Laminar natural convection above a horizontal laser beam

The steady laminar natural convective plume above a horizontal laser beam has been studied. The plume, which is caused by absorption of thermal energy from the beam, is three-dimensional. The three-dimensionality is a consequence of mass continuity and the variation in the thermal energy absorption in the propagation direction. Flow visualizations have verified the three-dimensionality in that a significant velocity component, in a direction opposite to that of laser beam propagation, was observed. The problem is reduced by similarity analysis to a system of ordinary differential equations which are solved numerically for the Prandtl number, Pr = 1.0. Integral approximations are also presented for Pr = 0.7, 1.0, 10.0 and 100.0. The effect of Pr on the velocities, and temperature boundary layer thicknesses is discussed in detail.