Laminar mixed convection in two-dimensional far wakes above heated/cooled bodies: model and experiments

Abstract

A heated or cooled body is positioned in a vertically rising forced flow. This develops both a kinematic and a thermal wake, the latter adding buoyant effects to the otherwise forced flow field. An asymptotic model is developed to treat this mixed convection in both plane and axisymmetric geometry. The model holds for laminar flow in the boundary layer approximation and uses a far-wake expansion for weak buoyant forces. For plane geometry the model is validated against both experiments in water and FEM simulations.It is found for a heated wake that buoyant forces accelerate the fluid in the thermal wake such that the vertical velocity deficit in the kinematic wake is reduced. For strong heating this may even lead to vertical velocities larger than the forced flow amplitude. In conjunction the entrainment is intensified in a heated wake. The effects in a cooled wake are opposite in that the vertical velocity deficit is increased within the thermal wake and the horizontal flow into the wake is weakened. In a strongly cooled wake the horizontal flow may even invert, going from the wake centre into the ambient. The Prandtl number controls the width of the thermal wake and, thus, the portion of the kinematic wake which is affected by buoyant forces. Large Prandtl numbers superimpose a narrow buoyant plume, small Prandtl numbers a wide buoyant plume, onto the kinematic wake.