Level-set method based transient 2D simulation of developing oil-water smooth-stratified (SS) and wavy-stratified (WS) flow in a horizontal and inclined plane-channel is done; for various inlet-velocity (u(in)), inlet-interface-height (H(in)), inclination-angle (0), reduced surface-tension (sigma <= sigma(ow)) and reduced gravity (g <= g(e)). At the certain critical value of the governing parameters, SS to WS flow transition is captured, analyzed and reasoned. Increase in u(in), H(in) and 0 and a decrease in sigma(ow) and g(e) are found to destabilize the SS flow. For fully-developed SS flow, a detailed analytical solution of interface-height, maximum axial-velocity, its transverse location, pressure-gradient and wall-shear stress is proposed for an inclined channel; an excellent agreement between the present analytical and numerical results is also reported. The SS flow analytical-results are also compared with the time-averaged WS flow numerical-results (near the channel-outlet), to understand the reasons for flow-transition. Flow development is studied with the help of axial variation of interface-height and maximum (over the cross-section of the channel) axial velocity: time-averaged for WS flow. Furthermore, the variation of development-length for SS flow and WS flow is studied. Finally, stretching of interface-area due to onset of WS flow is presented with the help of interfacial-area-concentration. Its calculation directly from the Dirac-delta function of the level set method is a novel-contribution. (C) 2011 Elsevier Ltd. All rights reserved.