SECTION A
1.
(a)
A copper wire length l and radius r1 of resistivity, ?, and thermal conductivity, k1, is carrying a current I. The wire is covered with a plastic coating with outer radius, r2 and thermal conductivity k2. The wire is cooled by air with a convective heat transfer coefficient, h. Use this information to obtain an algebraic relationship between the current, I, carried by the wire, the
temperature at the interface between the plastic insulation and the copper wire, T1, and the
external, air temperature, T2. Clearly state any assumptions you make in your analysis.
NB: The resistance of a wire R = ?l/A where l is the length of the wire and A is the cross-
sectional area.
(b) Assuming that resistance heating happens uniformly throughout the copper wire, derive an algebraic equation that relates the temperature distribution in the copper wire to the heat generated per unit volume, q? .
(c) The resistivity of copper is 17 nO m, the thermal conductivity is 398 W m–1 K–1. The thermal conductivity of the plastic coating is 0.3 W m–1 K–1. The convective heat transfer coefficient of air is 10 W m–2 K–1. The diameter of the copper wire is 0.8 mm and the thickness of the plastic coating is 0.5 mm. If the maximum allowable temperature difference between the surface of the copper wire and the external air temperature is 30ºC use your result from part a) to determine the maximum current that the wire can carry.
(d) Assuming that the wire is carrying the maximum current determined in part (c) use your result from part (b) to determine how much hotter the copper wire is on its centreline than on its edge.
(e) If a 5 A current is passed through the wire and the air temperature is 22ºC what is the outer surface temperature of the insulation?
2. (a) What is black body radiation?
(b) What is the grey body approximation?
(c) What is a shape factor and why is it relevant to radiative heat transfer?
(d) Describe briefly an electrical …