Electric Heaters Power Calculations

Absorbed Energy, Heat Required to Raise the Temperature of a Material Because substances all heat differently, different amounts of heat are required in making a temperature change. The specific heat capacity of a substance is the quantity of heat needed to raise the temperature of a unit quantity of the substance by one degree. Calling the amount of heat added Q, which will cause a change in temperature ∆T to a weight of substance W, at a specific heat of material Cp, then Q =w • Cp • ∆T. Since all calculations are in watts, an additional conversion of 3.412 Btu = 1 Wh is introduced yielding:

Equation 1

QA or QB = w • Cp • ∆T

                            3.412

QA = Heat Required to Raise Temperature of Materials During Heat-Up (Wh)

QB = Heat Required to Raise Temperature of Materials Processed in Working Cycle (Wh)

w = Weight of Material (lb)

Cp = Specific Heat of Material (Btu/Ib • °F)

∆T = Temperature Rise of Material (TFinal – TInitial)(°F)

This equation should be applied to all materials absorbing heat in the application. Heated media, work being processed, vessels, racks, belts, and ventilation air should be included.

Example:

How much heat energy is needed to change the temperature of 50 lbs of copper from 10°F to 70°F?

Q = w • Cp • ∆T

= (50 lbs) • (0.10 Btu/Ib • °F) • (60°F) = 88 (Wh)

Electric Heaters Power Calculations

Heat Required to Melt or Vaporize a Material In considering adding heat to a substance, it is also necessary to anticipate changes in state that might occur during this heating such as melting and vaporizing. The heat needed to melt a material is known as the latent heat of fusion and represented by Hf. Another state change is involved in vaporization and condensation. The latent heat of vaporization Hv of the substance is the energy required to change a substance from a liquid to a vapor. This same amount of energy is released as the vapor condenses back to a liquid.

Equation 2

QC or QD = w • Hf    OR   w • Hv

                       3.412             3.412

QC = Heat Required to Melt/Vaporize Materials During Heat-Up (Wh)

QD = Heat Required to Melt/Vaporize Materials Processed in Working Cycle (Wh)

w = Weight of Material (lb)

Hf = Latent Heat of Fusion (Btu/Ib)

Hv = Latent Heat of Vaporization (Btu/lb)

Example:

How much energy is required to melt 50 lbs of lead?

Q = w • Hf 

= (50 lbs) • (9.8 Btu/Ib) = 144 (Wh)

          3.412 Btu/(Wh)

Changing state (melting and vaporizing) is a constant temperature process. The Cp value (from Equation 1) of a material also changes with a change in state. Separate calculations are thus required using Equation 1 for the material below and above the phase change temperature.

Conduction Heat Losses

Heat transfer by conduction is the contact exchange of heat from one body at a higher temperature to another body at a lower temperature, or between portions of the same body at different temperatures.

Equation 3A - Heat Required to Replace Conduction Losses

QL1 = k • A • ∆T • te

               3.412 • L

QL1= Conduction Heat Losses (Wh)

k = Thermal Conductivity (Btu • in./ft2 • °F • hour)

A = Heat Transfer Surface Area (ft2)

L = Thickness of Material (in.)

∆T = Temperature Difference Across Material (T2-T1) °F

te = Exposure Time (hr)

This expression can be used to calculate losses through insulated walls of containers or other plane surfaces where the temperature of both surfaces can be determined or estimated.

Safety Factor Calculation

Heaters should always be sized for a higher value than the calculated figure, often referred to as adding in a safety factor. Generally speaking, the fewer variables and outside influences—the smaller the safety factor.

Here are some general guidelines:

• 10 percent safety factor for large heating systems or when there are very few unknown variables.
• 20 percent safety factor for small to medium heating systems where you are not 100 percent sure you have accurate information.
• 20 to 35 percent for heating systems where you are making many assumptions.