Abstarct: In this thesis, different natural convection boundary laxyers flow for both double-diffusive and mono-diffusive fluids over a vertical flat plate in a saturated porous medium and in the presence of a nanofluid are studied. Non thermal equilibrium model is assumed in the porous medium. The vertical plate in two boundary conditions would studied. In the first case the temperature and other studied parameters on the wall are a power law function of distance from the bottom of the wall. In the other case all fluxes throughout the wall vary exponentially. Use of nanofluid give rise to entering effects of Brownian motion and Thermophoresis effect to the problem and with considering Double-diffusion; Soret and Dofour effects are accounted in the governing equations. Combined heat and mass transfer is applied. Darcy law and Boussinesq approximation are used to model momentum equation in porous medium. Following the case case a similarity parameter for any wall boundary conditions is defined and with aid of that the governing equations transported to ordinary differential equations and solved by finite difference method. The results show that using of nanofluid as operating fluid, increases thermal boundary laxyer thickness and cause to nanoparticle Sherwood namber abate considerably. Also results show temperature boundary laxyer of solid phase and fluid phase will be coincide as heat transfer coefficient H and thermal conductivity ratio γ tend to infinite or in other state solid phase and fluid phase attend to thermal equilibrium state.