An electrical wire of 2 mm diameter and 5 m length is insulated with a plastic layer of thickness 2 mm and thermal conductivity k = 0.1 W/(m·K). It is exposed to ambient air at 30°C. For a current of 5 A, the potential drop across the wire is 2 V. The air-side heat transfer coefficient is 20 W/(m²K). Neglecting the thermal resistance of the wire, the steady state temperature at the wire-insulation interface is ____ °C (rounded off to 1 decimal place).

Question

Accepted Answer

The correct answer is 38.5 to 39.1. GATE 2025 official key: 38.5 to 39.1°C. Heat generated q' = IV/L = 10/5 = 2 W/m. R'_cond = ln(r₂/r₁)/(2πk) ≈ 1.75, R'_conv = 1/(h·2πr₂) ≈ 2.65 (m·K/W). ΔT = q'(R'_cond+R'_conv) ≈ 8.8°C, so T_interface ≈ 30+8.8 ≈ 38.8°C.