Natural convection

Un article de Surface du verre et interfaces.

This work is motivated by the need to understand heat and mass transfers in glass melting tanks. The actual problem is complicated by the geometrical and physical characteristics. Nevertheless, furnaces are longer than high or wide. Moreover, the glass dynamical viscosity is high and the thermal conductivity is small. So, the Prandtl number is large enough, greater than 100.

In order to get insight into this problem, we study an idealized situation whereby a high Prandtl number fluid is differentially heated in a bidimensional shallow cavity. A first situation was studied where the temperature is applied on vertical walls. We shown that the only one parameter is needed to describe the kinematic regimes. This parameter is the product of Rayleigh number, based on the height of the cavity, by the square of cavity aspect ratio.

Recently, this work has been extended by imposition of the temperature on the upper limit of the enclosure which is close to the industrial situation. The heat and mass transfer is studied where the Péclet and Nusselt numbers are determined by using asymptotic and numerical analysis. In this last situation, the product of Rayleigh number by the square of cavity aspect ratio is again the relevant parameter to describe the kinematics and the heat flux.

 

Publications

• F. Pigeonneau and J.-M. Flesselles. Convection laws for glass furnaces revisited. Verre, 9(2) :14–16, 2003.

• J.-M. Flesselles and F. Pigeonneau. Kinematic regimes of convection at hight Prandtl number in a shallow cavity. C. R. Mécanique, 332 :783–788, 2004.

• F. Pigeonneau and J.-M. Flesselles. Natural convection of a high Prandtl number fluid in a long cavity heated from above. Int. J. Heat & Mass Transfer, under review, 2009.