Heat Transfer Problem

  • #1
Suppose you have a cylindrical rocket engine with surface temperature T and you want to measure temperature on the inner wall T0 of the combustion chamber (assume 1 dimensional heat transfer). The chamber has thickness d, and heat transfer coefficient k. If combustion is assumed to occur instantaneously, and the engine runs at steady state (constant chamber temperature) what is the inner wall temperature if the outer surface has temperature T after t seconds?

Some background: I have a rocket engine that I need to measure the inner wall temperature on using thermocouples affixed to various locations on the outer surface. The operation time was previously 6 seconds. I'm assuming steady state operation, and one dimensional heat transfer from the inner wall to the reference junction of the thermocouple. I just haven't taken heat transfer and don't know the relationship between outer temperature, inner temperature, wall thickness, heat transfer coefficient, and time.

Any help would be greatly appreciated.
Thanks!
 

Answers and Replies

  • #2
20,766
4,494
Suppose you have a cylindrical rocket engine with surface temperature T and you want to measure temperature on the inner wall T0 of the combustion chamber (assume 1 dimensional heat transfer). The chamber has thickness d, and heat transfer coefficient k. If combustion is assumed to occur instantaneously, and the engine runs at steady state (constant chamber temperature) what is the inner wall temperature if the outer surface has temperature T after t seconds?

Some background: I have a rocket engine that I need to measure the inner wall temperature on using thermocouples affixed to various locations on the outer surface. The operation time was previously 6 seconds. I'm assuming steady state operation, and one dimensional heat transfer from the inner wall to the reference junction of the thermocouple. I just haven't taken heat transfer and don't know the relationship between outer temperature, inner temperature, wall thickness, heat transfer coefficient, and time.

Any help would be greatly appreciated.
Thanks!
This might not be a steady state heat transfer situation, since you are asking what is happening as a function of time. I'm guessing that it is a transient heat transfer situation. Let me see if I understand correctly. You are measuring the temperature on the outer surface as a function of time and trying to deduce what the temperature on the inside surface of the chamber was as a function of time. Correct?
 
  • #3
This might not be a steady state heat transfer situation, since you are asking what is happening as a function of time. I'm guessing that it is a transient heat transfer situation. Let me see if I understand correctly. You are measuring the temperature on the outer surface as a function of time and trying to deduce what the temperature on the inside surface of the chamber was as a function of time. Correct?
That would be correct, yes the heat transfer would be transient... I am assuming that the combustion process is steady state, hence, constant inner wall temperature, with outer wall temperature a function of time.
 
  • #4
20,766
4,494
That would be correct, yes the heat transfer would be transient... I am assuming that the combustion process is steady state, hence, constant inner wall temperature, with outer wall temperature a function of time.
So it still isn't clear what you are trying to determine. It's much easier to figure out what the inside temperature is if you have time to wait until the system reaches steady state. Then, all you need to know is the thermal conductivity of the metal and the outside heat transfer coefficient. On the other hand, what is the rationale for measuring the outside temperature vs time and using that to deduce the inside temperature? Your resolution is going to be very low at the beginning because it takes time for the temperature profile to propagate across the metal wall. I guess I just don't have a good idea of what you are trying to accomplish.

Chet
 

Related Threads on Heat Transfer Problem

  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
14
Views
3K
Replies
1
Views
2K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
2
Views
866
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
19
Views
4K
Replies
2
Views
9K
  • Last Post
Replies
11
Views
3K
  • Last Post
Replies
3
Views
13K
Top