# 2-D Transient Heat Conduction – Part 2

In **this** previous post, I have demonstrated the mathematical concept behind a Gauss-Seidel iterative solution to the Laplace Equation, i.e. the equation below:

For a numerical computation, this differential equation has been discretized by the Finite Difference Scheme to obtain an approximate representation:

Now coming to HOW we obtain a value of = 0.2.

Consider Aluminium as your 2-D sheet material. As we know, . For Aluminium, the Thermal Diffusivity is roughly 84.18 mm^{2}/s. Next, we chose total number of time steps as 30,000. So taking one time step as 0.01 seconds, we are allowing 300 seconds to reach steady state (sounds comfortable). Our 2-D square metal sheet has 512 grid nodes in each direction. Since , we know that (where is the side length of the square). Since we chose , we can now calculate that , i.e. roughly 2 mm.

That means we are approximating a grid length of , which seems perfectly fine (a grid size of 1×1 m^{2}).

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