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Q12. A wire of diameter 3 mm carries an electric current, and each metre length generates 2.5 watts of heat. The surrounding air is at 20°C and the surface heat transfer coefficient is 12 W/m²K.

(a) Determine the temperature of the wire.

(b) The wire is to be covered with insulation 1.5 mm thick and of thermal conductivity 0.1 W/mK. The heat transfer coefficient at the outer surface may be assumed to remain the same. Show that this reduces the temperature of the wire.

(c) Explain why in this case the added insulation increases the heat flow rate.