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

AI Thread Summary
To determine the final temperature of the iron bar after one hour, the formula T_final = F + Q/(u*A*L) is proposed, where F updates the temperature based on initial conditions. The term Q/(u*A*L) accounts for the temperature increase due to the electric cable's power, with Q set at 22.5 kW. The discussion includes specific parameters such as the bar's dimensions, mass, heat capacity, and environmental conditions, indicating a non-insulated bar starting at 5 degrees Celsius in an external temperature of -4 degrees Celsius. The goal is to validate the correctness of the temperature increment term and calculate the new internal temperature after one hour. The inquiry seeks assistance in confirming the calculations and understanding the heat transfer dynamics involved.
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.
 
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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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