3. Find the solution to the heat conduction problem: 24t = Urr, 0x 2n, t> 0...

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3. Find the solution to the heat conduction problem: 24t = Urr, 0≤x≤ 2n, t> 0 u₂ (0, t) u₂ (2n, t) u(x,0) = = = 0 0 I = f(x) Again, the mechanics of this problem are very VERY similar to the previous problem. In fact, that's the case with most of the heat equation problems. The main difference is in the eigenvalue/eigenfunction part! Note that this time around we have Neumann boundary conditions (the boundary conditions are on the spatial derivative of the function; think of this as insulation, no heat flow in or out). 3. Find the solution to the heat conduction problem: 24t = Urr, 0≤x≤ 2n, t> 0 u₂ (0, t) u₂ (2n, t) u(x,0) = = = 0 0 I = f(x) Again, the mechanics of this problem are very VERY similar to the previous problem. In fact, that's the case with most of the heat equation problems. The main difference is in the eigenvalue/eigenfunction part! Note that this time around we have Neumann boundary conditions (the boundary conditions are on the spatial derivative of the function; think of this as insulation, no heat flow in or out).

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Answer We use separation of variables Let ux t XrTt Then uur becomes XzT t XxTt We divide both sides by XzTt to obtain So we have X0 X2T 0 where A is a constant What happens to the boundary conditions ... View the full answer