In a curing process for plastic and other polymer-based materials, a plastic sheet, which initially is 25°C, is placed on a hot metal surface that is maintained at 250°C. If the back (or opposite) side of the 5-mm-thick plastic film is considered to be insulated, how long does it take for the back side to reach temperature of 90°C. Assume the following plastic properties: c = 1450 J/(kg K), k= 0.23 W/(m K), and ?= 1975 kg/m3
GIVEN
• Initial temperature of plastic sheet (T0)= 250C
• Sheet thickness (2L) = 5 mm = 0.005 m
• Opposite side or back is insulated
• Metal surface temperature (T?)= 2500C
• The thermal conductivity of the plastic (k) = 0.23 W/(m K)
• Density(?) = 1975 kg/m3
• Specific heat capacity (c)= 1450 J/(kg K)
FIND
Time taken for backside to reach temperature of 900C
ASSUMPTIONS
• The initial temperature of the sheet is uniform
• The temperature of the steel plates is constant
• The thermal conductivity of the sheet is constant
SKETCH
For one-dimensional time dependent equation in conduction we have
The solution for such infinite plate conduction problem is given by
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