Conduction Heat Transfer Cross Check

In summary, the conversation is about a provided equation that needs to be double checked for self consistency using the energy method. The professor wants the solution to be cross-checked using a global method, after initially using a local method. The poster has tried using electrical analogies but is still struggling. Images of the equation and initial setup are also provided. The poster is asking for help with symbolically double checking the equation.
  • #1
mattox1231
1
0
Hi, I was provided a http://eng-tips.com/viewthread.cfm?qid=372664# that I'm lost on. I was given an equation that we solved for earlier in the semester using the finite difference (dx method). (first image below). The http://eng-tips.com/viewthread.cfm?qid=372664# wasn't clear when assigning homework, and says he wants us to double check this equation to make sure it's "self consistent" using the energy method.

I approached the professor with additional questions but he kept repeating himself, that he wants us to cross-check the solution. He said we used a "local" method to solve for this solution, and he wants us to use a "global" method to double check the solution.

I have tried using electrical analogies with thermal resistance to resolve the solution, but can't seem to get it right.

The first image is the equation, the second image is the setup we used initially to derive the solution.
http://imgur.com/HaXiH8A
http://imgur.com/K3FXMlM

Does anyone know how I should go about symbolically double checking this http://eng-tips.com/viewthread.cfm?qid=372664# ?

Thanks in advance!
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

1. What is conduction heat transfer?

Conduction heat transfer is the transfer of heat through direct contact between two objects or substances. It occurs when there is a temperature difference between the two objects, and the heat is transferred from the hotter object to the colder one.

2. How does conduction heat transfer differ from other types of heat transfer?

Conduction heat transfer differs from other types of heat transfer, such as convection and radiation, in that it does not involve the movement of particles or electromagnetic waves. Instead, it relies on direct contact between objects for heat to be transferred.

3. What is the role of thermal conductivity in conduction heat transfer?

Thermal conductivity is a measure of a material's ability to conduct heat. In conduction heat transfer, the rate at which heat is transferred depends on the thermal conductivity of the materials involved. Materials with higher thermal conductivity will transfer heat more quickly than those with lower thermal conductivity.

4. How can conduction heat transfer be calculated or measured?

Conduction heat transfer can be calculated using Fourier's Law, which states that the rate of heat transfer through a material is proportional to the temperature gradient and the cross-sectional area of the material. It can also be measured using specialized equipment, such as thermal conductivity meters or heat flux sensors.

5. What factors affect the rate of conduction heat transfer?

The rate of conduction heat transfer is affected by several factors, including the temperature difference between the two objects, the thermal conductivity of the materials involved, the distance between the objects, and the surface area of contact. Other factors such as humidity and surface roughness may also play a role.

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