A new approach to model viscosity in the conservation of momentum equations is presented and discussed. Coefficient of viscosity is modeled in such a way that it reaches asymptotically to infinity at the solid boundary but still yields a finite value for the shear stress at the solid wall. Basic objective of this research is to show that certain combinations of higher order normal velocity gradients become zero at the solid boundary. Modified solutions for the couette flow and poiseuille flow between parallel plates are obtained by modeling the coefficient of viscosity in a novel way. Also, viscous drag computed by our model is expected to yield higher values than the values predicted by the existing models, which matches closely to the experimental data.