Canada Builds

Sizing a Radiator

The work of Stefan and Boltzmann in the late 1880's proved that the amount of radiation emitted from a 'perfect radiator' or 'blackbody' is proportional to the fourth power of the Kelvin Temperature. It is possible to use the Stephan-Boltzmann law of radiation to size a radiator with the excel sheet below. The equation can be derived as follows:
H = σ (T1 4 - T2 4)

H = Heat radiated in kilocalories per second per square metre or kcal / sec m2
T1 = Kelvin Temperature of the radiating body
T2 = Kelvin Temperature of the surroundings
σ = Radiation Constant with a value of 1.35 x 10 -11 kcal / sec m2 K4 (or 5.67 x 10 -8 W / m2 K4)

A radiator is operating with a surface temperature of 180 °F with an effective surface area of 10 square feet. How many Btu's per hour (or Btuh) will the radiator emit to a room whose average temperature is 70 °F (21 °C)? Use the excel worksheet below to place these values into the equation.

A note on the chart below - You can type values into the chart below to see and compare calculations. Type only the red numbers. If you type another cell, the formula will get erased. If this happens, simply hit F5 or 'refresh the page'.

In essence, the information you get from this calculation is the amount of btu/hr that a radiator of a certain size at a certain tempertature will give off. For instance, a radiator with a surface area of 10 square feet that is heated up to a temperature of 180 degrees farenheit will emit about 6000 btu/hr into a surrounding area (i.e. a room) that is 70 degrees farenheight. We could convert to metric and use units other than those listed above. First though you want to get a sense of what is going on and what is being described in common language. Metric makes it much more complicated. Especially when you go out to buy a radiator or a furnace to see that they are sold and advertised based on their 'btu' output. For this reason, you might be better off using imperial calculations and converting once finished.