Natural convection of triangular enclosure filled with water-based nanofluid under the influence of Brownian diffusion and thermophoresis is studied numerically in two cases by depending on wall boundary conditions. The high (hot) temperature vertical wall and the insulated bottom wall are considered in case (i) and the other case the bottom wall is uniformly heated while the vertical wall is thermally insulated. In both cases, the inclined wall is maintained low temperature (i.e., cold inclined wall). The coupled governing vorticity–stream function formulation equations are employed by the help of finite difference method (FDM). The influence of the Rayleigh number, Lewis number on fluid flow, heat have been examined through graphically and discussed. It has been found that in the case of uniform heating is high sensitive to rising of the Ra, while the uniform heating of the left wall of the cavity is not so sensitive to changes of Ra. © 2021, Springer Nature Singapore Pte Ltd.