The two-dimensional formulation of tile separated model conservation equations has been modified, and the advection and diffusion effects on the hydrodynamic behavior of two-component (air/water) two-phase flows have been investigated theoretically. The interfacial transport terms are modeled and imported to the governing equations, solved by numerical computation. They give a good fit with experimental data obtained previously. Basically, three flow regimes, bubble, complex and annular flows in a narrow channel have been modeled, and the general characteristics of the prediction have been discussed. Because of the considerable difficulties in modeling, the flow is assumed as steady state, and transient terms are canceled. However, comparison of the measured pressure-drop values and the calculated ones, by using the interfacial transport terms, the interfacial area and the driving force, is quite Satisfactory. Thus, it is concluded that the discrepancies between the measured and the calculated pressure-drop values reported in the literature are due to the lack of advection and diffusion terms derived from both shear stresses and interfacial drag forces.