<p>This study offers an analysis of the gravity-driven thermally stratified laminar nanoliquid flow past a permeable stretching surface with vanishing flux of nanoparticles. Two-phase fluid model is used for the nanofluids. By the application of similarity transformations, the partial differential equations (PDEs) that govern the problem are converted to ordinary differential equations (ODEs) which are extremely nonlinear. By using the shooting technique and Runge–Kutta (R–K) method, those equations are numerically solved. Shear stress at the surface and rate of surface mass transfer decrease but rate of heat transport at the surface rises for the enhancement of mass transpiration parameter. Temperature and concentration of the nanofluid are found to fall, but the liquid’s velocity rises with the rising buoyancy parameter. Concentration of the nanofluid increases but velocity of the liquid and temperature diminish when the thermal stratification parameter increases.</p>