Stefan flow induced natural convection suppression on high-flux evaporators

High-flux evaporators are important for various fundamental research and industrial applications. Understanding the heat loss mechanisms, especially the contribution of natural convection during evaporation is thus a ubiquitous process to predict and optimize the performance of evaporators. However, a comprehensive analysis on natural convection heat transfer, where the vertical Stefan flow due to evaporation couples with buoyancy driven convective flow has not been carefully considered. In this work, we developed a theoretical framework to elucidate the effect of Stefan flow on natural convection during evaporation. This theory incorporates the vertical Stefan flow into the conventional boundary layer theory. We found that a significant suppression of natural convection can be induced by a weak Stefan flow owing to the increase of boundary layer thickness. To understand this phenomenon, we discuss the governing mechanisms at different Stefan flow regimes. We provide a theoretical correlation to the overall heat transfer which includes both effects of the Stefan flow velocity and the buoyancy force. We finally predict the effect of natural convection on an evaporator at different operating temperatures. The heat loss from natural convection no longer monotonically increases with the superheat temperature due to the effect of Stefan flow suppression. As a result, there is an approximately 40% overestimation of the natural convection contribution at saturation temperature using conventional theory. This work improves the fundamental understanding of the natural convection during evaporation and can help guide future high-performance evaporator designs.