Question Bank • QB_PARAMETRIC_DFE_CND_014NAT • 1 Mark
Section 7: Dairy and Food Engineering
Steady-State Conduction & Shape Factors
Subtopic: Critical radius of insulation for cylindrical pipe
Question Statement:
A steam pipe in a dairy plant is to be covered with insulation having thermal conductivity $k = 0.05\text{ W/(m}\,\text{K)}$. The outer convective heat transfer coefficient with ambient air is $h = 10.0\text{ W/(m}^2\,\text{K)}$. The critical radius of insulation is ________ $\text{mm}$ (round off to one decimal place). (Variation QB_PARAMETRIC_DFE_CND_014)
Answer Key:
5.0
Step-by-Step Solution & Explanation
The critical radius of insulation for a circular cylinder is:
$r_c = \frac{k}{h}$
Given $k = 0.05\text{ W/(m K)}$ and $h = 10.0\text{ W/(m}^2\text{ K)}$:
$r_c = \frac{0.05}{10.0} = 0.0050\text{ m} = 5.0\text{ mm}$