Problem

Exhaust gases from a manufacturing plant are being discharged through a 10-m tall exhaust...

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/m2 · 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.