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Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method

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Abstract

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u (y, t) has been studied and the results are plotted.

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References

  1. Gerhart P M.Fundamentals of Fluid Mechanics [M]. Wesly Publishing Comp Inc. 1993, 11–20.

  2. Vujanovic B, Stauss A M, Djukic Dj, A variational solution of the Rayleigh problem for a power law non-Newtonian conducting fluid [J].Ingenieur-Archiv, 1972,41:381–386.

    Article  MATH  Google Scholar 

  3. Sapunkov Ya G. Rayleigh problem of non-Newtonian electroconductive fluids [J].J Appl Math Tech Physics 1970,2:50–55.

    Google Scholar 

  4. Vujanovic B. An approach to linear and nonlinear heat transfer problem using a Lagrangian [J].J AIAA, 1971,9:327–330.

    Article  Google Scholar 

  5. Birkhoff G. Mathematics for engineers [J].Elect Eng, 1948,67:1185–1192.

    Google Scholar 

  6. Morgan A J A. The reduction by one of the number of independent variables in some systems of nonlinear partial differential equations [J].Quart J Math Oxford, 1952,3(2):250–259.

    MATH  Google Scholar 

  7. Abd-el-Malek M B, Badran N A. Group method analysis of unsteady free-convective laminar boundary-layer flow on a nonisothermal vertical circular cylinder [J].Acta Mechanica, 1990,85: 193–206.

    Article  MATH  MathSciNet  Google Scholar 

  8. Abd-el-Malek M B, Boutros YZ, Badran N A. Group method analysis of unsteady free-convective boundary-layer flow on a nonisothermal vertical flat plate [J].J Engineering Mathematics, 1990,24:343–368.

    Article  MATH  MathSciNet  Google Scholar 

  9. Boutros Y Z, Abd-el-Malek M B, El-Awadi A, et al. Group method for temperature analysis of thermal stagnant lakes [J].Acta Mechanica, 1999,114:131–144

    Article  MathSciNet  Google Scholar 

  10. Fayez H M, Abd-el-Malek M B. Symmetry reduction to higher order nonlinear diffusion equation [J].Int J Appl Math, 1999,1:537–548.

    MathSciNet  Google Scholar 

  11. Ames W F. Similarity for the nonlinear diffusion equation [J].J & EC Fundamentals, 1965,4: 72–76.

    Article  Google Scholar 

  12. Moran M J, Gaggioli RA. Reduction of the number of variables in partial differential equations with auxiliary conditions [J].SIAM J Applied Mathematics, 1968,16:202–215.

    Article  MATH  MathSciNet  Google Scholar 

  13. Burden R, Faires D.Numerical Analysis [M] Prindle: Weberand Scmidt, 1985.

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, 21544, Alexandria, Egypt

    Mina B. Abd-el-Malek & Nagwa A. Badran

  2. Department of Basic and Applied Science, Arab Academy for Science and Technology and Maritime Transport, P O Box 1029, Alexandria, Egypt

    Hossam S. Hassan

Authors
  1. Mina B. Abd-el-Malek
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  2. Nagwa A. Badran
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  3. Hossam S. Hassan
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Communicated by WU Cheng-ping

Biographies: M. B. Abd-el-Malek

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Abd-el-Malek, M.B., Badran, N.A. & Hassan, H.S. Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method. Appl Math Mech 23, 639–646 (2002). https://doi.org/10.1007/BF02437647

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  • DOI: https://doi.org/10.1007/BF02437647

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