Some new exact solutions for MHD aligned creeping flow and heat transfer in second grade fluids by using Lie group analysis

The Lie group analysis and the basic similarity reductions are performed for the MHD aligned slowly flowing and heat transfer in second grade fluid with neglecting the inertial terms. When the inertia terms are simply omitted from the equations of motions the resulting solutions are valid approximately for Re≺≺1. This fact can also be deduced from the dimensionless form of the momentum and energy equations. By employing Lie group theory, the full one-parameter infinitesimal transformation group leaving the equations of motion invariant is derived along with its associated Lie algebra. Subgroups of the full group are then used to obtain a reduction by one in the number of independent variable in the system. Two new exact solutions generated from the similarity transformation to these equations, are provided. Comparisons with previously work is performed and the result is found to be inexcellent. Finally, some boundary value problems are discussed.