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.