Nice. I like being wrong. Honestly I don't really care about the transient problem.
As a final check what would be wrong with using that grid we were discussing. An energy balance in and out of any node would yield:
k(Δy)(T1-Tn)/Δx + 2*pi*k*(T2-Tn)/ln((Rn+Δy)/Rn) + k(Δy)(T3-Tn)/Δx +...
In 200 words or less explain how the the grid in the last attached picture can both simulate a object that is long in the z-direction and round.
If not, you sir are wrong.
So, in a nutshell, correct me if I'm wrong. There is no way a 2D time-marching model can definitely account for the curvature of the cone.
See attached
If incorrect explain why.
The 2D plane can account for the fact that the heat won't flow only perpendilcar to the inner pipe. True. But it doesn't account for the curvature of the cone. It assumes that the z-direction can be neglected b/c the the length in the z-direction is very long. See pic attached
Unless there is...
The rise is 7"/6".
I think we're on the same page here in understanding that a "2D" model done in slices to account for the changing thickness is truly just a series of 1D models. Or are we thining about different ways to approach this?
See attached for the 2 heat flow lanes. One shows...
A 2D model couldn't simultaneously take into account the curvature of the cone (e.g. Time marching a flat grid to steady state) and the fact that heat will flow in the path of least resistance (e.g. In the of just using cylindrical cords)
Have a fluid flow in a cylindrical pipe with insulation around it. The insulation is in the shape of a truncated cone. It starts at a thickness with a radius only slightly thicker than the pipe and the radius increases as you move along the pipe. The radius increases at a constant rate.
The...