Numerical and analytical study of reversed flow and heat transfer in a heated vertical duct

Numerical calculation is performed to study the buoyancy effect on the reversed flow structure and heat transfer processes in a finite vertical duct with a height to spacing ratio of 12. One of the walls is heated uniformly and the opposite wall is adiabatic. Uniform air flow is assumed to enter the duct. In general, the trend predicted agrees well with the one observed in the previous experiments. In the ranges of the buoyancy parameter of interest here for both assisted and opposed convection, a reversed flow, which can be observed to initiate in the downstream region close to the exit, propagates upstream as Gr/Re² increases. The increase of the Reynolds number has the effect of pushing the reversed flow downstream. Simple analytical models are developed to predict the penetration depth of the reversed flow for both assisted and opposed convection. The models can accurately predict the penetration depth when the transport process inside the channel is dominated by natural convection. Local and average Nusselt numbers at different buoyancy parameters are presented. Correlations are given of the average heat transfer parameter Nū/Re^0.4 in terms of the buoyancy parameter.