New asymptotic models are formulated to capture the thermal transfer across falling films. These models enable to simulate a wide range of Biot and Peclet number values, without displaying nonphysical behaviors. The models correctly capture the onset of the thermally developed regime at the inlet of the flow. To evaluate the parameter space of acceptability, a comparison has been made with the primitive equation solution for periodic boundary conditions, as well as for an open flow with a periodic forcing at inlet.A good agreement is obtained for moderate to high Peclet numbers.
IntroductionFalling films form thin layers of liquid flowing on a tilted plate, with a thickness of the order of a millimeter or less. Starting with the works of Nusselt [17], followed by Kapitza and Kapitza [12], this topic has been heavily studied and the hydrodynamic of a tilted falling film flowing on a smooth plate is well known. Curiously, the interplay between heat or mass transfers and the wavy dynamics of a falling films has been far less studied, even though Frisk and Davis [7], Yoshimura et al. [24] demonstrated that the wavy regime of the film can indeed increase several folds the heat and mass transfer coefficients between the liquid and the gas. Most studies on heat and mass transfer across the film focus on the wave-less smooth film situation [13]. Only a few studies have been devoted to the wavy regime and addressed heat transfer and hydrodynamics couplings by solving the Fourier equation across the film, the hydrodynamics being dealt with the
Scikit-FDiff is a new tool for Partial Differential Equation (PDE) solving, written in pure Python, that focuses on reducing the time between the development of the mathematical model and the numerical solving.
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