How Does Fourier's Law Apply to Heat Flow Through a Composite Wall?

In summary, Fourier's Law of Conduction is a fundamental principle in thermodynamics that describes the transfer of heat through a solid material. It states that the rate of heat transfer is directly proportional to the temperature gradient and the area of heat transfer, and inversely proportional to the distance between the two temperatures. The mathematical equation for Fourier's Law of Conduction is q = -kA(dT/dx), and it is used to analyze heat transfer in various engineering and scientific applications. However, it has limitations as it assumes certain conditions and does not account for all forms of heat transfer. It is also related to the first and second laws of thermodynamics.
  • #1
Jay K
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Using Fourier’s law and an electrical analogy, derive the expression given below for the heat flow, Q, through a flat composite wall of surface area, A, with three layers of thicknesses x1, x2 and x3 and thermal conductivities k1, k2 and k3, and an overall temperature difference ΔT. State any assumptions.
 

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Welcome to PF!

Hi Jay! Welcome to PF! :smile:
Jay K said:
Using Fourier’s law and an electrical analogy …

What do you think the electrical analogy is? :wink:

(and what is Fourier's law?)
 

What is Fourier's Law of Conduction?

Fourier's Law of Conduction is a fundamental principle in thermodynamics that describes the transfer of heat through a solid material. It states that the rate of heat transfer is directly proportional to the temperature gradient and the area of heat transfer, and inversely proportional to the distance between the two temperatures.

What is the mathematical equation for Fourier's Law of Conduction?

The mathematical equation for Fourier's Law of Conduction is: q = -kA(dT/dx), where q is the heat flux, k is the thermal conductivity of the material, A is the cross-sectional area, and dT/dx is the temperature gradient.

What are the limitations of Fourier's Law of Conduction?

Fourier's Law of Conduction assumes that the material is homogeneous, isotropic, and in a steady state. It also does not take into account heat transfer through radiation or convection.

How is Fourier's Law of Conduction used in engineering and science?

Fourier's Law of Conduction is used to analyze heat transfer in various engineering and scientific applications, such as in building materials, electronics, and thermal management systems. It is also used in the design and optimization of heat exchangers and other heat transfer devices.

How does Fourier's Law of Conduction relate to other laws of thermodynamics?

Fourier's Law of Conduction is a specific application of the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred or converted. It also relates to the second law of thermodynamics, which states that heat always flows from hot to cold objects, and never the other way around.

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