New asymptotic heat transfer model in thin liquid films

•An improved Nusselt solution is derived, which takes into account heat transfer phenomena across the free surface.•This model is studied and validated numerically by comparing with 2D direct simulations of the heat transfer equation.•A dynamical system analysis of the proposed model is performed.•Coupling between the heat transfer and the hydrodynamics is taken into account.•The proposed model is strictly hyperbolic and provides the predictions with improved accuracy. In this article, we present a model of heat transfer occurring through a liquid 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 is obtained, 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.