Rarefied Conditions in the Convective-Diffusive Regimes of a Disc in Natural Convection

A numerical investigation has been conducted on a heated circular disc immersed in quiescent air in an enclosed environment and for rarefied conditions. For moderate to low Rayleigh numbers, laminar natural convection can be described by two regimes and a transitional region which separates the diffusive limit and laminar boundary layer, or convective limit. A practical scenario was simulated which involved lowering Rayleigh number and increasing Knudsen number of the disc simultaneously to examine the convective-diffusive relationship under a rarefied condition. The numerical model used to solve the continuum equations has been extended using a first order slip condition and assessed based on the available experimental data from literature. Although similar convective-diffusive regimes exist, there is a divergence from the classical continuum diffusive limit when operating in rarefied conditions with Knudsen numbers of order 10⁻³ or higher. The conditions for this second transitional region in heat transport from the surface have been highlighted and have been attributed to the temperature jump condition. This has resulted in recommendations on the limitation of existing analytical heat transfer models when applied to rarefied conditions. The findings also have practical significance to thermal metrology and aerospace industries where buoyancy induced flows and low ambient pressures are frequently experienced.