This book deals with the numerical study of convection-diffusion problems related to free and forced convection boundary layer flows in porous or ordinary fluid medium using advanced computing techniques, namely, Newton s Shooting technique and finite difference technique. In the case when the set of governing partial differential equations are reduced by means of similarity transformations, to ordinary one, the newton s shooting method coupled with Runge-Kutta integrations scheme has been used. In the cases when similarity transformation is not possible, the partial differential equations have been solved using Crank Nicholson type of finite difference scheme.