This paper presents a segregated algorithm to solve numerically the superfluid helium (He II) equations using the two-fluid model. In order to validate the resulting code and illustrate its potential, different simulations have been performed. First, the flow through a capillary filled with Hell with a heated area on one side is simulated and results are compared to analytical solutions in both Landau and Gorter-Mellink flow regimes. Then, transient heat transfer of a forced flow of He Ills investigated. Finally, some two-dimensional simulations in a porous medium model are carried out.