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Question

Large brass plate of 40 mm thickness having temperature of 20C,ρ=8530 kg/m3,Cp=380 K/kgK and K=110 W/mK are heated in a furnace, maintained at 500C. Taking the combined convection and radiation coefficient as 120 W/m2 K, the surface temperature of plate after 7 min with a Fourier number of 35.6 is

A
280C
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B
500C
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C
420C
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D
210C
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Solution

The correct option is A 280C
Ti=20C, T=500C,Fe=35.6,h=120W/m2k, k=110W/mcharacteristic length (L)=12(for plate)=0.042=0.02 mBiot number=hLk=120×0.02110=0.0281<0.1Bi<0.1;lumped capacity analysis can be applied.According to lumped capacity analysisTiTTT=e(Bi×Fe)480T500=e0.0281×35.6480T500=2.1743T500=220.756T=279.24T280C

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