Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
A stainless steel steam pipe of outer diameter $50\text{ mm}$ (radius $r_1 = 25\text{ mm}$) is insulated with glass wool insulation ($k = 0.05\text{ W/(m}\cdot\text{K)}$) in surrounding air with convective heat transfer coefficient $h = 5.0\text{ W/(m}^2\cdot\text{K)}$. The critical radius of insulation ($r_c = k / h$) in millimeters is ________ (answer in integer).
Answer Key:
10
Step-by-Step Solution & Explanation
Critical radius of insulation for a cylinder:
$r_c = \frac{k}{h} = \frac{0.05\text{ W/(m}\cdot\text{K)}}{5.0\text{ W/(m}^2\cdot\text{K)}} = 0.010\text{ m} = 10\text{ mm}$
Since the pipe outer radius ($25\text{ mm}$) already exceeds $r_c$, any added insulation will monotonically reduce the heat loss rate.