New asymptotic heat transfer model in thin liquid films
This work provides a more accurate and formally derived model for heat transfer in thin films, relevant to engineers studying coating flows or heat exchangers.
The authors derive a new asymptotic model for heat transfer in thin liquid films flowing down a vertical wall, incorporating coupled Marangoni and temperature-dependent viscosity effects. The model shows good agreement with full numerical solutions of the Fourier equations.
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.