New asymptotic heat transfer model in thin liquid films

TL;DR

This paper introduces a new asymptotic model for heat transfer in thin liquid films flowing down vertical surfaces, incorporating coupled Marangoni and temperature-dependent viscosity effects, and compares it with numerical solutions.

Contribution

The paper develops a fully coupled asymptotic heat transfer model for thin liquid films, including Marangoni and viscosity effects, differing from previous weighted residual methods.

Findings

The new model accurately predicts heat transfer in thin films.

Coupled effects significantly influence heat transfer dynamics.

Comparison with numerical solutions validates the asymptotic approach.

Abstract

In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.