A variational solution of the Rayleigh problem for a power law non-Newtonian conducting fluid

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 nonstationary flow of this electrically conducting fluid in a transverse magnetic field is then analyzed. The solution to this highly non-linear problem is obtained by means of a new variational principle developed by the authors. This new principle allows one to obtain the solution in a straightforward manner. Unlike other variational techniques in dissipative physics the authors' possesses a pure Hamiltonian structure and obeys all the laws of the classical variational calculus. It is shown that the influence of the magnetic field is greater on the coefficient of friction of dilatant fluids than pseudo-plastic fluids. In the absence of a magnetic field the thickness of the boundary layer increases with increasing powers of the fluid. Finally, the shape of the velocity profile is more strongly dependent on the magnetic field strength for pseudo-plastic fluids than for dilatant fluids. © 1972 Springer-Verlag.