Prandtl number effects for Marangoni convection over a flat surface

Abstract

Marangoni convection, which is induced by the variation of the surface tension with temperature along a surface, influences crystal growth melts and other processes with liquid–vapor interfaces, such as boiling in both microgravity and in normal gravity in some cases. This paper presents a similarity solution for Marangoni flow over a flat surface for both the momentum equations and the energy equation assuming a developing boundary layer along a surface. Solutions are presented for the surface velocity, the total flow rate and the heat transfer for various temperature profiles and various Prandtl numbers. The analysis also shows how the heat transfer variation with Prandtl number changes for Prandtl numbers from much less than one to much greater than one. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble.