# Estimated Heating Times for Electric Radiators

We sell a range of Electric Heating Elements allowing you to avoid having to plumb in your cast iron radiators to a heating system. These are often used in older properties where the plumbing is challenging. Many of the Traditional Radiators we have sold to National Trust properties are with electric heating elements. However, when choosing an electric element and a cast iron radiator, there are certain combinations of heating elements and radiators that will work best together.

To establish the heating requirement of an electric radiators, we can do a calculation for any radiator which we know the weight and water volume of. Here is an example calculation:

Supposed we want to estimate the heating time for a 12 Section Sovereign 4 Column 480 with a 1200W Heating Element.

First we calculate the total weight of iron in the radiator, this is 2 x the leg section weight + 10 x the mid-section weight = 51.2 kg. The total volume of water in the radiator is 0.67 x 12 = 8.04 litres which weighs 8.04kg.

We now use the specific heat of iron and water to calculate how much energy is required to raise the temperature of the radiator by 1 degree. (The specific heat of a substance tells us how many Joules per kg per Kelvin are required to raise the temperature of the substance). The specific heat of Iron is approximately 0.45 KJ/Kg.K and the specific heat of water is much higher at 4.2 KJ/Kg.K.

Multiplying these specific heats by the weight of water and iron in the radiator tells us how much energy is required to heat the radiator through 1 degree of temperature.

Iron: 51.2 x 0.45 = 23.04 KJ / K

Water: 8.04 x 4.2 = 33.768 KJ/K

Total: 56.808 KJ / K

So the energy required to raise the temperature of the radiator (both water and iron) by 1 Kelvin (an increase in 1 Kelvin is exactly equivalent to an increase of one degree Centigrade) is 56,808 Joules. We need to calculate the time taken to heat the radiator through each degree of temperature rise and add all these times together to calculate the total time taken to reach a given temperature.

When the radiator is first turned on, we assume it is at room temperature so ΔT=0 and no heat is lost to the surrounding room. (Remember ΔT is the difference between the average radiator temperature and the surround room temperature). The heat input from the heating element is 1500W, and since a Watt is a Joule per second, the time in seconds to raise the radiator temperature to 1 degree above room temperature is 56,808/1200= 47.34 Seconds. This works out at 0.79 minutes

Now ΔT=1, and the radiator is just beginning to heat the room.

We must now consider the heat output of the radiator. The heat output of one section at ΔT=50 is 62.4 Watts so the heat output of the entire twelve section radiator is 748.8Watts ( at ΔT=50). As the radiator's temperature rises above the room temperature the heat output increases with ΔT (but not in a linear way). Experiments have shown that the heat output at different temperatures is best modelled by (ΔT/50)^1.3 multiplied by the heat output at ΔT=50.

Doing the calculation shows that the heat output of the radiators at ΔT=1 is just 4.63 watts, the heat available to heat the radiator is 1200-4.62W=1195.37w. So the time taken to raise the temperature by the next 1 degree is 56,808/1195.37= 47.52 seconds.

We continue step by step for each degree of temperature rise. So for example when ΔT=25, the radiators heat output is 0.406 x 748.8 w= 304.1 w, the heat input is still 1200w so the surplus heat available to heat the water and iron in the radiator is 1200-304.1=895.9W. The time taken to heat the radiator by 1 degree is now 56,808/895.9 =63.41 seconds or 1.06 minutes.

By adding all the step times together we can now estimate the time to reach a given temperature. The Heating Elements heat the water to a maximum temperature of 65 C, for a 20C ambient room temperature this corresponds to ΔT=45, and for a 15C ambient room temperature this corresponds to ΔT=50. We assume a room temperature between these values, and therefore give an estimated heating time between the time taken to reach ΔT=45 and ΔT=50. In this case 49-59minutes.

If all this is too much for you to follow, give us a call on 01723 321 000 and we will go through this with you. It should be noted that the heat output of an electric element is generally below wet plumbing.