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The system of equations 7 and 12 with their boundary conditions has been solved numerically with Shooting method where the results were in best agreement with previous studies . Moreover, for the first time, an equation for generated entropy is introduced and minimized within the boundary layer over a moving plate. Having considered the concept of λ, the issue is analyzed for λ<0, λ<1 and λ>1. It is worth mentioning that we've supposed that at Eq.20,〖 θ〗_∞=2, Re=1000, Pr=1, Ec=0.01. Fig.1 shows velocity profile for a moving plate in opposite direction to free flow velocity, i.e. λ<0. As it is clear we can divide this profile into two sub-profiles. The zone 1 leaves the border layer thicker than the plate is standstill. It's worth mentioning that the value of critical plate velocity ratio that beyond that there's no solution exists,λ_c=-0.35410 is in the best agreement with previous studies . In Fig.2 we have demonstrated the velocity profile when 0<λ<1. Because of difference between the maximum and minimum speed vectors, boundary layer thickness decreases. This trend continues till the plate moves faster than the fluid i.e. λ>1. In this condition the plate brings the fluid alongside it friction force got reverse and boundary layer thickness increases with increasing in λ.see Fig.3. Fig.5 shows how plate's speed impacts the speed profile. As it's evident for λ>1 the velocity profile varies noticeably where the profile carries a decreasing fashion and reaches the free flow velocity outside the border. It's worth mentioning that for λ<1, because of high momentum transfer inside the border, the boundary layer thickness decreases. The variation of velocity gradients with λ has been shown in...