Consider a $1m$ long electric wire $)=(15\frac{W}{m}.C$ with a diameter of $20cm$ in which heat is generated uniformly at a constant rate. A current of $200$amp passes through the wire, having a resistance of $0\mathrm{.}13.$ The wire is insulated with two layers $(1^{st}$ layer magnesium with $k=0\mathrm{.}02\frac{W}{m}.C$ and $2^{nd}$ layer fiberglass with $k=0\mathrm{.}06\frac{W}{m}.C)$ of each $50mm$ thick insulation. If the outer surface temperature of the fiberglass is $50C,$ do the following at steady$-$state conditions:

a$)$ draw a thermal circuit of this problem statement.

b$)$ the center temperature of the wire

$q=I^2{R}_e$