In this paper, the solution of transient mass, momentum and energy balances in superfluid helium are discussed by means of a finite element algorithm. A simple linearization procedure is used for the non-linear pseudo-diffusion term in the energy balance arising because of the unique counterflow heat transport mechanism in superfluid helium. The linearization algorithm is analyzed for accuracy order and stability. The reliability of the algorithm devised is shown in practical tests, comparing the numerical solutions with experimental data available in the literature.
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Bottura et al. (1999) studied this question.
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