Question

For a current carrying wire of 20 mm diameter exposed to air $(h=20W/m^2$K), maximum heat dissipation occurs when thickness of insulation (0.5 W/mK) is

• A. 30 mm
• B. 25 mm
• C. 20 mm
• D. 15 mm

Answer 1

The correct option is D 15 mm

Given data :
d=20 mm
$\therefore r=\frac{d}{2}=\frac{20}{2}=10mm$
$h_0=20W/m^{2}K$
$k=0.5W/mK$

For maximum heat dissipation,
critical radius,
$r_c=\frac{k}{h}$ for cylinder or wire
$=\frac{0.5}{20}=0.025m$
$=25mm$
Thickness of insulation,
$=r_c-r=25-10$
$=15mm$