1. The problem statement, all variables and given/known data A copper wire has a diameter of 204.3 mil (1 mil = 0.001 in) and a resistance per unit length of 8.31x10^-4 ohm/m. The wire is coated with plastic insulation with thermal conductivity k = 0.20 W/(m K). The upper temperature limit of the plastic is 400 K. The air surrounding the insulation is at 300 K with heat transfer coefficient h = 10 W/(m2 K). Find the maximum current (A) that the wire can carry. Approximate answer: 200 A. 2. Relevant equations r_cr = k/h A (using_r1) = 0.005m^2 k=0.2 w/mK T1 = 400K q = hA(thetaT) A(using_r_cr) = .02m^2 h=10 w/m^2K Tinf = 300K 3. The attempt at a solution I have been working on this problem for about an hour. I know that I need to use the critical insulation radius. I have solved for q" and for R using R= (ln(r/r1) / 2pi*r*h) + 1/(2pi*r*h)), but can figure out how to get the answer. If someone can just give a starting point it would be very helpful. ps. sorry the bad notation, I m new to the site! Thanks!