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.