An electrical wire having a diameter of 1.5 mm and covered with a plastic insula

Question

An electrical wire having a diameter of 1.5 mm and covered with a plastic insulation (thickness = 2.5 mm) is exposed to air at 300 K, and h0 = 20 W/m2 K. The insulation has a k of 0.4 W/m K. It is assumed that the wire surface temperature is constant at 400 K and is not affected by the insulation. Find the heat loss per unit length of the wire with the insulation present. (Hint: Base your calculation on an overall heat transfer coefficient composed of the insulation resistance and the air-film coefficient.)

Explanation / Answer

resistance = R = ln(Ro/Ri)/(2.pi.k.l) + 1/h.2.pi.Ro.L

here do = 1.5 + 2 x 2.5 = 6.5 mm

and di = 1.5 mm

so, R = ln (6.5/1.5)/(2.pi x 0.4 x 1) + 1/ (20 x pi x 0.0065 x 1) (here length = 1m as we have to find heat per unit length)

= 0.583 + 2.45 = 3.03

UA = 1/R

so, U = 1/ (R x area) = 1/ (3.03 x pi x 0.0065x 1) {here U = overall heat transfer coeeficient based on outer area}

= 16.16 W/m^2.K

so, Q = U.A.dT = 16.16 x (pi x 0.0065 x 1) x (400 - 300)

= 33 W/m

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