What is the temperature of an iron bar after 1 hour of convection heating?

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SUMMARY

The discussion centers on calculating the temperature of an iron bar after one hour of convection heating using an electric cable with a power output of 22.5 kW. The formula provided for the final temperature is T_final = F + Q/(u*A*L), where Q is the power, u is the coefficient of convective exchange, A is the area of the iron bar, and L is the length of the cable. Given the initial temperature of 5 degrees Celsius and an external temperature of -4 degrees Celsius, the parameters for the iron bar include a mass of 529.13 kg, an area of 1.68 m², and a heat capacity of 450 J/kg*K. The discussion seeks validation of the temperature increment term Q/(u*A*L) for accuracy.

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dvd84
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Hello, my problem is the following:

I have an iron bar, which can be heated by convection through an electric cable with power Q.
I want to know the temperature of the iron bar after 1 hour has passed, both in the case when the power is
turned on and when it is off (Q=0).

the input parameters are the temperature of the iron bar at instant zero and the environmente temperature,
the output is the new temperature of the iron bar after 1 hour.

Thank you.
 
Last edited:
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Dr. Courtney said:
Is this a homework problem?

https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/

no it is not an homework problem, I have a solution which is

T_final = F + Q/(u*A*L)

where F is the formula that updates the temperature and it works quite well.
The term

Q/(u*A*L)

represents the increment of temperature due to the electric cable, where Q is the power, u the coefficient of convective exchange, A the area of the iron bar and L the length of the cable. I want to check the correctness of the term Q/(u*A*L), if you may help me.
 
I have an iron bar not insulated, of length 6 meters, heigth 28 cm and width 4 cm, hence the area is 1.68 m^2 and the mass is 529.13 Kg.
The heat capacity of iron is 450 J/Kg*K.
The thermal conductivity of iron is 0.023 W/m*K.
The thermal expansion coefficient is 0.0037 C^-1.
The density of air is 1.30 Kg/m^3.
The dynamic viscosity of air is 17.157 * 10^-6 Pa*sec.
I assume that at time zero the internal temperature of the iron bar is 5 degrees Celsius, the external temperature is -4 degrees Celsius (the bar is not insulated).
The power Q that pass through the cable is 22,5 KWatt, and the length of the cable is 14 meters, the heat transfer between the cable and the iron bar is by convection.

I need to know after 1 hour has passed the new internal temperature of the iron bar.

Thanks
 

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