Horizontal convection in water heated by infrared radiation and cooled by evaporation: scaling analysis and experimental results

Abstract

An experimental study of horizontal convection with a free surface has been conducted. Fresh water was heated from above by an infrared lamp placed at one end of a tank, and cooled by evaporation as the water moved away from the heat source. The heat radiated from the lamp was absorbed in a thin (less than 1 mm) layer next to the surface, and then advected and diffused away from the lamp region. Latent heat loss dominated the surface cooling processes and accounted for at least 80% of the energy loss. The velocity and temperature fields were recorded with PIV technology, thermometers and an infrared camera. In similarity with previous horizontal convection experiments the measurements showed a closed circulation with a gradually cooling surface current moving away from the lamp. Below the surface current the water was stably stratified with a comparatively thick and slow return current. The thickness and speed, and hence the mass transport, of the surface-and the return current increased with distance from the lamp.

The latent cooling at the free surface gives a heat flux which increases with the temperature difference between the surface water and the air above it. Hence the surface temperature relaxes towards an equilibrium value, for which the heat flux is zero. The main new result is a scaling law, taking into account this relaxation boundary condition for the surface temperature. The new scaling includes a (relaxation) length scale for the surface temperature, equivalent to the distance the surface current travels before it has lost the heat that was gained underneath the lamp. The length scale increases with the forcing strength and the (molecular) thermal diffusivity but decreases with the strength of the relaxation. Numerical simulations of this problem for a shallow tank have also been performed. The velocity and temperature in the laboratory and numerical experiments agree with the scaling laws in the upper part of the tank, but not in the lower.