Advertisement

Applied Mathematics and Mechanics

, Volume 23, Issue 6, pp 639–646 | Cite as

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

  • Mina B. Abd-el-Malek
  • Nagwa A. Badran
  • Hossam S. Hassan
Article

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.

Key words

Rayleigh problem group method non-linearity conducting fluid non-Newtonian power law fluid 

CLC numbers

O361.4 O152.9 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Gerhart P M.Fundamentals of Fluid Mechanics [M]. Wesly Publishing Comp Inc. 1993, 11–20.Google Scholar
  2. [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.zbMATHCrossRefGoogle Scholar
  3. [3]
    Sapunkov Ya G. Rayleigh problem of non-Newtonian electroconductive fluids [J].J Appl Math Tech Physics 1970,2:50–55.Google Scholar
  4. [4]
    Vujanovic B. An approach to linear and nonlinear heat transfer problem using a Lagrangian [J].J AIAA, 1971,9:327–330.CrossRefGoogle Scholar
  5. [5]
    Birkhoff G. Mathematics for engineers [J].Elect Eng, 1948,67:1185–1192.Google Scholar
  6. [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.zbMATHGoogle Scholar
  7. [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.zbMATHMathSciNetCrossRefGoogle Scholar
  8. [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.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [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, 1999,114:131–144MathSciNetCrossRefGoogle Scholar
  10. [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.MathSciNetGoogle Scholar
  11. [11]
    Ames W F. Similarity for the nonlinear diffusion equation [J].J & EC Fundamentals, 1965,4: 72–76.CrossRefGoogle Scholar
  12. [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.zbMATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    Burden R, Faires D.Numerical Analysis [M] Prindle: Weberand Scmidt, 1985.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

  • Mina B. Abd-el-Malek
    • 1
  • Nagwa A. Badran
    • 1
  • Hossam S. Hassan
    • 2
  1. 1.Department of Engineering Mathematics and Physics, Faculty of EngineeringAlexandria UniversityAlexandriaEgypt
  2. 2.Department of Basic and Applied ScienceArab Academy for Science and Technology and Maritime TransportAlexandriaEgypt

Personalised recommendations