Concentric Cylinders — Natural Convection
Calculates the natural-convection heat transfer across the annular gap between two long concentric cylinders held at constant temperatures Ti (inner) and To (outer). The Raithby–Hollands method represents the buoyant flow in the gap as an enhanced conduction: heat is conducted through a stationary fluid of effective conductivity keff>k.
Gap Rayleigh Number
Properties are evaluated at the mean temperature Tf=(Ti+To)/2. The characteristic length is the radial gap b=(Do−Di)/2:
Rad=ν2gβ(Ti−To)b3PrModified Rayleigh Number and Effective Conductivity
Rac∗=b3(Di−3/5+Do−3/5)5[ln(Do/Di)]4Rad kkeff=0.386(0.861+PrPr)1/4(Rac∗)1/4The correlation is valid for 102≤Rac∗≤107; below Rac∗=100 buoyancy is negligible and keff=k (pure conduction).
Heat Rate
Q=ln(Do/Di)2πkeffL(Ti−To)References
- Raithby, G. D. and Hollands, K. G. T., A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems, Advances in Heat Transfer, Vol. 11, Academic Press, pp. 265–315, 1975.
- Incropera, F. P. and DeWitt, D. P., Fundamentals of Heat and Mass Transfer, eqs. 9.58–9.60.