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MHD free convective flow past semi-infinite vertical permeable wall

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Abstract

In this paper, the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partial differential equations are reduced to a set of non-linear ordinary differential equations by applying a suitable similarity transformation. Approximate solutions of the transformed equations are obtained by employing the perturbation method for two cases, i.e., small and large values of the suction parameter. From the numerical evaluations of the solution, it can be seen that the velocity field at any point decreases as the values of the magnetic and suction parameters increase. The effect of the magnetic parameter is to increase the thermal boundary layer. It is also found that the velocity and temperature fields decrease with the increase in the sink parameter.

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Abbreviations

Ha :

magnetic parameter (Hartmann number)

B 0 :

magnetic field

cp :

specific heat at constant pressure

f w :

dimensionless wall mass transfer coefficient

g :

acceleration due to gravity

N :

temperature gradient

Pr :

Prandtl number

T :

temperature of the fluid

T ∞ :

temperature of the free steam

T w :

temperature of the wall

u, υ :

fluid velocity components in the x- and ydirection in the non-dimensional form

x :

coordinate along the wall

y :

coordinate perpendicular to the walls

β :

coefficient of thermal expansion

κ :

thermal conductivity

µ:

dynamic viscosity of the fluid

θ :

temperature of the fluid in the nondimensional form

ϑ :

kinematic viscosity of the fluid

υ 0 :

suctionvelocity

ρ :

fluid density

ϕ :

dimensionless heat source/sink parameter

φ :

dimensionless positive parameter (ϕ = −φ) for small suction

ρ :

electrical conductivity of the fluid

Ψ :

stream function

g8 :

free-stream condition

References

  1. Pohlhausen, E. Der wareastausch zwischen festen korpenn und flussigkeiten mit kleineer reibung und kleinerwarmeletung. Zeitschrift für Angewandte Mathematik und Mechanik, 1, 115–121 (1921)

    Article  MATH  Google Scholar 

  2. Ostrach, S. An Analysis of Laminar Free Convection Flow Heat Transfer about a Flat Plate Parallel to the Direction of the Generating Body Force, NASA Report No. 1111, Washington, D. C. (1953)

  3. Siegel, R. Transient free convection from a vertical flat plate. Transactions of the American Society of Mechanical Engineers, 80, 374–375 (1958)

    Google Scholar 

  4. Gebhart, B. Transient natural convection from vertical elements. ASME Journal of Heat Transfer, 83C, 61–70 (1961)

    Article  Google Scholar 

  5. Cheng, P. Combined free and forced convection about inclined surface in porous medium. International Journal of Heat and Mass Transfer, 28, 807–814 (1977)

    Google Scholar 

  6. Singh, A. K. Boundary-layer flows with swirl and large suction. Applied Scientific Research, 35, 59–65 (1979)

    Article  MATH  Google Scholar 

  7. Singh, A. K. and Rai, K. D. Unsteady free convective flow of water at 4 °C past a semi-infinite vertical plate by finite difference method. Modeling Simulation and Control B, 12, 9–16 (1987)

    Google Scholar 

  8. Ali, M. and Al-Yousef, F. Laminar mixed convection form a continuously moving vertical surface with suction or injection. Heat and Mass Transfer, 33, 301–306 (1998)

    Article  Google Scholar 

  9. Raptis, A. and Perdikis, C. Free convection flow of water near 4 °C past a moving plate. Forschung im Ingenieurwesen, 67, 206–208 (2002)

    Article  Google Scholar 

  10. Chandran, P., Sacheti, N. C., and Singh, A. K. Natural convection near a vertical plate with ramped wall temperature. Heat and Mass Transfer, 41, 459–464 (2005)

    Article  Google Scholar 

  11. Patel, M. and Timol, M. G. Numerical solution of the equation for unsteady boundary layer flow of non-Newtonian fluids past semi-infinite plate. International Journal of Applied Mathematics and Mechanics, 5, 22–29 (2009)

    Google Scholar 

  12. Kulandaivel, T., Loganathan, P., and Muthucumaraswamy, R. Chemical reaction on moving vertical plate with constant mass flux in presence of thermal radiation. International Journal of Applied Mathematics and Mechanics, 5, 84–95 (2009)

    Google Scholar 

  13. Hartmann, J. Hg-dynamics I theory of the laminar flow of an electrically conductive liquid in a homogenous magnetic field. Det Kongelige Danske Videnskabernes Selskab Mathematisk-fysiske Meddeleser, XV, 1–27 (1937)

