Heat and Mass Transfer - finding surface temp

[Boom100]

Homework Statement

A wire is conducting electricity, given values of :

R' = .4 ohms/m D = .002 m Tinf=300k Tsur=300k k=380W/m*C

emissivity = 1 h=10W/m^2*C Ts = Find this sigma=Stefan boltzmann

Plot the Temperature of the wire versus the current I for 0<I<10 amps.

Homework Equations

P = I^2*R' = q'

Convective heat = h(Ts-Tinf) + sigma(Ts^4-Tsur^4) = I^2*R' / pi*D = q'/pi*D = q''

The Attempt at a Solution

Ok So my attempt as essentially to break down the equation I have set to convective heat. After breaking things up and solving for Ts, I found :

"(I^2*R' / pi*D) + (h*Tinf) + (sigma*(Tsur)^4)" = Ts(h+sigma*(Ts)^3)

**Ill use " ... " for the left hand side of the equation

So my attempt was to break into into two equations:

"..." = Ts and Ts = Cubed Root ( ("..." - h)/sigma)

For some reason whenever I go to solve for Ts, I get pretty absurd numbers.

Using Kelvin I get 3932 K for I=0
I don't even think I can use celsius here because of the stefan boltzman constant (My equations are not temperature differences).

Where am I going wrong and is this approach even possible?

 

[Mapes]

Where are you getting the approach of "break[ing it] into...two equations"? Like if A = BC, then A = B and A = C? That doesn't make sense to me.

How about solving the equation numerically, or calculating the magnitudes of the convective and radiative heat transfer and seeing if one dominates over the other?