Laminar free convection near the lower stagnation point on an isothermal curved surface

Abstract

This paper deals with some aspects of the three dimensional laminar free convection boundary layer near the stagnation point on a general curved isothermal surface, which is maintained at a temperature above the ambient temperature of the fluid. Thus the stagnation point is defined as the lowest (elliptic) point on the surface and such that the tangent plane at this point is horizontal. Boundary-layer equations are formulated and it is shown that the flow at the stagnation point depends on the ratio of the two principal radii of curvature at this point, the Prandtl number and the Grashof number. These equations are solved numerically for Prandtl number 0.72 and for various values of the ratio of the two principal radii of curvature. For the stagnation point flow there are two limiting cases, namely the flow at the lower stagnation line on a uniform horizontal cylinder and that at the lower stagnation point on a sphere. The numerical solutions for the sphere and cylinder are then used to develop an approximate method of solution for the stagnation point on a general curved surface; good agreement with the precise numerical solutions was obtained.