Exposure to high concentration of gaseous ammonia can cause lung damage. To
prevent gaseous ammonia from leaking out, ammonia is transported in its liquid
state through a pipe \((k=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), $D_{i
\text {, pipe }}=2.5 \mathrm{~cm}, D_{a \text {, pipe }}=4 \mathrm{~cm}$, and
\(\left.L=10 \mathrm{~m}\right)\). Since liquid ammonia has a normal boiling
point of \(-33.3^{\circ} \mathrm{C}\), the pipe needs to be properly insulated
to prevent the surrounding heat from causing the ammonia to boil. The pipe is
situated in a laboratory, where air at \(20^{\circ} \mathrm{C}\) is blowing
across it with a velocity of \(7 \mathrm{~m} / \mathrm{s}\). The convection heat
transfer coefficient of the liquid ammonia is $100 \mathrm{~W} /
\mathrm{m}^{2} \cdot \mathrm{K}$. Calculate the minimum insulation thickness
for the pipe using a material with $k=0.75 \mathrm{~W} / \mathrm{m} \cdot
\mathrm{K}$ to keep the liquid ammonia flowing at an average temperature of
\(-35^{\circ} \mathrm{C}\), while maintaining the insulated pipe outer surface
temperature at \(10^{\circ} \mathrm{C}\).
