isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body.(adsbygoogle = window.adsbygoogle || []).push({});

the equation boils down to

[tex]\left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}+\frac{\partial^{2}u}{\partial z^{2}} \right) = 0 [/tex]

The book proceeds to simplify it in such a way that changes the time scale: t' = (k/cρ)t, dropping the prime giving:

[tex]\frac{\partial u}{\partial t} - \left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2}u}{\partial y^{2}}+\frac{\partial^{2}u}{\partial z^{2}} \right) = 0 [/tex]

What happened??

If you can just talk me through what happens when the time scale is changed, I will try to work through the computation.

Thanks in advance.

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# Equation of Diffusion, trouble simplifying, PDE

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