Deductive group symmetry analysis for a free convective boundary-layer flow of electrically conducting non-Newtonian fluids over a vertical porous-elastic surface

General group symmetry analysis so-called deductive group-theoretical method is applied to analyze the free convective boundary-layer problem due to the motion of an elastic surface into an electrically conducting a class of non-Newtonian fluid. The symmetry groups admitted by the corresponding boundary value problem are obtained. Particular attention is paid on the deductive group which provides the similarity solution of the problem. Also, the admissible form of the data, in order to be conformed to the obtained symmetries, is provided. Finally, with the use of the entailed similarity variables the problem is transformed into a boundary value problem of ODEs and is solved numerically for particular non-Newtonian fluid so-called powell-eyring fluid.