Heat Transfer by Thermo-Capillary Convection

Abstract

This paper describes the results of a sounding rocket experiment which was partly dedicated to study the heat transfer from a hot wall to a cold liquid with a free surface. Natural or buoyancy-driven convection does not occur in the compensated gravity environment of a ballistic phase. Thermo-capillary convection driven by a temperature gradient along the free surface always occurs if a non-condensable gas is present. This convection increases the heat transfer compared to a pure conductive case. Heat transfer correlations are needed to predict temperature distributions in the tanks of cryogenic upper stages. Future upper stages of the European Ariane V rocket have mission scenarios with multiple ballistic phases. The aims of this paper and of the COMPERE group (French-German research group on propellant behavior in rocket tanks) in general are to provide basic knowledge, correlations and computer models to predict the thermo-fluid behavior of cryogenic propellants for future mission scenarios. Temperature and surface location data from the flight have been compared with numerical calculations to get the heat flux from the wall to the liquid. Since the heat flux measurements along the walls of the transparent test cell were not possible, the analysis of the heat transfer coefficient relies therefore on the numerical modeling which was validated with the flight data. The coincidence between experiment and simulation is fairly good and allows presenting the data in form of a Nusselt number which depends on a characteristic E. Fuhrmann · M. Dreyer (B)

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

“…On the other hand, Marangoni convection occurs when the surface tension of an interface (generally liquid–air) depends on the concentration of a species or on the temperature distribution. In the case of temperature dependence, the Marangoni effect is also called thermocapillary convection . The Marangoni effect is of primary importance in the fields of welding, crystal growth, and electron beam melting of metals.…”

“…In the case of temperature dependence, the Marangoni effect is also called thermocapillary convection. 39 The Marangoni effect is of primary importance in the fields of welding, crystal growth, and electron beam melting of metals. The mechanism of Marangoni flow is that since a liquid with a high surface tension pulls more strongly on the surrounding liquid than one with a low surface tension, the presence of a gradient in surface tension will naturally cause the liquid to flow away from regions of low surface tension.…”