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Example B.12

(a) Consider a large steel vessel, wall thickness 16 mm protected by 40 mm of vermiculite cement. Find the metal temperature after 1 and 2 h in a flux of 100 kW m−2 for surface emissivities of 1 (~black), 0.3 (~aluminum paint), and 0.1 (~white). Properties of steel are density 7800 kg m−3, specific heat 0.5 kJ kg−1 K−1 and properties of vermiculite are density 430 kg m−3, specific heat 0.84 kJ kg−1 K−1 and thermal conductivity 9.5 × 10−5 kW m−1 K−1.

ANSWER

Surface temperature 100=5.6697×1011(Ts42934)+0.01ε(Ts293)Ts=856,797,640°Cforε=1,0.3,and0.1
Insulation time constant tc=(WRsRAR+xIρIsI2)xIkI=(7,800×0.016AR×0.5

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