Numerical investigation of effects of buoyancy around a heated circular cylinder in parallel and contra flow

Two-dimensional, steady, incompressible Navier-Stokes and energy equations are expressed in the stream function/vorticity formulation and solved numerically by finite difference method to study effects of buoyancy on fluid flow and heat transfer from a horizontal circular cylinder. The cylinder is exposed to approaching flow stream, for parallel (parallel flow) and opposing (contra flow) directions to the buoyant force. Two different thermal boundary conditions were considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results elucidating the dependence of the flow and heat transfer characteristics on the Richardson number 0≤ Ri ≤ 2, Prandtl number 0 ≤ Pr ≤ 100 and Reynolds number 0 ≤ Re ≤ 40 are presented. Overall, for parallel flow regime, an increase in the Ri led to a raise in both Nusselt number and drag coefficient. However, for contra flow regime, these trends were reversed. For both regimes, the aforementioned behaviors were more pronounced for CT boundary condition than that for the CHF boundary condition.