Heat transport in a liquid layer locally heated on its free surface

Abstract

A strong heat flux, localized on the upper surface of a fluid, sets up strong convection motions through thermocapillary forces, which limits the temperature elevation in the pool, therefore limiting the efficiency in fusion welding processes. We propose a theoretical estimate of the temperature elevation when the fluid motion is laminar or turbulent, the weld pool surface remaining flat. Our treatment follows the theoretical work of Shraiman and Siggia [Phys. Rev. A 42, 3650 (1990)] in Rayleigh-B\'enard convection. In the laminar case, the temperature elevation is proportional to the incident power to the $\frac{3}{4}$ power, in agreement with earlier estimates, and in the turbulent case, to the incident power to the $\frac{2}{3}$ power.