A new family of reduced models for non-isothermal falling films

TL;DR

This paper introduces a new family of asymptotic reduced models for non-isothermal falling films that accurately simulate thermal transfer across a wide range of Biot and Peclet numbers, aligning well with primitive equation solutions.

Contribution

The paper develops novel asymptotic models that effectively capture thermal transfer in falling films across various flow regimes, improving upon existing models.

Findings

Models accurately simulate thermal transfer for moderate to high Peclet numbers.

Good agreement with primitive equation solutions for different boundary conditions.

Models correctly predict the onset of thermally developed regimes.

Abstract

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.