A large 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on the one side is 28 W/(m2 K) and on the other side is 57 W/(m2 K). If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it will take for the copper plate to reach a temperature of 82°C.
GIVEN
• A large copper plate between two air streams whose temperatures suddenly change
• Plate thickness (2L) = 2.54 cm = 0.0254 m
• The heat transfer coefficients are
? lch = 28 W/(m2 K)
? 2ch = 57 W/(m2 K)
• Air temperature changes from 38°C to 93°C
FIND
• How long it will take for the copper plate to reach a temperature of 82°C
ASSUMPTIONS
• The initial temperature of the plate is 38°C
• The plate can be treated as an infinite slab
SKETCH
The Biot number for this case, using the larger of the heat transfer coefficients is
Therefore, the internal resistance of the slab can be neglected (the temperature of the slab remains uniform)
and the temperature-time history can be calculated from an energy balance
Change in internal energy = heat flow from both sides
Integrating between a temperature of To at time = 0 to a temperature of T at time = t yields
Solving this for the time
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