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The base plate of an iron has a thickness of L 7 mm and is made from an aluminum alloy ( 2800 kg/m3 , c 900 J/kg ∙ K, k = 180 W/m∙K, ε = 0.80). An electric resistance heater is attached to the inner surface of the plate, while the outer surface is exposed to ambient air and large surroundings at T∞ = Tsur 25°C. The areas of both the inner and outer surfaces are As = 0.040 m2.
If an approximately uniform heat flux of q”h = 1.25 × 104 W/m2 is applied to the inner surface of the base plate and the convection coefficient at the outer surface is h = 10 W/m2 ∙ K, estimate the time required for the plate to reach a temperature of 135°C.
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