Similarity solution for convection heat transfer due to Marangoni flow over a flat surface

Marangoni convection occurs along any liquid-vapor interface that has a surface tension gradient. The surface tension gradient can result from either temperature or concentration gradients along the surface. Marangoni convection is of importance in crystal growth melts and during boiling as it influences the flow around the vapor bubbles. The influence of Marangoni induced convection is more obvious under microgravity but also occurs in earth gravity. This paper presents a similarity solution for Marangoni induced flow for both the velocity and temperature profiles, assuming developing boundary-layer flow along a surface with various imposed temperature profiles. The surface velocity, the total flow rate, and the heat transfer characteristics are given for various temperature profiles and various Prandtl numbers. Since the predicted boundary layer thickness would be much less than the diameter of vapor bubbles during nucleate boiling, the bubble surface curvature effects can be neglected and this analysis can also be used as a first estimate of the effect of Marangoni flow around a vapor bubble.