Importance of the fundamental entropy for determining interfacial thermal resistance temperature jump differences

Abstract

This work presents a method for calculating the difference in temperature jumps observed at the solid–water and water–solid interfaces when heat is flowing under steady state conditions from a hot to a cold solid separated by an intermediate water phase. The method is based on a hypothesis stating that the entropy flux is maximized where the heat flux is constrained, i.e., at the solid–water interfaces. By focusing on the entropy rather than the heat flux and by maximizing its value vs the magnitude of the temperature jump over the interfaces where the latter is constrained, simple analytical expressions for the jump differences independent of the actual heat flux are established only depending on the absolute temperature of the hot and cold solid. The results show that the temperature jump at the hotter interface, therefore, must be higher than the jump at the colder because of the differences in absolute temperature between the two interfaces, supported by many observations. The results, furthermore, show that the temperature jump asymmetry between the two interfaces should increase with decreasing absolute temperature of the system. The work, therefore, finally indicates that there are two quantities contributing to the magnitude of any temperature jump, the heat and entropy flux. More investigations about their relationship under different conditions are encouraged since the topic is not systematically acknowledged and, therefore, investigated in the literature.