Skip to main content
Log in

Homotopy analysis method for chemical reaction and thermophoresis effects on heat and mass transfer for mhd hiemenz flow over a porous wedge in the presence of heat radiation

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

An analytical technique, namely, the homotopy analysis method, is applied to analyze the effect of chemical reaction and thermophoresis particle deposition on the MHD mixed convective heat and mass transfer for a Hiemenz flow over a porous wedge in the presence of heat radiation. The fluid is assumed to be viscous and incompressible. Analytical and numerical calculations are carried out for different values of dimensionless parameters, and an analysis of the results obtained shows that the flow field is influenced appreciably by the buoyancy ratio as well as by the thermal diffusion and suction/injection parameters. The effects of these parameters on the process characteristics are investigated methodically, and typical results are illustrated. An explicit, totally analytical, and uniformly valid solution is derived which agrees well with numerical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. A. Fuchs, The Mechanics of Aerosols, Macmillan Co., New York (1964).

    Google Scholar 

  2. S. L. Goren, Thermophoresis of aerosol particles in laminar boundary layer on flat plate, J. Colloid Interface Sci., 61, 77–85 (1977).

    Article  Google Scholar 

  3. W. G. England and A. F. Emery, Thermal radiation effects on laminar free convection boundary layer of an absorbing gas, J. Heat Transfer, 31, 37–44 (1969).

    Google Scholar 

  4. A. Raptis, Flow of a micropolar fluid past a continuously moving plate by the presence of radiation, Int. J. Heat Mass Transfer, 41, 2865–2866 (1998).

    Article  MATH  Google Scholar 

  5. K. Hiemenz, Die Grenzschicht an einem in den gleichformigen Flussigkeitsstrom eingetauchten geraden Kreiszylinder, Dingl. Polytech. J., 326, 321–410 (1911).

    Google Scholar 

  6. E. R. G. Eckert, Die berechnung des warmeubergangs in der laminaren grenzschung auf dem gebiete des Ingenierwesens, Forschungsheft Journal, 416, 1–6 (1942).

    MathSciNet  Google Scholar 

  7. P. D. Ariel, Hiemenz flow in hydromagnetic, Acta Mech., 103, 31–43 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  8. K. A. Yih, The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media, Acta Mech., 130, 147–158 (1998).

    Article  MATH  Google Scholar 

  9. P. L. Chambre and J. D. Acrivos, Analysis of catalytic surface reactions in hydrodynamic flows, J. Appl. Phys., 27, 1322–1329 (1956).

    Article  Google Scholar 

  10. P. L. Chambre and A. Acrivos, Diffusion of a chemically reactive species in a laminar boundary layer flow, Ind. Eng. Chem., 49, 1025–1031 (1957).

    Article  Google Scholar 

  11. H. Schlichting, Boundary Layer Theory, McGraw Hill Inc., New York (1979), pp. 164–165.

    MATH  Google Scholar 

  12. T. Watanabe, Thermal boundary layer over a wedge with uniform suction or injection in forced flow, Acta Mech., 83, 119–126 (1990).

    Article  Google Scholar 

  13. N. G. Kafoussias and N. D. Nanousis, Magnetohydrodynamic laminar boundary layer flow over a wedge with suction or injection, Can. J. Phys., 75, 733–745 (1997).

    Article  Google Scholar 

  14. M. Kumari, Effect of large blowing rates on the steady laminar incompressible electrically conducting fluid over an infinite wedge with a magnetic field applied parallel to the wedge, Int. J. Eng. Sci., 36, 299–306 (1998).

    Article  MATH  Google Scholar 

  15. Kuo Bor-Lih, Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method, Int. J. Heat Mass Transfer, 48, 5036–5046 (2005).

    Article  MATH  Google Scholar 

  16. W. T. Cheng and H. T. Lin, Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge, Int. J. Eng. Sci., 40, 531–539 (2002).

    Article  Google Scholar 

  17. S. P. Anjali Devi and R. Kandasamy, Thermal stratification effects on laminar boundary layer flow over a wedge with suction or injection, Mech. Res. Commun., 28, 349–354 (2001).

    Article  MATH  Google Scholar 

  18. S. P. Anjali Devi and R. Kandasamy, Effects of heat and mass transfer on MHD laminar boundary layer flow over a wedge with suction or injection, J. Energ. Heat Mass Transf., 23, 167–172 (2001).

    Google Scholar 

  19. A. J. Chamkha and A. R. A. Khaled, Similarity solutions for hydromagnetic simultaneous heat and mass transfer, Heat Mass Transfer, 37, 117–124 (2001).

    Article  Google Scholar 

  20. A. Pantokratoras, The Falkner–Skan flow with constant wall temperature and variable viscosity, Int. J. Therm. Sci., 45, 378–389 (2006).

    Article  Google Scholar 

  21. M. A Hossain, M. A. Alim, and D. A. S. Rees, The effects of radiation on free convection from a porous plate, Int. J. Heat Mass Transfer, 42, 181–191 (1999).

    Article  MATH  Google Scholar 

  22. A. J. Chamkha and K. K. Khaled, Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media, Int. J. Numer. Methods Heat Fluid Flow, 10, 94–115 (2000).

    Article  MATH  Google Scholar 

  23. A. M. Rashad, Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles, Commun. Nonlin. Sci. Numer. Simul., 13, 2213–2222 (2008).

    Article  Google Scholar 

  24. S. Gill, A process for the step-by-step integration of differential equations in an automatic digital computing machine, Proc. Cambridge Philos. Soc., 47, 96–108 (1951).

    Article  MATH  MathSciNet  Google Scholar 

  25. S. J. Liao, The Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problems, Ph.D. Dissertation, Shanghai Jiao Tong University, Shanghai (1992).

    Google Scholar 

  26. S. J. Liao, An approximate solution technique which does not depend upon small parameters: a special example, Int. J. Nonlin. Mech., 30, 371–380 (1995).

    Article  MATH  Google Scholar 

  27. S. J. Liao, A uniformly valid analytic solution of two-dimensional viscous flow over a semi-infinite flat plate, J. Fluid Mech., 385, 101–128 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  28. S. J. Liao, An explicit, totally analytic approximate solution for Blasius viscous flow problems, Int. J. Nonlin. Mech., 34, 759–778 (1999).

    Article  MATH  Google Scholar 

  29. S. J. Liao, An analytic approximation of the drag coefficient for the viscous flow past a sphere, Int. J. Nonlin. Mech., 37, 1–18 (2000).

    Article  Google Scholar 

  30. S. J. Liao and A. Campo, Analytic solutions of the temperature distribution in Blasius viscous flow problems, J. Fluid Mech., 453, 411–425 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  31. J. L. Bansal, Boundary Layer Theory, Oxford and IBM Publishing Co. (1986), pp. 169–170.

  32. R. Kandasamy, K. Periasamy, and K. K. Sivagnana Prabhu, Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects, Int. J. Heat Mass Transfer, 48, 4557–4561 (2005).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. Puvi Arasu.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal Vol. 84 No. 3 pp. 458–469 May–June 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kandasamy, R., Muhaimin, I., Puvi Arasu, P. et al. Homotopy analysis method for chemical reaction and thermophoresis effects on heat and mass transfer for mhd hiemenz flow over a porous wedge in the presence of heat radiation. J Eng Phys Thermophy 84, 495–508 (2011). https://doi.org/10.1007/s10891-011-0497-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-011-0497-5

Keywords

Navigation