In the present study, an immersed-boundary method is adopted to simulate natural and forced convection within a domain with complex geometry. The method is based on the direct momentum and energy forcing on a Cartesian grid and issues involving implementation of both the thermal (Dirichlet and Neumann) and dynamic (stationary and nonstationary) boundary conditions are addressed. The second order accuracy of the present method was validated based on natural convection in an annulus between horizontal concentric cylinders. Simulations of flow over a stationary cylinder with heat convection were further conducted to validate the capability of present technique for both temperature boundary conditions. Finally, the influence of the lock-on phenomenon in heat transfer is investigated for flow over a transversely oscillating cylinder. All computed results are in generally good agreement with previous experimental measurements and numerical simulations.

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