Some exact solutions for MHD flow and heat transfer to modified second grade fluid with variable thermal conductivity in the presence of thermal radiation and heat generation/absorption

We develop a new method - Optimal Auxiliary Functions Method (OAFM) to obtain some exact solutions for axisymmetric magneto-hydrodynamic flow and heat transfer to modified second grade fluid with variable thermal conductivity taking into consideration the thermal radiation and heat generation/absorption. The relevant partial differential equations are reduced using suitable transformations, into ordinary differential system. The contribution of different parameters like material constants, generalized second grade parameter, the power-law index, the generalized Prandl number, thermal conductivity parameter, heat generation parameter, generalized magnetic parameter and some combinations between these is analyzed. This paper demonstrates the general validity and the great potential of the OAFM.