Entropy Generation Due to the Heat Transfer for Evolving Spherical Objects

Abstract

Heat transfer accompanying entropy generation for the evolving mini and microbubbles in solution is discussed based on the explicit solutions for the hydrodynamic equations related to the bubble motion. Even though the pressure difference between the gas inside the bubble and liquid outside the bubble is a major driving force for bubble evolution, the heat transfer by conduction at the bubble-liquid interface affects the delicate evolution of the bubble, especially for sonoluminescing the gas bubble in sulfuric acid solution. On the other hand, our explicit solutions for the continuity, Euler equation, and Newtonian gravitational equation reveal that supernovae evolve by the gravitational force radiating heat in space during the expanding or collapsing phase. In this article, how the entropy generation due to heat transfer affects the bubble motion delicately and how heat transfer is generated by gravitational energy and evolving speed for the supernovae will be discussed. The heat transfer experienced by the bubble and supernovae during their evolution produces a positive entropy generation rate.

Gas-Vapor Mixture Temperature in the Near-Surface Layer of a Rapidly-Evaporating Water Droplet

“…The main consistent patterns of heat and mass transfer processes, when single droplets of liquid fuels and their aerosol flows of different particle sizes are heated and evaporate, were established by the results of theoretical and experimental research, generalized in study [ 5 ]. The influence of the temperature difference along the spherical fuel droplet radius on the intensity of heat exchange with the external gas medium was studied in papers [ 6 , 7 , 8 , 9 ]. Quite simple approaches have been developed to calculate the characteristics of heat and mass transfer in the “fuel droplet–gases” system [ 3 , 10 ].…”