Skip to main content

Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface


The effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The velocity profiles are compared with previously published works and are found to be in good agreement. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite element method. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first-order chemical reaction the concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.

This is a preview of subscription content, access via your institution.


  1. Gebhart, B.: Heat transfer. New York: McGraw Hill, 1971.

  2. Soundalgeker, V. M.: Free convection effects on Stokes problem for a vertical plate. J. Heat Transfer ASME 99C, 499–501 (1977).

    Google Scholar 

  3. Soundalgeker, V. M., Patil, M. R.: Stokes problem for vertical plate with constant heat flux. J. Astrophys Space Sci. 64,165–172 (1980).

    Google Scholar 

  4. Gebhart, B., Pera, L.: The nature of vertical natural convection flow resulting from the combined buoyancy effects of thermal and mass diffusion. J. Heat Mass Transfer 14, 2025–2050 (1971).

    Google Scholar 

  5. Fairbanks, D. F., Wike, C. R.: Diffusion and chemical reaction in an isothermal laminar flow along a soluble flat plate. Ind. Eng. Chem. Res. 42, 471–475 (1950).

    Google Scholar 

  6. Soundalgekar, V. M., Birajdar, N. S., Darwekar, V. K.: Mass transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux. Astrophys. Space Sci. 100, 159–164 (1984).

    Google Scholar 

  7. Muthucumaraswamy, R, Ganesan, P.: On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species. Forsch. Ing.-Wes. 66, 17–23 (2000).

    Google Scholar 

  8. Ghaly, A. Y., Seddeek, M. A.: Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity. Chaos Solitons Fractals 19, 61–70 (2004).

    Google Scholar 

  9. Goren, S. L.: The role of thermophoresis in laminar flow of a viscous and incompressible fluid. J. Colloid Interface Sci. 61, 77 (1977).

    Google Scholar 

  10. Tsai, R.: A simple approach for evaluating the effect of wall suction and thermophoresis on aerosol particle deposition from a laminar flow over a flate plate. Int. Comm. Heat Mass Transf. 26, 249–257 (1999).

    Google Scholar 

  11. Chang, Y. P.,Tsai, R., Sui, F. M.: The effect of thermophoresis on particle deposition from a mixed convection flow onto a vertical flat plate. J. Aerosol Sci. 30,1363–1378 (1999).

    Google Scholar 

  12. Chamkha, A. J., Camille, I.: Effects of heat generation/absorption and thermophoresis on hydromagnetic flow with heat and mass transfer over a flat surface. Int. J. Num. Meth. Heat Fluid Flow 10, 432–448 (2000).

    Google Scholar 

  13. 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 Transf. 31, 421–430 (2004).

    Google Scholar 

  14. Herwing, H., Gersten, K.: The effect of variable properties on laminar boundary layer flow. Wärme Stoffübertr 20, 47–52 (1986).

    Google Scholar 

  15. Seddeek, M. A.: The effect of variable viscosity on hydromagnetic flow and heat transfer past a continuously porous boundary with radiation. Int. Comm. Heat Mass Transf. 27, 1037–1048 (2000).

    Google Scholar 

  16. Seddeek, M. A.: Effects of magnetic field and variable viscosity on forced non–Darcy flow about a flat plate with variable wall temperature in porous media in the presence of suction and bellowing. J. Appl. Mech. Tech. Phys. 43, 13–17 (2002).

    Google Scholar 

  17. Ling, J. X., Dybbs, A.: Forced convection over a flat plate submersed in a porous medium, variable viscosity case. Paper 87-WA/HT-23. New York: ASME 1987.

  18. Weast, R. C.: Hand book of chemistry and physics, 67th ed. Boca Raton: C.R.C. Press 1986–1987.

  19. Talbot, L., Cheng, R. K., Scheffer, R. W., Wills, D. P: Thermophoresis of particles in a heated boundary layer. J. Fluid Mech. 101, 737–758 (1980).

    Google Scholar 

  20. Shen, C.: Thermophoretic deposition of particles onto cold surface of bodies in two–dimensional and axi-symmetric flows. J. Colloid Interface Sci. 127, 104–115 (1989).

    Google Scholar 

  21. Batchelor, G. K., Shen, C.: Thermophoretic deposition in gas flow over cold surfaces. J. Colloid Interface Sci. 107, 21–37 (1985).

    Google Scholar 

  22. White, F.: Viscous fluid flow. 1st ed. New York: McGraw-Hill, 1974.

  23. Reddy, J. N.: An introduction to the finite element method. McGraw-Hill International Editions 1984.

  24. Bejan, A.: Convection heat transfer. 3rd ed. New York: Wiley 2004.

  25. Bhargava, R., Kumar, L., Takhar, H. S.: Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet. Int. J. Engng Sci. 41, 2161–2178 (2003).

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to M. A. Seddeek.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Seddeek, M.A. Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface. Acta Mechanica 177, 1–18 (2005).

Download citation


  • Heat Transfer
  • Finite Element Method
  • Heat Surface
  • Buoyancy Force
  • Chemical Reaction Parameter