How Do I Derive the Specific Thermal Diffusion Equation?

[bon]

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!

 

[bon]

*bump*

 

[mrmiller1]

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.

 

[bon]

Sorry I still don't understand how to derive the first part of the question.. Any help would be greatt

 

[bon]

where does the 2/a come from?