Natural convection heat transfer below downward facing horizontal surfaces (Q1058936)

The laminar steady-state convection below a horizontal infinite strip and below a horizontal circular plate is determined analytically for the limiting case of high Prandtl numbers. The plate surface is assumed to be either isothermal or uniformly heated. This convection is caused by the non-uniform temperature distribution at the edges of the plate. Therefore, this problem has to be described by an elliptic differential equation which was not taken into account in earlier integral methods. Applying the method of matched asymptotic expansions, similarity solutions are deduced for a region around the stagnation point. Moreover, an interpolation with the limiting case of low Prandtl numbers yields heat transfer correlations for arbitrary Prandtl numbers.