2) Joule heating – Wrap up. In class, we discussed how the temperature profile in a wire that carries current would look

[answerhappygod]

2 Joule Heating Wrap Up In Class We Discussed How The Temperature Profile In A Wire That Carries Current Would Look 1 (88.84 KiB) Viewed 46 times

2) Joule heating – Wrap up. In class, we discussed how the temperature profile in a wire that carries current would look like. The wire uniformly generates heat due to Joule heating. a. Consider the case where the wire has plastic insulation around the copper core, as shown below. Plastic wire insulation T. S h, T Copper wire b. Develop a macroscopic energy balance and calculate the surface temperature of the insulation: T₁=T + - + I² PR 2л²R,R³h 2 In part d and e, you are asked to compare your simplified solutions against the ones that you obtained in parts a & b. R 0 R T 0
c. Develop a shell balance within the insulation and show that rq = constant. Then, obtain an expression for To ³: T₁=T+; I² PR 2n²R³U Here, U is the overall heat transfer coefficientª: 1 In (R₁/R₁) 1 U = + k Rh d. The amount of current that a wire can carry is limited by the amount of heat which will be generated by Joule heating. In real practice, the recommended temperature rise levels are actually very strict, usually few tens of K. For a temperature difference of 10 K above the ambient, calculate maximum recommended current for AWG 10 copper wires. U = 18 W/m²K. First, you will need to extract the resistivity of copper from the table given below. Does your result agree with the value given in the table? AWG 0000 (4/0) 0.46 Diameter Diameter Area Resistance Resistance Max Current Max Frequency [inches] [mm] [mm²] [Ohms / 1000 ft] [Ohms / km] [Amperes] for 100% skin depth 11.684 107 10.40384 85 9.26592 67.4 0.049 0.16072 302 125 Hz 000 (3/0) 0.4096 0.202704 239 160 Hz 0.0618 0.0779 00 (2/0) 0.3648 0.255512 190 200 Hz 0 (1/0) 0.0983 0.322424 150 250 Hz 0.3249 8.25246 53.5 0.2893 7.34822 42.4 1 0.406392 119 325 Hz 0.1239 0.1563 2 0.2576 6.54304 33.6 0.512664 94 410 Hz 3 0.2294 5.82676 26.7 0.197 0.64616 75 500 Hz 4 0.2043 5.18922 21.2 0.81508 60 650 Hz 0.2485 0.3133 5 0.1819 4.62026 16.8 1.027624 47 810 Hz 6 0.162 4.1148 13.3 0.3951 1.295928 37 1100 Hz 7 0.1443 3.66522 10.5 0.4982 1.634096 30 1300 Hz 0.1285 3.2639 8.37 0.6282 2.060496 24 1650 Hz 0.1144 2.90576 2.598088 19 2050 Hz 6.63 0.1019 2.58826 5.26 0.7921 0.9989 3.276392 15 2600 Hz 0.0907 2.30378 4.17 1.26 4.1328 12 3200 Hz 0.0808 2.05232 3.31 5.20864 9.3 4150 Hz 1.588 2.003 7.4 5300 Hz 0.072 1.8288 2.62 0.0641 1.62814 2.08 6.56984 8.282 2.525 5.9 6700 Hz 0.0571 1.45034 1.65 3.184 10.44352 4.7 8250 Hz coo 9 10 11 12 13 14 15