Opposing mixed convection flow in a wall jet over a horizontal plate

The coupling of the temperature and velocity fields by buoyancy in a laminar two-dimensional wall jet over a finite-length horizontal plate is studied numerically and analytically in the asymptotic limit of infinite Reynolds number. Two configurations are considered leading to a cold layer of fluid over the plate, namely an ambient-temperature jet over a cooled plate and a cold jet over an insulated plate. In both cases buoyancy generates an adverse pressure gradient that may separate the flow if the Froude number is sufficiently small and always makes the solution everywhere over the plate dependent on the conditions at the downstream boundary. In the limit of very small Froude number separation occurs in a viscous-inviscid interaction region near the origin of the jet, leading to a separation bubble that covers a fraction of the plate dependent on the Prandtl number. The scalings of the solution in this asymptotic limit are obtained by order of magnitude estimations in the different regions of the bubble and in the buoyancy-dominated flow beyond the bubble, and the results are checked against the numerical solutions of the boundary layer equations. A separate analysis is carried out for very large Prandtl numbers showing that the recirculation bubble is then much shorter than the plate, also in agreement with the numerical results.