This page calculates the natural convection heat transfer between two concentric
cylinders maintained at constant temperatures. The calculation is based on Rayleigh number and is valid for Rayleigh
numbers below 10^{7}.

The heat transfer between the cylinders *(q _{c})* is calculated as:

q_{c} = 2Pi L k_{eff} (T_{i}_{ }- T_{o})
/ ln(D_{o}/D_{i})

Where *L* is the length of the cylinders, *T _{i}* is the temperature of the
inner cylinder and

k_{eff} / k = 0.386(Ra_{c}^{*})^{1/4}(Pr
/ (0.861+Pr))^{1/4} ^{
}where Ra_{c}^{*} = Ra_{d}_{ }(ln(D_{o}/D_{i}))^{4
}/ (d^{3}(D_{i}^{-3/5}+D_{o}^{-3/5})^{5})

Ra_{d}_{ }= gB rho^{2}C_{p}(T_{i}-T_{o})d^{3} /
kµ

For the above equations *Ra _{d}* is the Rayleigh
number based on the distance R

In addition, you must define the fluid properties at the film
temperature *T _{f}* defined as follows, except for the density
which is defined at the reference temperature of 20 C.

T_{f} = (T_{p} + T_{a}) / 2

The fluid density at the film temperature is automatically calculated from the following relationship based on the perfect gas law:

Rho = Rho_{ref} (T_{ref} +273) / (T_{f}
+ 273)

**References**

Raithby, G. D., and K. G. T. Hollands, *A General Method
of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection
Problems,*
in T. F. Irvine and J. P. Hartnett, Eds., Advances in Heat Transfer, Vol. 11,
Academic Press, New York, pp 265-315, 1975.

Incropera, De Witt., *Fundamentals of Heat and Mass Transfer*,
3rd ed., John Wiley & Sons, p563, eq 9.58-9.60, 1990.