Chapter 3, Problem 3.45P

A steam pipe of 0.12-m outside diameter is insulated with a layer of calcium silicate.

1. If the insulation is 20 mm thick and its inner and outer surfaces are maintained at $T_{s,1}=800\text{K}$ and $T_{s,2}=490\text{K,}$ respectively, what is the heat loss per unit length $\left(q\text{'}\right)$
of the pipe?
2. We wish to explore the effect of insulation thickness on the heat loss $q\text{'}$ and outer surface temperature $T_{s,2}$ with the inner surface temperature fixed at $T_{s,1}=800\text{K}\text{.}$ The outer surface is exposed to an airflow $\left(T_{\infty }=25°\text{C}\right)$ that maintains a convection coefficient of $h=25{\text{W/m}}^{\text{2}}\cdot \text{K}$ and to large surroundings for which $T_{sur}=T_{\infty }=25°\text{C}\text{.}$ The surface emissivity of calcium silicate is approximately 0.8. Compute and plot the temperature distribution in the insulation as a function of the dimensionless radial coordinate, $\left(r-r_1\right)/\left(r_2-r_1\right)$ where $r_1=0.06\text{m}$ and $r_2$ is a variable $\left(0.006<r_2\le 0.20\text{m}\right).$ Compute and plot the heat loss as a function of the insulation thickness for $0\le \left(r_2-r_1\right)\le 0.14\text{m}\text{.}$