zbMATHCrossRefGoogle Scholar
  10. 10.
    Hsieh J.C., Chen T.S., Armaly B.F.: Int. J. Heat Mass Transf. 36, 1485 (1993)zbMATHCrossRefGoogle Scholar
  11. 11.
    Cheng P.: Int. J. Heat Mass Transf. 20, 807 (1987)Google Scholar
  12. 12.
    Vargas J.V.C., Laursen T.A., Bejan A.: Int. J. Heat Fluid Flow 16, 211 (1995)CrossRefGoogle Scholar
  13. 13.
    Bhattacharyya S., Pal A., Pop I.: Int. Commun. Heat Mass Transf. 25, 743 (1998)CrossRefGoogle Scholar
  14. 14.
    Hossain M.A., Bhowmick S., Gorla R.S.R.: Int. J. Eng. Sci. 44, 607 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Ranganathan P., Viskanta R.: Numer. Heat Transf. 7, 305 (1984)ADSzbMATHGoogle Scholar
  16. 16.
    Chen C.H., Chen T.S., Chen C.K.: Int. J. Heat Mass Transf. 39, 1157 (1996)CrossRefGoogle Scholar
  17. 17.
    Goren S.L.: Chem. Eng. Sci. 21, 515 (1986)Google Scholar
  18. 18.
    Kumaran V., Pop I.: Int. J. Heat Mass Transf. 49, 3240 (2006)zbMATHCrossRefGoogle Scholar
  19. 19.
    Takhar H.S., Perdikis C.P.: Int. Commun. Heat Mass Transf. 13, 605 (1986)CrossRefGoogle Scholar
  20. 20.
    Gorla R.S.R., Stratman R.A.: Int. Comm. Heat Mass Transf. 13, 403 (1986)CrossRefGoogle Scholar
  21. 21.
    Raptis A., Pop I.: Lett. Heat Mass Transf. 9, 309 (1982)CrossRefGoogle Scholar
  22. 22.
    Ling S.C., Nazar R., Pop I., Merkin J.H.: Transp. Porous Media 70, 307 (2007)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ling S.C., Nazar R., Pop I.: Transp. Porous Media 69, 359 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Engineering Sciences, PN Engineering CollegeNational University of Science and TechnologyKarachiPakistan
  2. 2.Department of Mechanical EngineeringCleveland State UniversityClevelandUSA

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