Analytical and numerical study for two-phase stratified-flow in a plane channel subjected to different thermal boundary conditions

• Proposed physical-model and operating-conditions for obtaining analytical solution.
• Derived analytical solution for fully-developed two-phase stratified flow, with and without phase-change.
• Simulated both the cases using Level-Set Method; reported excellent agreement with the analytical results.
• Verified the physical-model and operating-conditions from numerical developing-flow results.
• Applicable to a problem where no heat-transfer and minimum/maximum temperature at the interface, is desired.

Analytical solution is proposed for two-phase stratified fully-developed flow in a plane channel for two problems: without and with phase change; discussed with the help of a physical model. The first problem – on flow of two immiscible liquids – is studied for the channel subjected to uniform-heat-flux boundary-condition; whereas, the second problem is studied also for constant-wall-temperature and convection-heat-transfer boundary-condition. For the first problem, fully-developed analytical solution is proposed only for heat-transfer; whereas, for the second problem, additionally fluid-flow solution is also derived. The present analytical solution is compared with numerical solution, obtained from a level set method based in-house code; and an excellent agreement is reported. The numerically obtained developing flow results are consistent with the physical-model and operating-conditions proposed here. The analytical solutions will be useful for benchmarking a numerical method for two-phase flow; and more importantly in those engineering applications, of stratified flow, where no heat-transfer/phase-change or minimum/maximum temperature is desired at the interface.