Heat transfer in transient buoyancy driven flow adjacent to a horizontal rod

The problem of heat transfer in transient buoyancy driven flow in the neighbourhood of a horizontal rod of circular cross-section is investigated. The rod, which is placed in a quiescent Boussinesq unbounded fluid, is heated either suddenly or gradually to a constant surface temperature. The investigation is based on the solution of the unsteady two-dimensional conservation equations of mass, momentum and energy in the range of Rayleigh number 10 < Ra < 1000 while keeping Prandtl number constant at Pr = 0.7. Results are presented for the unsteady local and average Nusselt numbers along with some details of the transient temperature and velocity fields. In order to validate the method of solution employed, the steady-state values of average and local Nusselt numbers were also computed and compared with known experimental and theoretical results. The comparison shows a satisfactory agreement.