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Thermoforming Example (cont.):

Warm-up Time:

                                Watt-Hour / in²
Warm-up Time =    ^{__________________}   x  60        Minutes
                                   Watt / in²

                          .179
1 min. =    ^{________________}   x  60
                      Watt / in²

Solve the "time" equation for Watt / in²:

                     (.179)(60)
Watt / in² =  ^____________    =  10.74
                        1 min
Watt / in² = 10.74

This is the amount of infrared radiant energy that must be absorbed into the PVC sheet to heat the sheet to 350 °F (177 °C) in 1 minute.

At this point one can use Planck's Law and the spectral absorption curve for PVC by superimposing these curves on each other and calculating the total area under the curves at which the two curves intersect (provided that accurate curves are available). This can be extremely time consuming.

A simplified method of estimating the power radiated and absorbed into the PVC sheet is given by the following:

The effective emissivity between two parallel plates is given by:

                    1                                  1
e =   ^{__________________     =     __________________}
        ( 1/e₁ + 1/e₂ - 1)            ( 1/.9 + 1/.9 - 1)

   = .82

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