Interaction between internal natural convection in an enclosure and an external natural convection boundary-layer flow

Abstract

An analysis in made of natural convection in a square enclosure, of which one vertical wall is cooled by an external natural convection boundary-layer flow. The other vertical wall is maintained at a uniform temperature while the horizontal walls are adiabatic. The resulting conjugate internal-external natural-convection problem was solved numerically for Grashof numbers between 10 3 and 10 7 and for a Prandtl number of 0.7. Approximate solutions were also obtained using a model which avoids conjugatetype computations. For comparison purposes, a set of solutions were carried out for the standard naturalconvection enclosure problem characterized by prescribed uniform temperatures on the vertical walls and adiabatic horizontal walls. For the overall heat transfer characteristics encompassing both the internal and external flows, the average Nusselt number displayed a power-law dependence on the Grashof number given by ¯Nu = 0.0907 Gr 0.285 for Gr ≥ 10 4. These Nusselt numbers are about sixty per cent of those for the standard enclosure, at common values of the respective Grashof numbers. The local heat flux variations along the convectively cooled wall were found to be appreciably smaller than those along the heated isothermal wall, reflecting the counterflow nature of the heat exchange between the internal and external flows. In addition, the temperature variations along the convectively cooled wall increased with increasing Grashof number. The Grashof number also decisively affected the temperature distributions along the adiabatic walls. Streamline maps revealed little difference between the flow fields adjacent to the thermally active and thermally passive walls at low Grashof numbers, but marked differences were in evidence at high Grashof numbers. For the external natural convection, the local heat transfer coefficients were generally larger than those predicted by the local application of the classical isothermal-plate heat transfer coefficient formula.