The buoyancy-driven thermofluid dynamics of a solid/hollow cylinder with concave surfaces have been studied in a laminar regime () using the finite-volume method to analyze the effects of ( and . Conservation equations for mass, momentum, and energy have also been solved in a 2-D axisymmetric geometry . Second-order upwind and central difference schemes have been deployed to discretize the convective and diffusive terms. Heat dissipation increases with irrespective of for both cylinders. However, the remains constant with the ratio for a hollow concave cylinder increases with whereas, decreases. Multiple vortices appear at the outside surface at a low (i.e. = 0.2), and these vortices almost disappear at high (i.e. = 0.6), affecting the outside average Nusselt number from low to high. In all cases, is higher than The thermofluid dynamics of solid and hollow cylinders have been delineated through different countour and vector plots, and two correlations for Nu have been deveoped.