Exhaust gases from a manufacturing plant are being discharged through a
\(10-\mathrm{m}-\) tall exhaust stack with outer diameter of \(1 \mathrm{~m}\).
The exhaust gases are discharged at a rate of \(0.125 \mathrm{~kg} /
\mathrm{s}\), while temperature drop between inlet and exit of the exhaust
stack is \(30^{\circ} \mathrm{C}\), and the constant pressure-specific heat of
the exhaust gases is \(1600 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). On a
particular calm day, the surrounding quiescent air temperature is \(33^{\circ}
\mathrm{C}\). Solar radiation is incident on the exhaust stack outer surface at
a rate of \(500 \mathrm{~W} / \mathrm{m}^{2}\), and both the emissivity and
solar absorptivity of the outer surface are \(0.9\). Determine the exhaust stack
outer surface temperature. Assume the film temperature is \(60^{\circ}
\mathrm{C}\).