Steady-state and transient heat transfer on a flat plate at one end of a rectangular duct with an orifice were measured in He II for bath temperatures of 1.8 K to 2.14 K at atmospheric pressure. The steady-state critical heat flux (CHF) was slightly affected by the orifice location. The transient heat transfer for a stepwise heat input with a magnitude larger than the CHF showed a quasi steady-state with a certain lifetime on the extrapolation of steady-state Kapitza conductance curve. The relation between the lifetime and step heat flux was significantly affected by the orifice location. Numerical analysis was performed for the steady-state and the transient heat transfer in the duct with the orifice by using the two-dimensional computer code named SUPER-2D based on the two-fluid model and the theory of mutual friction. The solutions of CHF and lifetime agreed well with the experimental data. The heat transport mechanism was clarified by the analysis.