This study presents a numerical investigation of laminar free convection flow between vertical parallel flat plates subjected to asymmetric uniform wall temperatures. The left and right walls are maintained at constant but different temperatures, with the right wall being hotter. A fluid at a uniform temperature, less than or equal to the cooler left wall temperature, enters the channel. The governing equations are solved using the finite volume method in OpenFOAM v13. A grid convergence study is conducted using systematically refined meshes to ensure the spatial independence of the results. The numerical solutions demonstrate excellent agreement with classical analytical profiles for fully developed flow. The linear analytical temperature profile is accurately captured even on coarser grids. In contrast, the cubic velocity profile requires more grid resolution to be precisely reproduced. The results validate the numerical methodology and provide insight into the mesh requirements for accurately simulating such natural convection flows.