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.
Rayleigh problem group method non-linearity conducting fluid non-Newtonian power law fluid
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Gerhart P M.Fundamentals of Fluid Mechanics [M]. Wesly Publishing Comp Inc. 1993, 11–20.Google Scholar
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
Sapunkov Ya G. Rayleigh problem of non-Newtonian electroconductive fluids [J].J Appl Math Tech Physics 1970,2:50–55.Google Scholar
Vujanovic B. An approach to linear and nonlinear heat transfer problem using a Lagrangian [J].J AIAA, 1971,9:327–330.CrossRefGoogle Scholar
Birkhoff G. Mathematics for engineers [J].Elect Eng, 1948,67:1185–1192.Google Scholar
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
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
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
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
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
Ames W F. Similarity for the nonlinear diffusion equation [J].J & EC Fundamentals, 1965,4: 72–76.CrossRefGoogle Scholar
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