Where k is thermal conductivity of air and L is the characteristic length. Note that N is a dimensionless quantity.
In our case, which does involve turbulent flow, we are interested in temperature variation along the length of a metal cylinder, so we will take the characteristic length L to be the length of the cylinder.
Applications:
Natural convection heat transfer is extensively used in the following areas of engineering:
1. Cooling of commercial high voltage electrical power transformers.
2. Heating of houses by electrical baseboard heaters.
3. Heat loss from steam pipe lines in power plants and heat gain in refrigerant pipe lines in air conditioning applications.
4. Cooling of reactor cores in nuclear power plants, though often the coolant is driven by pumps, resulting in more efficient heat transfer by forced convection.
5. Cooling of electronic devices (chips, transistors) by finned heat sinks, though a fan is often present to augment the natural convection with forced convection.