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

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. We will study the non-stationary flow of an electrically conducting non-Newtonian fluid of infinite extent in a transverse external magnetic field. The rheological model of this fluid is given by the well-known expression for a power law fluid [Ing. Arch. 41 (1972) 381] τ ij=−pδ ij+k| 1 2 I 2| (n−1)/2e ij, where τ ij is the shear stress, p is the pressure, δ ij is the Kronecker symbol, k the coefficient of consistency, I 2 the second strain rate invariant, e ij the strain rate tensor and n is a parameter characteristic of the non-Newtonian behavior of the fluid. For n=1, the behavior of the fluid is Newtonian, for n>1, the behavior is dilatant and for 0< n