(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider unsteady state heat conduction through an infinitely wide slab of solid material of thickness 2L. There is no internal heat generation and the thermal properties of the material are independent of temperature and position. Starting from an energy balance, show that the temperature T at a distance z from the central plane at time t is described by an equation of the form

[itex]\frac{dT}{dt}[/itex] = A [itex]\frac{\partial^{2}T}{\partial\eta^{2}}[/itex]

where η = z/L and A is a group of parameters. Define A.

3. The attempt at a solution

I want to perform a energy balance, which should come out in the form:

aq = a(q+dq)+[itex]\frac{\partial H}{\partial t}[/itex]

where a is the area and then I can probably solve it from there

However, in this case I can't do so as because the slab is infinitely wide I can't get a. Is there a problem with the way I'm visualising it in three dimensions or should I be taking a different approach to the energy balance?

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# Transient heat conduction in a slab

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