Numerical analysis was performed on steady-state and transient heat transfer from a flat plate located at one-end of a rectangular duct with an orifice in pressurized He II for liquid temperatures from 1.8 to 2.1 K to clarify the effect of heat flow contraction and expansion. The model duct has a dimension of 10×40×100 mm3 and has an orifice at the center of the duct. The flat plate heater is 10 mm wide and 40 mm long. Two-dimensional computer code named SUPER-2D based on the two-fluid model and the theory of mutual friction was used. Steady-state CHF and the time lag from the application of a step heat input to the occurrence of λ transition, that is called a lifetime, were obtained for various values of step heat flux, for the ratio of the cross-sectional area of the orifice to that of the duct from 9.0 % to 100 %. The effects of orifice were clearly observed. The solutions were compared with the experimental data for the ducts with the same sized orifices and the corresponding conditions. They agreed well with the experimental data. The heat transport mechanism in the duct with an orifice was clarified by the analysis.