Heat transfer and temporal behavior of the laminar mixed-convection flow around a ducted flat-plate thermal flow sensor

We present experimental results of heat transfer processes in mixed-convective flow from a ducted vertical hot-plate thermal flow sensor for aiding (upward) and opposing (downward) flows. The results are obtained for three different Gashof numbers, Gr = 289, 411, and 456, using air, in the Reynolds number range from 0 to 120. The Nusselt number for aiding flows can be adequately described by Nu_tot - Nu₀ = (Nu_forcedⁿ + Nu_freeⁿ)^1/n, with Nu₀ = 0.5, as originally proposed by Churchill for free flat plate. For n, a value of 1.5-1.7 is found. For opposing flows in the mixed-flow region (0.1 ≤ Gr/Re² ≤ 10), flow visualization shows an oscillating buoyant plume around the flat plate. In the transition from free to mixed and to essentially forced convection, distinct sequences of instabilities of this plume are observed, leading to several local minima and maxima in the heat transfer from the plate. The results are summarized in a bifurcation diagram. Here, several windows with instabilities are found, both nonperiodic, with strong indications of chaotic behavior, and (quasi-) periodic. Typical fundamental frequencies of the instabilities range from 0.15 to 1 Hz.