This paper reports numerical investigation of buoyant convection of nanofluid in a tilted parallelogrammic porous enclosure. The upper and lower portions of the geometry are preserved at thermally insulated condition; left and right surfaces are linearly heated and uniformly cooled, respectively. The momentum equations are modeled by utilizing Darcy’s law and thermal processes are considered using transient energy equation. The partial differential equations governing the physical processes are numerically solved by FDM-based ADI and SLOR techniques. In this analysis, we have used an appropriate coordinate transformations to transform the model equations from the parallelogram domain to rectangular-shaped computational domain. The flow and thermal distributions are illustrated through streamlines and isotherms, while the thermal transport rates are measured using the Nusselt number. Numerical computations predict the influences of sidewall inclination angle and nonuniform thermal condition on the flow and thermal distributions and heat transport rates for wide parametric ranges chosen in the present study.