Exhaust gases from a manufacturing plant are being discharged through a 10-m tall exhaust stack with outer

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Exhaust gases from a manufacturing plant are being discharged through a 10-m tall exhaust stack with outer diameter of 1 m, wall thickness of 10 cm, and thermal conductivity of 40 W/m·K. The exhaust gases are discharged at a rate of 1.2 kg/s, while temperature drop between inlet and exit of the exhaust stack is 30°C, and the constant pressure specific heat of the exhaust gasses is 1600 J/kg · K. On a particular day, the outer surface of the exhaust stack experiences radiation with the surrounding at 27°C, and convection with the ambient air at 27°C also, with an average convection heat transfer coefficient of 8 W/m· K. Solar radiation is incident on the exhaust stack outer surface at a rate of 150 W/m2, and both the emissivity and solar absorptivity of the outer surface are 0.9. Assuming steady one-dimensional heat transfer,
(a) Obtain the variation of temperature in the exhaust stack wall and
(b) Determine the inner surface temperature of the exhaust stack.

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