Question

A 10 mm diameter electrical conductor is covered by an insulation of 2 mm thickness . The conductivity of the insulation is 0.08 W/mK and the convection coefficient at the insulation surface is 10 W/m${}^2$K. Addition of further insulation of the same material will

• A. increase heat loss continuously
• B. decrease heat loss continuously
• C. increase heat loss to a maximum and then decrease heat loss
• D. decrease heat loss to a minimum and then increase heat loss

Answer 1

The correct option is C increase heat loss to a maximum and then decrease heat loss

Given data:
$d_i$=10 mm
$\therefore$ $r_i$=$\frac{d}{2}$=$\frac{10}{2}$=5 mm
t = 2 mm
$\therefore$ $r_o$= $r_i$+t
= 5 + 2 = 7 mm
k=0.08 W/mK
$h_o=10W/m^{2}K$

Critical radius,
$r_c$ = $\frac{K}{h_0}$=$\frac{0.08}{10}$
$=0.008m=8mm$
As $r_o$<$r_c$, the heat loss increase to a maximum and then decrease heat loss by addition of insulation.