Abstract
New full-statement 3D mathematical model of joint motion of thin liquid film and gas in a microchannel at local heating developed by taking into account the heat transfer by flows, evaporation and condensation, as well as the heat transfer at the gas-liquid interface is derived. The model is based on the full system of the Navier-Stokes equations, taking into account the convective terms of motion equations in the phases. Comparison of the numerical results obtained using the model based on the full Navier-Stokes equations and using the simplified model developed in the framework of the thin layer approximation has been performed. The comparison shows that at low Reynolds numbers, simplified model well describes all the main characteristics of the gas and liquid motion. With the gas Reynolds numbers significant increase difference between numerical results starts to grow.
Highlights
New full-statement 3D mathematical model of joint motion of thin liquid film and gas in a microchannel at local heating developed by taking into account the heat transfer by flows, evaporation and condensation, as well as the heat transfer at the gas-liquid interface is derived
Comparison of the numerical results obtained using the model based on the full Navier-Stokes equations and using the simplified model developed in the framework of the thin layer approximation has been performed
Flows of thin liquid films driven by various forces such as gas flow, gravity, capillarity, thermocapillarity and intermolecular forces are encountered in cooling devices, heat-exchangers, microfluidic devices, in wetting and spreading, in condensers, as well as in biomedical and geophysical applications
Summary
Flows of thin liquid films driven by various forces such as gas flow, gravity, capillarity, thermocapillarity and intermolecular forces are encountered in cooling devices, heat-exchangers, microfluidic devices, in wetting and spreading, in condensers, as well as in biomedical and geophysical applications. The first model of joint liquid and gas motion taking into account convective heat transfer in liquid and gas phases, as well as evaporation, which has been. The hydrodynamics has been described in the framework of the lubrication approximation, whereas convective heat transport in both phases and convective diffusive vapor transport in the gas phase have been taken into account. It should be noted that full statement three-dimensional models, describing the liquid films motion taking into account the gas phase and the phase changes at the free boundaries are still very rare in literature. In the present work new full statement three-dimensional mathematical model of joint motion of a viscous liquid film and gas in a microchannel at local heating developed by taking into the inertial terms in motion equations as well as convective heat transport in both phases and convective diffusive vapor transport in the gas phase.
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