This page calculates the heat transfer coefficient, heat
convected and heat radiated from an isothermal horizontal cylinder assuming natural convection. The
convection calculation is based on Rayleigh number and is valid for Rayleigh
numbers between 10^{-5} and 10^{12}. The ends of the cylinder
are assumed to be adiabatic.

The heat loss from the cylinder *(q _{c})* is calculated as:

q_{c} = hA (T_{c }- T_{a})

Where *h* is the average heat transfer coefficient, *A* is the
total area of the cylinder, *T _{c}* is the average temperature of the
cylinder and

h = Nu k / D

Where *Nu* is the Nusselt Number, *k* the conductivity of the
fluid and *D* the diameter of the cylinder. The Nusselt number is calculated as:

Nu = { 0.60 + (0.387Ra_{D}^{1/6}) / [1+(0.559/Pr)^{9/16}]^{(8/27)} }^{2
}where Ra_{D} = gB rho^{2}C_{p}(T_{c}-T_{a})D^{3} /
kµ

For the above equations *Ra _{D}* is the Rayleigh
number based on the diameter of the cylinder,

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)

The radiative heat transfer is calculated as follows:

Qrad = Sigma A x E x(T_{c}^{4} - T_{a}^{4})

where Sigma, the Stefan-Boltzman constant = 5.678e-8

A is the
cylinder area

E is the
surface emissivity

T_{c}
and _{ }T_{a} are the plate and ambient temperatures
respectively, in degrees Kelvin.

**References**

Churchill, S. W., and H. H. S. Chu, *Correlating
Equations for Laminar and Turbulent Free Convection from a Horizontal Cylinder,*
Int. J. Heat Mass Transfer, 18, 1049 1974.

Incropera, De Witt., *Fundamentals of Heat and Mass Transfer*,
3rd ed., John Wiley & Sons, p551, eq 9.34, 1990.