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 equa- tions are solved analytically using (OHAM) for general conditions. The velocity, tempera- ture, and concentration profiles within the boundary layer are plotted and discussed in details for various values of the different parameters such as Brownian parameter, thermo- phoresis 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.