Electric cable in a Vertical Tube: Estimate the Conductor Temperature

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SUMMARY

The discussion centers on estimating the temperature of an electric conductor within a vertical steel tube exposed to solar radiation. The user, Steve, employs the equation QCable + Qsun - Qradiated = mc(Tfinal - TAmbient) to derive the final temperature, incorporating parameters such as the radiation constant (k = 4E-8), ambient temperature (TAmbient = 34°C), and specific heat capacity of steel (c = 473 J/kg·K). After resolving a quartic equation for Tfinal, Steve seeks assistance in calculating the conductor's temperature over a 24-hour period but initially encounters unreasonably high temperature results. Ultimately, he confirms that he has resolved his issue.

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  • Familiarity with the equations of heat transfer, including radiation and conduction
  • Knowledge of specific heat capacity and thermal mass calculations
  • Basic proficiency in solving quartic equations
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stevekho
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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
 
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Ooooooook I found it :)