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

A heated or cooled body is positioned in a vertically rising forced flow. T his develops both a kinematic and a thermal wake, the latter adding buoyant effects to the otherwise forced flow field. An asymptotic model is develop ed to treat this mixed convection in both plane and axisymmetric geometry. The model holds for laminar flow in the boundary layer approximation and us es a far-wake expansion for weak buoyant forces. For plane geometry the mod el is validated against both experiments in water and FEM simulations. It is found for a heated wake that buoyant forces accelerate the fluid in t he thermal wake such that the vertical velocity deficit in the kinematic wa ke is reduced. For strong heating this may even lead to vertical velocities larger than the forced flow amplitude. In conjunction the entrainment is i ntensified in a heated wake. The effects in a cooled wake are opposite in t hat the vertical velocity deficit is increased within the thermal wake and the horizontal flow into the wake is weakened. In a strongly cooled wake th e horizontal flow may even invert, going from the wake centre into the ambi ent. The Prandtl number controls the width of the thermal wake and, thus, t he 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.