Re: Heat transfer -- possible in mathematica?
- To: mathgroup at smc.vnet.net
- Subject: [mg79280] Re: Heat transfer -- possible in mathematica?
- From: antononcube <antononcube at gmail.com>
- Date: Mon, 23 Jul 2007 03:45:04 -0400 (EDT)
- References: <f7v4n2$t31$1@smc.vnet.net>
If the equation you have in mind is
D[u[x, y, t], t] == D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}]
you can try these commands:
Plot3D[Piecewise[{{1, 1/4 < x^2 + y^2 < 1/1.5}}], {x, -1, 1}, {y, -1,
1}, PlotRange -> All]
sol = NDSolve[{D[u[x, y, t], t] ==
D[u[x, y, t], {x, 2}] + D[u[x, y, t], {y, 2}],
u[x, y, 0] == Piecewise[{{1, 1/4 < x^2 + y^2 < 1/2}}],
u[-1, y, t] == 0, u[1, y, t] == 0, u[x, -1, t] == 0,
u[x, 1, t] == 0}, {u[x, y, t]}, {t, 0, 1/4}, {x, -1, 1}, {y, -1,
1}, PrecisionGoal -> 4, AccuracyGoal -> 4]
Plot3D[u[x, y, t] /. sol /. t -> 1/32., {x, -1, 1}, {y, -1, 1},
PlotRange -> All]
If by transient heat equation you mean a heat equation that has
convection you can take a look at this talk:
http://library.wolfram.com/infocenter/Conferences/6532/
(I can provide the code if it fits your computation.)
Anton Antonov,
Wolfram Research, Inc.
On Jul 22, 3:32 am, meaton01 <mike.ea... at gmail.com> wrote:
> Greetings,
>
> I'm attempting to solve a 2-dimensional, transient heat transfer calculation (rectangular slab) with uniform generation. Is this (relatively easily?) possible in mathematica, or should I simply resort to trying to program a finite element solution to the problem? Additionally, if anyone knows of a notebook already constructed, I'd love to see it.
>
> Thanks!
> Mike