How Do I Derive the Specific Thermal Diffusion Equation?

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Homework Help Overview

The discussion revolves around deriving the specific thermal diffusion equation, with participants exploring the foundational concepts of thermal diffusion and the heat equation. The original poster expresses confusion regarding the derivation process and the application of the divergence theorem in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the general derivation of the thermal diffusion equation and the application of the divergence theorem. There are questions about the relevance of heat flux and the specific conditions of the problem, such as the assumption of copper rods and the terms involved in the heat equation.

Discussion Status

Some participants have suggested starting from the heat equation and modifying it for the specific scenario, while others continue to seek clarification on the derivation process. There is an ongoing exploration of the assumptions and terms that apply to the problem, indicating a productive dialogue without a clear consensus.

Contextual Notes

Participants note the specific conditions of the problem, including the assumption of copper rods and the potential irrelevance of certain terms in the heat equation, such as convection. There is also mention of confusion regarding specific coefficients in the equation.

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Homework Statement



Please see question attached..


Homework Equations





The Attempt at a Solution



Not sure how to go about the derivation..

I know the general derivation of the thermal diffusion equation where we imagine a surface S bounding a volume V, then integral of J.dS = d/dt integral over volume of CT dV

So using divergence theorem, the thermal diffusion equation pops out..

But how do i derive the equation here?

the heat flux isn't really across a surface..im a bit confused :S

Thanks!
 

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*bump*
 
You can derive that equation from the heat equation. Just cancel out terms in the equation that don't apply. He/she tells you to assume the plates are copper rods, so that's why the laplacian is only in the x direction. In the heat equation there is an accumulation term, a convection term, a conduction term, and a removal or generation term. I don't think you need the convection term here unless you want to add in a fan or something. See my attachment.
 

Attachments

Sorry I still don't understand how to derive the first part of the question.. Any help would be greatt
 
where does the 2/a come from?
 

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