Abstract
A new numerical model is developed to study the unique features of flow and heat transfer in superfluid helium or He II. The model, called the simplified model, is derived from the original two-fluid model. It consists of a conventional continuity equation, a momentum equation for the total fluid in the form of a modified Navier-Stokes equation, and an energy equation in the form of the conventional temperature-based energy equation, in which the heat flux due to Gorter-Mellink internal convection is properly incorporated. To verify the validity of the simplified model, the analytical results by the simplified model are compared with those by the original two-fluid model in the analysis of one-dimensional heat transfer in a vertical He II duct heated at the bottom boundary. To demonstrate the capability of the present model for multi-dimensional problems, two-dimensional analysis is performed for internal-convection heat transfer in an He II pool with one of the walls partially heated. The two-dimensional results obtained by the present model are also compared with that by the modified two-dimensional model by Ramadan and Witt.
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