Convection Flows Due to Local Heating of a Horizontal Surface

Abstract

Local boundary layer approximations of first order are computed for the steady laminar convection flow of a semi-infinite medium, which is produced by nonuniform axisymmetric heating or cooling of an infinite horizontal surface. Velocity, pressure, and temperature profiles as well as Nusselt numbers are presented for the Prandtl numbers 0.7 and 7, and for various Grashof and Eckert numbers. Critical Grashof numbers for a heated surface exist beyond which the flow field becomes unstable. A cooled surface always yields stable motions.