The emphasis of this communication is to make a synthesis of several results we have obtained in various mixed convection configurations. This study has been conducted for circular or rectangular ducts submitted to different ways of heating (vertical or horizontal thermal gradient in the rectangular case and combined vertical and horizontal in the circular case). The bibliography is rather poor for mixed convection in liquids, so the chosen working fluid used here is water. Moreover, a wide range of forced fluid flow and heat flux rates has been considered spreading from laminar to turbulent flow. The characterization of fluid flow and heat transfer regimes is based on temporal recording of temperature measurements obtained in several locations by means of thermocouples or infrared thermography. The analysis of these temperature signals highlights several regimes depending on control parameters. The flow structure in the cases of uniformly heated circular duct and the rectangular one heated from below is constituted of two longitudinal rolls and we notice only one roll in the case of the rectangular duct submitted to the horizontal thermal gradient. For low Reynolds and Rayleigh Numbers, the behavior of all these configurations is stable, however the increasing of these parameters induces thermal instability in the case of circular and rectangular ducts heated from below. That means that the thermal vertical gradient is responsible of the occurring of the thermal instability. This result shows that the horizontal thermal gradient is a stabilizing gradient while the vertical one is a destabilizing one. As this instability enhances heat transfer, it will be very helpful to characterize and to identify the domain where it is occurring in order to prevent or to provoke it depending on the expected performance of the heat exchanger. In this paper, we propose to establish a diagram showing the domain of occurrence of this instability for the various cases cited above and to describe the fluid flow and heat transfer associated to these configurations.
Two-Dimensional Analytical Solution of the Laminar Forced Convection in a Circular Duct with Periodic Boundary Condition
