Acta Mechanica Sinica

, 27:531 | Cite as

Lie group analysis for thermophoretic and radiative augmentation of heat and mass transfer in a Brinkman-Darcy flow over a flat surface with heat generation

  • Faiza A. SalamaEmail author
Research Paper


A boundary layer analysis is presented to investigate numerically the effects of radiation, thermophoresis and the dimensionless heat generation or absorption on hydromagnetic flow with heat and mass transfer over a flat surface in a porous medium. The boundary layer equations are transformed to non-linear ordinary differential equations using scaling group of transformations and they are solved numerically by using the fourth order Runge-Kutta method with shooting technique for some values of physical parameters. Comparisons with previously published work are performed and the results are found to be in very good agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles as well as the local skin-friction coefficient, wall heat transfer, particle deposition rate and wall thermophoretic deposition velocity. The results show that the magnetic field induces acceleration of the flow, rather than deceleration (as in classical magnetohydrodynamics (MHD) boundary layer flow) but to reduce temperature and increase concentration of particles in boundary layer. Also, there is a strong dependency of the concentration in the boundary layer on both the Schmidt number and mass transfer parameter.


Lie group analysis Brinkman-Darcy flow Boundary layer Heat and mass transfer 


  1. 1.
    Nield, D.A., Bejan, A.: Convection in Porous Media. (2nd edn), Springer, New York (1998)Google Scholar
  2. 2.
    Ingham, D.B., Pop, I.: Transport Phenomena in Porous Media. Pergamon Press, Oxford (1998)zbMATHGoogle Scholar
  3. 3.
    Vafai, K.: Handbook of Porous Media. Marcel Dekker, New York (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Pop, D.B. Ingham: Convective Heat Transfer: Mathematical and ComputationalModeling of Viscous Fluid and Porous Media. Pergamon Press, Oxford (2001)Google Scholar
  5. 5.
    Brinkman, H.C.: A calculation of the viscous forces extred by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. 47, 27–34 (1947)Google Scholar
  6. 6.
    Tong, T.W., Subramanian, E.: Boundary layer analysis for natural convection in porous Enclosure: use of the Brinkman extended Darcy model. Int. J. Heat Mass Transfer. 28, 563–571 (1985)zbMATHCrossRefGoogle Scholar
  7. 7.
    Lauriat, G., Prasad, V.: Natural convction in a vertical porous cavity: a numerical study for Brinkman-extended Darcy formulation. Trans. ASME J. Heat Transfer 109, 295–320 (1987)CrossRefGoogle Scholar
  8. 8.
    Nield, D.A.: Onset of thermohaline convection in a porous medium. Water Resour. Res. 4, 553–560 (1968)CrossRefGoogle Scholar
  9. 9.
    Khan, A.A., Zebib, A.: Double diffusive instability in a vertical layer of a porous medium. J. Heat Transfer 103, 179–181 (1981)CrossRefGoogle Scholar
  10. 10.
    Jang, J.Y., Chang, W.J.: The flow and vortex instability of horizontal natural convection in a porous medium resulting form combined heat and mass buoyancy effects. Int. J. Heat Mass Transfer 31, 769–777 (1988)zbMATHCrossRefGoogle Scholar
  11. 11.
    Seddeek, M.A.: The effect of variable viscosity on hydromagnetic flow and heat transfer past a continuously moving porous boundary with radiation. Int. Comm. Heat Mass Transfer 27,1037–1046 (2000)CrossRefGoogle Scholar
  12. 12.
    Abd El-Naby, M.A., Elbarabry, M.E., Abdelazem, Y.: Finite difference solution of radiation effects on MHD unsteady free-convection flow over vertical plate with variable surface temperature. J. of App. Math. 2, 65–86(2003)CrossRefGoogle Scholar
