The two-fluid model explains the unique features of flow and heat transfer in superfluid helium, of He II. In the multidimensional analysis with a two-fluid model, much CPU time will be necessary because this model consists of four complicated equations. Thus we propose a new numerical model, called the simplified model, which is derived from the two-fluid model. It consists of a conventional continuity equation, a momentum equation for total fluid in the form of a modified Navier-Stokes equation, and an energy equation in the form of a conventional temperature-based energy equation in which the heat flux resulting from the Gorter-Mellink internal convection is properly incorporated. To verify the validity of the simplified model, its results are compared with results of the 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 to deal with multidimensional problems, a two-deimensional analysis is performed for internal-convection heat transfer in an He II pool with one wall partially heated. Our purpose was to verify the validity of the simplified model in multidimensional analysis, so we compared the analytical results obtained by use of the simplified model with those obtained by the two-fluid model in a two-dimensional analysis. The validity of the analytical method, which obtained was adopted by Ramadan and Witt, is also discussed.
