Study of buoyancy driven heat transport in silicone oils and in liquid nitrogen in view of cooling applications

Motivated by applications for cooling superconducting pellets with liquid nitrogen, we consider a source with a fixed heating rate per unit volume, immersed in a liquid pool and cooled through natural convection. In one recent experimental investigation (Dubois et al., 2016) carried on silicone oils and liquid nitrogen, we have demonstrated that the velocity field satisfies specific scaling laws with respect to the temperature increase in the liquid pool. In this work, we pursue the analysis by modeling the heat transfer in a parallelepiped enclosure for a steady laminar flow regime. The Navier-Stokes equations are solved using a finite volume approach to obtain the detailed three-dimensional flow and heat-transfer characteristics. A quantitative analysis of the velocity field over the temperature field shows that the experimental power laws are reproduced in simulations. Following Dubois and Berge (1978), a theoretical law originally introduced in the context of the classical Rayleigh-Bénard experiment is shown to be satisfied in the simulations over a wide range of Rayleigh numbers (Ra), assuming the definition of the characteristic convection length is adapted to the investigated geometry. Moreover, the simulations are shown to correctly reproduce the main features of the flow, including the characteristic convection length, for different heater lengths.