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How Much Heat do You Need? Calculations for Heat Energy
Defining the heating problem
- Minimum start and finish temperatures expected
- Maximum flow rate of material(s) being heated
- Required time for start-up heating and process cycle times
- Weights and dimensions of both heated material(s) and containing vessel(s)
- Effects of insulation and its thermal properties
- Electrical requirements — voltage
- Temperature sensing methods and location(s)
- Temperature controller type
- Power controller type
- Electrical limitations
Calculating power requirements
Short method
Start-up Watts = A + C + 2/3L + Safety Factor
Operating Watts = B + D + L + Safety Factor
Safety Factor is normally 10 percent to 35 percent based on application.
A = Watts required to raise the temperature of material and equipment to the operating point, within the time desired
B = Watts required to raise the temperature of the material during the working cycle
The equation for A and B (Absorbed Watts for raising temperature)
Weight of material (lbs) x Specific heat of material (°F) x temperature rise (°F)
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Start-up or cycle time (hrs) x 3.412
C = Watts required to melt or vaporize material during the start-up period
D = Watts required to melt or vaporize material during the working cycle
The equation for C and D (Absorbed watts for melting or vaporizing)
Weight of material (lbs) x heat of fusion or vaporization (Btu/lb)
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Start-up or cycle time (hrs) x 3.412
L = Watts lost from surfaces by conduction use, radiation use heat loss curves or convection use heat loss curves
The equation for L (Lost conducted Watts)
Thermal conductivity of material or insulation (Btu x in./ft2 x °F x hr) x Surface area (ft2) x Temp. differential to ambient (°F)
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Thickness of material or insulation (in.) x 3.412
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 x Cp x ∆T.
Since all calculations are in Watts, an additional conversion of 3.412 Btu = 1 W-hr is introduced.
QA or QB = w x Cp x ∆T
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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 x °F)
∆T = Temperature Rise of Material (TFinal - TInitial)(°F)
Heat Required to Melt or Vaporize a Material
The heat needed to melt 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.
QC or QD = w x Hf or v
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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)
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.
QL1 = k x A x ∆T x te[1]
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3.412 x L
QL1= Conduction Heat Losses (Wh)
k = Thermal Conductivity (Btu x in./ft2 x °F x hour)
A = Heat Transfer Surface Area (ft2)
L = Thickness of Material (in.)
∆T = Temperature Difference Across Material (T2-T1)°F
Convection Heat Losses
Convection is a special case of conduction. Convection is defined as the transfer of heat from a high-temperature region in a gas or liquidas a result of the movement of the masses of the fluid.
QL2 = A • FSL • CF
QL2= Convection Heat Losses (Wh)
A= Surface Area (in2)
FSL = Vertical Surface Convection Loss Factor (W/in2) Evaluated at Surface Temperature
CF= Surface Orientation Factor: Heated surface faces up horizontally (1.29), Vertical (1.00), Heated surface faces down horizontally (0.63)
Radiation Heat Losses
Radiation losses are not dependent on the orientation of the surface. Emissivity is used to adjust for a material’s ability to radiate heat energy.
QL3 = A x FSL x e
QL3 = Radiation Heat Losses (Wh)
A = Surface Area (in2)
FSL = Blackbody Radiation Loss Factor at Surface Temperature (W/in2)
e = Emissivity Correction Factor of Material Surface
Combined Convection and Radiation Heat Losses
If only the convection component is required, then the radiation component must be determined separately and subtracted from the combined curve.
QL4 = A x FSL
QL4 = Surface Heat Losses Combined Convection and Radiation (Wh)
A = Surface Area (in2)
FSL = Combined Surface Loss Factor at Surface Temperature (W/in2)
Total Heat Losses
The total conduction, convection and radiation heat losses are summed together to allow for all losses in the power equations.
QL = QL1+ QL2 + QL3 If convection and radiation losses are calculated separately. (Surfaces are not uniformly insulated and losses must be calculated separately.)
OR
QL = QL1+ QL4 If combined radiation and convection curves are used. (Pipes, ducts, uniformly insulated bodies.)
Power evaluation
After calculating the start-up and operating power requirements, a comparison must be made and various options evaluated.
Shown in Reference 1 are the start-up and operating Watts, in a graphic format, to help you see how power requirements add up. With this graphic aid in mind, the following evaluations are possible:
Compare start-up watts to operating watts.
Evaluate the effects of lengthening start-up time such that start-up watts equals operating watts (use timer to start system before the shift).
Recognize that more heating capacity exists than is being utilized. (A short start-up time requirement needs more wattage than the process in wattage.)
Identify where most energy is going and redesign or add insulation to reduce wattage requirements.
Having considered the entire system, a review of start-up time, production capacity, and insulating methods should be made. Once you have your required heat, you should consider the application factors of your heater.