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Solving the 3d heat equation 
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#1
Mar1212, 11:16 PM

P: 52

Hi,
I've been trying to solve [itex]\frac{\partial \vec{u}(x,y,z,t)}{\partial t} = \nu \nabla^2 \vec{u}(x,y,z,t)[/itex] Where the Laplacian is 3d. My initial conditions are [itex]\vec{u}(x,y,z,0)=\vec{u_o}(x,y,z)[/itex]. And my BC is that [itex](u_z,v_z,w)= 0 [/itex] at z=0. where [itex]\vec{u} = (u,v,w)[/itex] I want to solve for [itex]\vec{u}(x,y,0,t)[/itex] i.e. at z=0. Here, [itex] (x,y) \in \mathbb{R}, z \in (\infty,0), t\in \mathbb{R}^+ [/itex]. Is there an analytic way to do this? So far I have only come across numerical schemes or examples for lower dimensions. Any suggestions would be appreciated, Nick Nick 


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