Flow topology and bifurcations of buoyancy and mixed convection in an elongated channel with an abrupt section variation

•Flow in an elongated duct with a sudden variation of the cross-sectional area is considered.•The sensitivity of this system to the presence of thermal buoyancy is investigated.•A kaleidoscope of solutions is obtained by exploring the space of relevant parameters.•The solution differ in terms of flow and plume patterning behavior and bifurcation scenario. A forward-facing step (FFS) located half-way in an elongated duct subjected to a horizontal pressure gradient and a vertical temperature difference is considered as a simplified geometrical model to investigate numerically typical problems of internal non-isothermal flow in the presence of blunt obstacles. The sensitivity of this system to thermal buoyancy for each considered rate of fluid injection (measured through the related Richardson number, Ri) is explored by varying parametrically the corresponding Rayleigh number (Ra) over a large interval of orders of magnitude (up to the onset of chaos) and assuming two alternate paradigms for the bottom of the considered channel, namely an adiabatic or kept-at-constant temperature (hot) boundary. Through this conceptual framework, a kaleidoscope of situations are revealed in the (Ri, Ra) space, differing in terms of flow patterning behavior, thermal plume generation phenomena, intensity of heat exchange at the walls and bifurcation scenario. In particular, while for the isothermal floor case a higher Ri leads to an increase in the value of the Rayleigh number needed for transition to time-dependent flow, the corresponding trend becomes non-monotonic if the same boundary is thermally insulated. In such a case the Nusselt number (Nu) calculated for the horizontal surface of the step is always smaller than the equivalent Nu evaluated for the vertical side. The latter is significantly lowered when the hot-floor condition is assumed.