Asymptotic heat transfer model in thin liquid films

Marx Chhay (1) , Denys Dutykh (2) , Marguerite Gisclon (2) , Christian Ruyer-Quil (1)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 LAMA - Laboratoire de Mathématiques

In this article, we present a modelling of heat transfer occuring through a liquid film flowing down a vertical wall. This model is formally derived thanks to asymptotic developpment, by considering the physical ratio of typical length scales of the study. A new Nusselt thermal solution is proposed, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms in the asymptotic model are numerically pointed out. The comparisons are provided against the resolution of the full Fourier equations in a steady state frame.

Mots clés: Heat transfer; thin liquid film; asymptotic modelling; long waves

Domaines: Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Formation de Structures et Solitons [nlin.PS]

Marx Chhay, Denys Dutykh, Marguerite Gisclon, Christian Ruyer-Quil. Asymptotic heat transfer model in thin liquid films. 2015. ⟨hal-01224182v1⟩