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miniradman
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Homework Statement
Plot the transient conduction of a material with k = 210 w/m K, Cp = 350 J/kg K, ρ = 6530 kg/m3
Where the material is a cylinder, with constant cross sectional area and is well insulated. The boundary conditions for the cylinder:
T(0,t) = 330K
T(l,t) = 299K
[itex]\frac{∂T}{∂t}(x,17)=0[/itex]
Homework Equations
Diffusion equation:
[itex]\frac{∂T}{∂t}=\alpha\frac{∂^{2}T}{∂x^{2}}[/itex]
rearranged diffusion equation in finite difference form
[itex]T(x,t+Δt)=\frac{\alphaΔt}{Δx^{2}}[T(x+Δx, t)-2T(x,t)+T(x-Δx,t)][/itex]
The Attempt at a Solution
Hi all
I've never used the finite difference equation before to solve a PDE and I'm unsure how to use it. I know how to find values such as α (thermal diffusivity), but I'm unsure on how to sub in my initial and boundary conditions. And which values would I use for T(x+Δx, t) or T(x-Δx,t)? Since I'm trying to find change in temperature over time at a fixed distance x, I would assume that Δx = 0? (which I know is incorrect).
I've tried looking online for PDE finite analysis techniques, but they're all either ODE examples or mesh analysis (something we haven't covered).