Numerical study of free convection in a thin layer between coaxial horizontal cylinders

Abstract

We consider free convection in 2D and 3D horizontal cylindrical layers with the inner hot and outer cold boundary at Ra (Rayleigh number) in range (4∙103 ÷ 4∙105) and the ratio δ ≈ 1:20 of the layer width to inner radius. Prandtl number was 0,71, fluid properties were taken for air at 293 K.It was shown that the flow in a 2D cylindrical layer can be divided into three regions. Stable symmetric convective rolls are formed in the layer’s upper part; regions with the transient flow appear at the lateral sides; transitional regions between the upper and the lateral regions have convective rolls of an unusual asymmetric shape.The flow in a 3D cylindrical layer in the upper part is organized into a spatially stable convective roll pattern. With increase of the Rayleigh number (Ra), roll pattern becomes suppressed by a transient plume pattern.The global Nu (the Nusselt number) is proportional to 0,0019∙Ra0,567 for the 2D case and to 0,22∙Ra0,192 for the 3D case. The 2D problem provides a reasonable estimation of the Nusselt number for Rayleigh number up to 4∙104 and overestimates Nu for higher Rayleigh number, which agrees with Lyapunov exponent values.

Keywords

• Convection
• Rayleigh-bénard
• Nusselt
• Lyapunov
• Coaxial cylinders