Thermal instabilities for a horizontal flow in mixed convection: a Lagrangian viewpoint

As part of the study of mixed convection in flow in a horizontal cylindrical duct uniformly heated at the wall, we show a thermal instability phenomenon. This manifests itself through large amplitude temporal fluctuations of the wall temperature which leads to an intermittent thermal behaviour of the system. Temperature fluctuations are characterized by variable stationary phases which succeed them. This paper provides, at first, a brief description of the experimental loop; then some numerical results corresponding to the stable state, and some experimental results related to the thermal instabilities are reported. Finally we propose a description of the properties of the phenomenon using a non-linear map. This map is defined by a characteristic function related to the thermohydrodynamic state of the flow. This approach based on a Lagrangian model allows us essentially to show the non-linear aspect of the system.