An aluminum wire is wrapped with insulation and surrounded by air. The wire conducts electricity. The electrical power resistance loss is 4 Watts per meter of wire, uniformly distributed across the wire cross-section. Assume steady 1-D radial heat conduction. The surrounding air at 300 K provides natural convection heat transfer to the insulation outer surface with a convection coefficient of 5 W/m^2-K. Radiation and contact resistance are negligible
Given: Wire radius, r1= 0.002 m, Aluminum, k = 240 W/m-K. Insulation, k = 0.40 W/m-K, layer thickness 0.0005 m, outside radius, r2 = 0.0025 m
a) Find the convective heat transfer rate to the air per unit length of wire, Q /L = ________(Watt/m)
b) Find the temperature distribution vs radius withmaximum temperature, Tmax = ____ K, T1=____K, T2 = ____ K
c) Plot (or carefully hand draw to scale) the temperature distribution T vs r in the wire and insulation.
d) Find the radial conduction heat transfer rate inthe wire at r = 0.001 m, ( Q /L) = ______(Watt/m)