  In this paper we discuss the application of nonconforming virtual element
methods(VEM) for the second order diffusion dominated convection diffusion
reaction equation. Stability of the virtual element methods has been proved for
the symmetric bilinear form. But the same analysis cannot be carried out for
the non-symmetric case. In this work we present the external virtual element
methods using $L^2$ projection operator and prove the well-posedness of VEM for
non symmetric bilinear form. We also proved polynomial consistency of discrete
bilinear form assuming $H^2$ regularity of approximate solution on each
triangle. We have shown optimal convergence estimate in the broken sobolev
norm.
