A similarity solution for combined forced and free convection flow over a horizontal plate

Abstract

The effect of buoyancy forces on the steady, laminar, plane flow over a horizontal plate is investigated within the framework of a first-order boundary layer theory, taking into account the hydrostatic pressure variation normal to the plate. An exact similarity solution is given for the case of a wall temperature that is inversely proportional to the square root of the distance from the leading edge. Remarkably, such a solution does not exist if the buoyancy parameter is smaller than a certain critical value, which is negative (decelerated flow) but not yet small enough to satisfy the separation criterion of vanishing shear stress at the wall. Although the wall temperature is different from the free-stream temperature, there is no local heat transfer at the wall except in the singular point at the leading edge. The total heat transfer is finite, independent of the plate length, and is calculated by applying the heat flux equation. The displacement thickness is also given. It is negative if the plate is heated sufficiently strongly.