Abstract
The effects of variable thickness, hydromagnetic flow, Brownian motion, heat generation, on heat transfer characteristics and mechanical properties of a moving surface embedded into cooling medium consists of water with nano-particles are studied. The governing boundary layer equations are transformed to ordinary differential equations. These equations are solved analytically using (OHAM) for general conditions. The velocity, temperature, and concentration profiles within the boundary layer are plotted and discussed in details for various values of the different parameters such as Brownian parameter, thermophoresis parameter, shape parameter, magnetic parameter and heat source parameter the effect of the cooling medium and flatness on the mechanical properties of the surface are investigated.