ANALYTIC SOLUTION OF HEAT AND MASS TRANSFER OVER A PERMEABLE STRETCHING PLATE AFFECTED BY CHEMICAL REACTION, INTERNAL HEATING, DUFOUR-SORET EFFECT AND HALL EFFECT

Abstract

The analytical solution is derived for the steady MHD mixed convection, laminar, heat and mass transfer over an isothermal, inclined permeable stretching sheet, immersed in a uniform porous medium in the presence of chemical reaction, thermal radiation, Dufour and Soret effects, an external transverse magnetic field, and internal heating. The governing equations are transformed into a dimensionless coupled system of non-linear ordinary differential equations and then solved analytically by the homotopy analysis method. A parametric study illustrating the influence of the chemical reaction, magnetic field, porous medium inertia parameter, and the Dufour and Soret numbers on the fluid velocity, temperature, and concentration are investigated through the obtained analytic solution. As well as the local Nusselt and the Sherwood numbers is conducted. The obtained results are presented graphically and the physical aspects of the problem are discussed. The obtained solution has been tested numerically for some values of the system parameters. Comparison with previously reported numerical results is tabulated and agreement is recorded. Analytic form of some characteristic parameters, e. g. the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, stress at the stretching surface, local mass transfer coefficient, the local wall mass flux, the local heat transfer coefficient and the local heat flux, are given due to the obtained analytic solution.

Keywords

Dates

  • Submission Date2008-06-12
  • Revision Date2008-11-26
  • Acceptance Date2009-02-15

DOI Reference

10.2298/TSCI0902183A

References

  1. Sakiadis, B. C., Boundary Layer Behavior on Continuous Solid Surface: I. Boundary Layer Equations for Two-Dimensional and Axisymmetric Flow, AIChE J., 7 (1961), 1, pp. 26-28
  2. Sakiadis, B. C., Boundary-Layer Behavior on Continuous Solid Surface: The Boundary Layer on a Continuous Flat Surface, AIChE J., 7 (1961), 2, pp. 221-225
  3. Crane, L. J., Flow Past a Stretching Plate, Z. Angew. Math. Phys., 21 (1970), 4, pp. 645-647
  4. Andersson, H. I., MHD Flow of a Visco-Elastic Fluid Past a Stretching Surface, Acta. Mech., 95 (1992), 1-4, pp. 227-230
  5. Dey, J., Nath, G., Mixed Convection Flow on Vertical Surface, Wärme Stoffübertragung, 15 (1981), 1, pp. 279-283
  6. De Hoog, F. R., Laminger, B., Weiss, R., A Numerical Study of Similarity Solutions for Combined Forced and Free Convection, Acta Mechanica, 51 (1984), 3-4, pp. 139-149
  7. Schneider, W., Laminar Mixed Convection Flows on Horizontal Surfaces, Third Caribbean Congress on Fluid Dynamics, Caracas, Venezuela, 1995, vol. 1, pp. 1-7
  8. Chamkha, A. J., Hameed, Al-Naser, Hydro-Magnetic Double-Diffusive Convection in a Rectangular Enclosure with Opposing Temperature and Concentration Gradients, International Journal of Heat and Mass Transfer, 45 (2002), 12, pp. 2465-2483
  9. Merkin, J. H., Pop, I., Mixed Convection along a Vertical Surface: Similarity Solutions for Uniform Flow, Fluid Dynamics Research, 30 (2002), 4, pp. 233-250
  10. Seddeek, M. A., Finite Element Method for the Effects Chemical Reaction, Variable Viscosity, Thermo-Phoresis and Heat Generation/Absorption on a Boundary-Layer Hydromagnetic Flow with Heat and Mass Transfer over a Heat Surface, Acta Mechanica, 177 (2005), 1-4, pp. 1-18
  11. Kandasamy, P., Periasamy, K., Sivagnana Prabhu, K. K., Effects of Chemical Reaction, Heat and Mass Transfer along a Wedge with Heat Source and Concentration in the Presence of Suction or Injection, Int. J. Heat and Mass Transfer, 48 (2005), 7, pp. 1388-1394
  12. Anjalidevi, S. P., Kandasamy, R., Effect of Chemical Reaction, Heat and Mass Transfer on Laminar Flow along a Semi Infinite Horizontal Plate, Heat and Mass Transfer, 35 (1999), 6, pp. 465-472
  13. Cortell, R., MHD Flow and Mass Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species, Ch. Eng. and Proc., 46 (2007), 8, pp. 721-728
  14. Kafoussias, N. G., Williams, E. W., Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Free-Forced Convective and Mass Transfer Boundary Layer Flow with Temperature Dependent Viscosity, International Journal of Engineering Science, 33 (1995), 9, pp. 1369-1384
  15. Afify, A., Effects of Temperature-Dependent Viscosity with Soret and Dufour Numbers on Non-Darcy MHD Free Convective Heat and Mass Transfer Past a Vertical Isothermal Surface Embedded in a Porous Medium, Transport in Porous Media, 66 (2007), 3, pp. 391-401
  16. Seddeek, M. A., Finite Element Method for the Effect of Various Injection Parameter on Heat Transfer for a Power-Law Non-Newtonian Fluid over a Stretched Surface with Thermal Radiation, Comp. Mater. Sci., 37 (2006), 4, pp. 624-627
  17. Afify, A., Effects of Variable Viscosity on Non-Darcy MHD Free Convection along a Non-Isothermal Vertical Surface in a Thermally Stratified Porous Medium, Appl. Math. Modeling, 31 (2007), 8, pp. 1621-1634
  18. 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 and Fractals, 19 (2004), 1, pp. 61-70
  19. Postelnicu, A., Influence of a Magnetic Field on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects, Int. J. Heat Mass Transfer, 47 (2004), 6-7, pp. 1467-1472
  20. Postelnicu, A., Influence of Chemical Reaction on Heat and Mass Transfer by Natural Convection from Vertical Surfaces in Porous Media Considering Soret and Dufour Effects, Heat Mass Transfer, 43 (2007), 6, pp. 595-602
  21. Seddeek, M. A., Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Free-Forced Convective Flow and Mass Transfer over an Accelerating Surface with a Heat Source in the Presence of Suction and Blowing in the Case of Variable Viscosity, Acta Mechanica, 172 (2004), 1-2, pp. 83-94
  22. Abd El-Aziz, M., Temperature Dependent Viscosity and Thermal Conductivity Effects on Combined Heat and Mass Transfer in MHD Three-Dimensional Flow over a Stretching Surface with Ohmic Heating, Meccanica, 42 (2007), 2, pp. 375-386
  23. Liao, S.-J., Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, Fla., USA, 2003
  24. Xu, H., Liao, S.-J., Dual Solutions of Boundary Layer Flow over an Upstream Moving Plate, Comm. Nonlin. Sci. Num. Sim., 13 (2008), 2, pp. 350-358.
  25. Abdallah, I. A., Homotopy Analytical Solution of MHD Fluid Flow and Heat Transfer Problem, Applied Mathematics and Information Sciences, 3 (2009), 2, pp. 223-233
  26. Liao, S.- J., An Analytic Solution of Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate, Commun. Non-Linear Sci. Numer. Simul., 11 (2006), 3, pp. 326-339
Volume 13, Issue 2, Pages183 -197