An analytical model for the heat transfer to a capillary groove

Abstract

An analytical model for describing the heat transfer from the wall of a capillary groove to the fluid in the groove has been developed. This model couples a one-dimensional conduction model in the wall to the surface heat transfer mechanisms resulting from a meniscus formed on the wall. The meniscus consists of three regions: 1) An equilibrium film region. 2) An evaporating film region. 3) An intrinsic meniscus region. The heat conducted up the solid wall is dissipated in four ways: 1) Convection to the liquid below the intrinsic meniscus region. 2) Heat conduction through the intrinsic meniscus to the liquid-vapor interface where evaporation takes place. 3) Evaporation of the liquid in the evaporating thin film region. 4) Convection to the vapor above the meniscus which is neglected in this study. The conduction resistance of the thin liquid film is neglected and only the resistance due to the short range attraction forces is considered in the evaporating film region. In the intrinsic meniscus region both the conduction effects through the film and the surface resistance to evaporation are accounted for. The results show that the heat transfer starts at approximately zero at the base of the equilibrium thin film and increases in the evaporating thin film region to a maximum at the transition region between the evaporating film and intrinsic meniscus. The heat transfer then decreases as the conduction resistance of the film increases. Data is presented illustrating the relative importance of each of these heat transfer mechanisms.