  13. 13.
    Salem, A.M.: Thermal-diffusion and diffusion-thermo effects on convective heat and mass transfer in a visco-elastic fluid flow through a porous medium over stretching sheet. Communication in Numerical Method in Eng. 22, 955–966 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Salem, A.M.: The influence of thermal conductivity and variable viscosity on the flow of micropolar fluid past a continuously semi-infinite moving plate with suction or injection. Il Nuovo Cimento, 121 B, N. 1, 3–28 (2006)Google Scholar
  15. 15.
    Gokoglu, S.A., Rosner, D.E.: Correlation of thermophoretically modified small particle diffusional deposition rates in forced convection systemwith variable properties, transpiration cooling and/or viscous dissipation. Int. J. Heat Mass Transfer 27, 639–646 (1984a)CrossRefGoogle Scholar
  16. 16.
    Tsai, R.: A simple approach for evaluating the effect of wall suction and thermophoresis on aerosol particle deposition from a laminar flow over a flat plate. Int. Comm. Heat Mass Trans. 26, 249–257 (1999)CrossRefGoogle Scholar
  17. 17.
    Jia, G., Cipolla, J.W., Yener, Y.: Thermophoresis of a radiating aerosol in laminar boundary-layer flow. J. of Thermophysics and Heat Transfer 6, 476–482 (1992)CrossRefGoogle Scholar
  18. 18.
    Jayaraj, S.: Finite difference modeling of natural convection flow with thermophoresis. Int. J. of Numerical Methods for Heat & Fluid Flow 9, 692–704 (1999)zbMATHCrossRefGoogle Scholar
  19. 19.
    Jayaraj, S., Dinesh, K.K., Pillai, K.L.: Thermophoresis in natural convection with variable properties. Heat and Mass Transfer/waerme und Stoffubertragung 34, 469–475 (1999)CrossRefGoogle Scholar
  20. 20.
    Chamkha, A.J., Issa, C.: Effects of heat generation/absorption and thermophoresis on hydromagnetic flow with heat and mass transfer over a flat surface. Int. J. of Numerical Methods for Heat & Fluid Flow 10, 432–448 (2000)zbMATHCrossRefGoogle Scholar
  21. 21.
    Chamkha, A.J., Pop, I.: Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium. Int. Comm. Heat Mass Transfer 31, 421–430 (2004)CrossRefGoogle Scholar
  22. 22.
    Chamkha, A.J., Takhar, H.S.: Radiation effects on free convection flow past a semi-infinite vertical plate with mass transfer. Chemical Eng. Journal 84, 335–342 (2001)CrossRefGoogle Scholar
  23. 23.
    Alam, M.S., Rahman, M.M., Sattar, M.A.: Effects of variable suction and thermophoresis on steady MHD combined free-forced convective heat and mass transfer flow over a semi-infinite permeable inclined plate in the presence of thermal radiation. Int. J. Thermal Sci. 47, 58–65 (2008)CrossRefGoogle Scholar
  24. 24.
    Cogley, A.C., Vincenti, W.G., Gilles, S.E.: Differential approximation for radiative transfer in a non-grey gas near equilibrium. AIAA J. 6, 551–553 (1968)CrossRefGoogle Scholar
  25. 25.
    Talbot, L., Cheng, R.K., Scheffer, R.W., et al.: Thermophoresis of particles in a heated boundary layer. J. Fluid Mechanics 101, 737–758 (1980)CrossRefGoogle Scholar
  26. 26.
    Batchelor, G.K., Shen, C.: Thermophoretic deposition of particles in gas flowing over cold surface. J. Colloid Interface Sci. 107, 21 (1985)CrossRefGoogle Scholar
  27. 27.
    Na, T.Y.: Computational Method in Engineering Boundary Value Problems. Academic Press, New York (1979)Google Scholar
  28. 28.
    White, F.: Viscous Fluid Flow. (1st edn), McGraw-Hill, New York (1974)zbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceSuez Canal UniversitySuezEgypt

Personalised recommendations