In the present study, we propose an upwind finite volume scheme for thermally-coupled Navier-Stokes equations on an unstructured mesh of triangles. The finite volume analysis of the scheme shows that apriori \(\Vert \cdot \Vert _{L^2}\) - estimate of the error for the velocity and temperature fields are of order h (spacial grid size). The theoretically established convergence relation is verified with the numerical outcomes for some known solutions. Further, the numerical simulations done for free convection problems reveal the presence of multicellular flow pattern, and temperature fields having thermal plumes and thermal layers. The numerical outcomes for different sets of flow parameters also have been validated with the pre-existing literature.
