b) A steel pipe with heat transfer coefficient of $42 \mathrm{~W} / \mathrm{mK}$ contains flowing water. The outer diameter of the pipe is $90 \mathrm{~mm}$ and the wall thickness is $3 \mathrm{~mm}$. Calculate:
i. The heat loss by convection and conduction per meter length of un-insulated pipe when the water temperature is $14^{\circ} \mathrm{C}$, the outside air temperature is $-10^{\circ} \mathrm{C}$, the water side heat transfer coefficient is $30 \mathrm{KW} / \mathrm{m}^{2} \mathrm{~K}$ and the outside heat transfer coefficient is $20 \mathrm{KW} / \mathrm{m}^{2} \mathrm{~K}$.
Answer
\(\boxed{33.58}\) W/m is the heat loss by convection and conduction per meter length of un-insulated pipe.
Step 1 ：Calculate the inner diameter of the pipe: D_inner = D_outer - 2 * t = 0.09 - 2 * 0.003 = \(0.084\) m
Step 2 ：Calculate the area of the pipe's inner surface and outer surface per meter length: A_inner = \(\pi * 0.084\) m, A_outer = \(\pi * 0.09\) m
Step 3 ：Calculate the heat loss by convection and conduction: Q = \(\frac{30000 * \pi * 0.084 * (14 - (-10)) + 42 * \pi * 0.09 * (14 - (-10))}{20000 * \pi * 0.09 + 42 * \pi * 0.084}\) W/m
Step 4 ：\(\boxed{33.58}\) W/m is the heat loss by convection and conduction per meter length of un-insulated pipe.
