Discussion
For a current carrying wire of 20mm diameter exposed to air (h = 20W/m2K), maximum heat dissipation occurs when thickness of insulation (0.5 W/mK) is :
Answer: D
The insulation thickness for maximum heat dissipation is 15 mm.
For a cylinder, heat loss is greatest when the outer radius of the insulation equals the critical radius:
\[ \begin{aligned} r_{c} &= \frac{k}{h} = \frac{0.5}{20} = 0.025\ \text{m} = 25\ \text{mm} \\ t &= r_{c} - r = 25 - 10 = 15\ \text{mm} \end{aligned} \]
The wire's radius is 10 mm, half its 20 mm diameter. 25 mm is the critical radius itself, not the thickness, and 30 mm and 20 mm come from using the diameter in place of the radius.
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