Does Figure C Show A Constant Temperature Profile for Plane Wall Heat Transfer?

In summary, the attached picture shows a temperature distribution with different conditions represented by the colors red, black, and green. The distribution for figure A is a constant temperature, while figure B has a linear temperature gradient. For figure C, if heat is leaving from the right hand side, the temperature distribution will be different than if heat is entering from the right hand side. However, there is no steady state for this scenario and the temperature will continue to increase indefinitely.
  • #1
no183
16
0
Refer to the attached picture,
condition : assume steady state
legend : red : insulated (adiabatic)
black : no condition
Green : Temperature distribution, T(X)
I started with figure A, from heat equation, A u will get the distribution with is just a constant temperature..
For B, u will get a linear temperature gradient as shown in the figure, how bout C?
 

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  • #2
What do you mean by "no condition"?
 
  • #3
mean, just a normal wall.. non-insulated
 
  • #4
Then why would there be a temperature gradient in part (a)? Is there another constraint that the temperature is held at certain (different) values on the left and right sides? If so, what are the temperature constraints in part (c)?
 
  • #5
ok, let's say heat is LEAVING from figure A RIGHT HAND SIDE (BLACK) so i will get the temperature distribution
While on B, heat is MOVING IN TO THE WALL from RIGHT HAND SIDE (BLACK) and i will get the temperature distribution
lastly C, what i will get if
a) heat LEAVING the wall on the right hand side
b) heat ENTERING the wall on the right hand side
 
  • #6
no183 said:
While on B, heat is MOVING IN TO THE WALL from RIGHT HAND SIDE (BLACK) and i will get the temperature distribution

I don't think so, for a couple reasons. First, heat flux is always coupled to a temperature gradient (this is Fourier's Law), so the temperature profile wouldn't be flat. Second, there's nowhere for this heat to go. Therefore, there won't be any steady state condition; the temperature will just keep increasing indefinitely.
 

What is "Plane Wall Heat Transfer"?

"Plane Wall Heat Transfer" refers to the transfer of heat through a flat surface or plane, such as a wall. This can occur through conduction, convection, or radiation.

What is the difference between conduction, convection, and radiation?

Conduction is the transfer of heat through a material due to direct contact. Convection is the transfer of heat through a fluid, such as air or water, due to the movement of the fluid. Radiation is the transfer of heat through electromagnetic waves.

What factors affect heat transfer through a plane wall?

The factors that affect heat transfer through a plane wall include the temperature difference between the two sides of the wall, the thermal conductivity of the material the wall is made of, the thickness of the wall, and the surface area of the wall.

How is heat transfer through a plane wall calculated?

The rate of heat transfer through a plane wall can be calculated using the Fourier's Law of Heat Conduction, which states that the rate of heat transfer is directly proportional to the temperature difference, the thermal conductivity, and the surface area, and inversely proportional to the thickness of the wall.

What is the importance of understanding plane wall heat transfer?

Understanding plane wall heat transfer is crucial in various engineering and scientific applications, such as building insulation, thermal management in electronic devices, and heat exchangers. It also helps in the design and optimization of energy-efficient systems and processes.

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