    Google Scholar 

  14. Cramer, K. R. and Pai, S. I. Magnetofluid Dynamics for Engineering and Applied Physicists, McGraw-Hill, New York (1973)

    Google Scholar 

  15. Takhar, H. S., Raptis, A., and Perdikis, C. MHD asymmetric flow past a semi-infinite moving plate. Acta Mechanica, 65, 278–290 (1987)

    Article  Google Scholar 

  16. Chandran, P., Sacheti, N. C., and Singh, A. K. Effects of rotation on unsteady hydrodynamic Couette flow. Astrophysics and Space Science, 202, 1–10 (1993)

    Article  MATH  Google Scholar 

  17. Chandran, P., Sacheti, N. C., and Singh, A. K. Haydromagnetic flow and heat transfer past a continuously moving porous boundary. International Communication in Heat and Mass Transfer, 23, 889–898 (1996)

    Article  Google Scholar 

  18. Chandran, P., Sacheti, N. C., and Singh, A. K. Unsteady hydromagnetic free convection flow with heat flux and accelerated boundary motion. Journal of Physical Society of Japan, 67, 124–129 (1998)

    Article  MATH  Google Scholar 

  19. Chandran, P., Sacheti, N. C., and Singh, A. K. An undefined approach to analytical solution of a hydromagnetic free convection flow. Scientiae Mathematicae Japonicae, 53, 467–476 (2001)

    MathSciNet  MATH  Google Scholar 

  20. Singh, A. K., Chandran, P., and Sacheti, N. C. Effects of transverse magnetic field on a flat plate thermometer problem. International Journal of Heat and Mass Transfer, 43, 3253–3258 (2000)

    Article  MATH  Google Scholar 

  21. Mohapatra, T. R. and Gupta, A. S. Magnetohydrodynamic stagnation-point flow towards a stretching sheet. Acta Mechanica, 152, 191–196 (2001)

    Article  Google Scholar 

  22. Takhar, H. S., Singh, A. K., and Nath, G. Unsteady MHD flow and heat transfer on a rotating disk in an ambient fluid. International Journal of Thermal Sciences, 41, 147–155 (2002)

    Article  Google Scholar 

  23. Sharma, P. R. and Singh, G. Unsteady MHD free convective flow and heat transfer along a vertical porous plate with variable suction and internal heat generation. International Journal of Applied Mathematics and Mechanics, 4, 1–8 (2008)

    Google Scholar 

  24. Ambethkar, V. Numerical solutions of heat and mass transfer effects of an unsteady MHD free convective flow past an infinite vertical plate with constant suction and heat source and sink. International Journal of Applied Mathematics and Mechanics, 5, 96–115 (2009)

    Google Scholar 

  25. Chamkha, A. J. MHD flow of numerical of uniformly stretched vertical permeable surface in the presence of heat generator/absorption and a chemical reaction. International Communications in Heat and Mass Transfer, 30, 413–422 (2003)

    Article  Google Scholar 

  26. Abdelkhalek, M. M. The skin friction in the MHD mixed convection stagnation point with mass transfer. International Communications in Heat and Mass Transfer, 33, 249–258 (2006)

    Article  Google Scholar 

  27. Singh, R. K., Singh, A. K., Sacheti, N. C., and Chandran, P. On hydromagnetic free convection in the presence of induced magnetic field. Heat and Mass Transfer, 46, 523–529 (2009)

    Article  Google Scholar 

  28. Ali, F. M., Nazar, R., Arifin, N. M., and Pop, I. MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field. Applied Mathematics and Mechanics (English Edition), 32, 409–418 (2011) DOI 10.1007/s10483-011-1426-6

    Article  MathSciNet  MATH  Google Scholar 

  29. Su, X. H. and Zheng, L. C. Approximate solutions to MHD Falkner-Skan flow over permeable wall. Applied Mathematics and Mechanics (English Edition), 32, 401–408 (2011) DOI 10.1007/s10483-011-1425-9

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    R. K. Singh & A. K. Singh

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Singh, R.K., Singh, A.K. MHD free convective flow past semi-infinite vertical permeable wall. Appl. Math. Mech.-Engl. Ed. 33, 1207–1222 (2012). https://doi.org/10.1007/s10483-012-1616-7

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  • DOI: https://doi.org/10.1007/s10483-012-1616-7

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