- #1
Boom100
- 4
- 0
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?