Electric cable in a Vertical Tube: Estimate the Conductor Temperature

[stevekho]

Hello,

I have an electric cable in a vertical steel Tube. I estimated the temperature that will reach the JTube exposed to sun radiation.

I came with these equations

QCable+ Qsun - Qradiated = mc( Tfinal - TAmbient)

where QRadiated= k.A.(Tfinal^4-TAmbient^4), QSun=234 [W/m^2] * A
A=Area of the Tube
K=Radiation constant= 4E-8
m=Mass of the tube
c=473 for steel

I finally find for a day the maximum Temp that will reach the Tube ( Resolved a quartic Equation with Tfinal as an unknown knowing that Tambient=34 for instance )

However I want to know what temperature will reach the conductor ( after a day =86400 Secs)

What I thought was

For each t ( from 0 to 86400 secs)

QCable = mc( Tfinal - TAmbient) - Qsun + Qradiated

For each t, I know the right side. I Find QCable and then Divide it by the Thermal Mass to find the Temperature :/

However I find extremely large Results so I think it might be wrong ( it shouldn't be bigger that 90 Degrees)

Hope someone will be able to help me because I am really losing Hope...

Thank you very much Guys

Steve

 

[stevekho]

Ooooooook I found it :)