Heat flux on a cylinder with two insulators

Click For Summary
SUMMARY

The discussion centers on calculating heat flux for a cylinder insulated with two different materials, each with distinct thermal conductivities. The user is accustomed to using the formula \(\frac{\partial Q}{\partial t} = \int -k \vec{\nabla} T \vec{ds}\) for heat transfer problems but is unsure how to apply it in this scenario due to the presence of two insulators. The conversation highlights the importance of boundary conditions, specifically whether the cylinder and its surroundings are maintained at fixed temperatures, which is crucial for determining the correct approach to solving the problem.

PREREQUISITES
  • Understanding of heat transfer principles
  • Familiarity with thermal conductivity coefficients
  • Knowledge of boundary conditions in thermal systems
  • Proficiency in mathematical modeling of heat flux
NEXT STEPS
  • Research methods for analyzing heat transfer in composite materials
  • Study the impact of boundary conditions on heat flux calculations
  • Learn about the use of thermal resistance networks for multi-layer insulation
  • Explore advanced heat transfer equations applicable to cylindrical geometries
USEFUL FOR

This discussion is beneficial for thermal engineers, physicists, and students studying heat transfer, particularly those dealing with complex insulation scenarios in cylindrical systems.

chrishans
Messages
6
Reaction score
0
I'm used to problems which ask me to find the heat flux for when, for example I have a very long cylinder covered with an insulator, each with their respective conductivity coefficient. I'd use the formula \frac{\partial Q} {\partial t} =\int -k\vec{\nabla} T \vec {ds}. But now I have a situation where the cylinder is covered with two insulators, one on the left half of it, and the other one on the right. So I don't know how to use the previous formula here, as k doesn't vary with ρ only, but also with φ. I found this very same problem on a web but, it didn't use that formula. Instead, an electric-like circuit was built, and so on (I'm NOT supposed to solve it this way) Any advice?

Thanks
 
Physics news on Phys.org
I suppose you need to know what are the boundary conditions to know how to solve this. Are the cylinder and the "outside" specified to be held at fixed temperatures or is it some other situation?
 

Similar threads

Heat flux analysis with transient heat conduction
  • · Replies 1 ·
Replies
1
Views
2K
Heat Flow Through a Truncated Cone
  • · Replies 3 ·
Replies
3
Views
4K
Thermal conductance of an angular section of a disc
  • · Replies 4 ·
Replies
4
Views
2K
What is the temperature at the wire/insulator interface?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Warm-up time for a hollow cylinder
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Relationship between the divergence of a field and its cause?
  • · Replies 3 ·
Replies
3
Views
2K
How Does Mixing Ideal Gases in a Thermally Insulated Cylinder Affect Pressure?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Interseasonal heat storage / sand battery insulation?
  • · Replies 27 ·
Replies
27
Views
6K
Different forms of fluid energy conservation equations
  • · Replies 32 ·
2
Replies
32
Views
4K
How to Solve a Heat Equation Using FFCT?
  • · Replies 52 ·
2
Replies
52
Views
7K