PDE models (thermal-3D)

[Gordon Haverland]

Hello

Reading about odepkg, brought up something I've been stewing on.

I've periodically looked for Linux packages on this, and nothing.
There are generic Linux packages to solve heat transfer PDEs (and
other), but seldom do they come with example code of this kind.  And
all of my PDE background, is in other kinds of equations.

I live on the eastern slopes of the Rockies at 56N.  We get winter.
Last year was exceptional in that winter was about 7 months long.

Shallow frost protected foundations are becoming known: nominally a
perimeter of insulation buried in the ground surrounding a foundation.
Heat (from radioactive decay in large part, somewhat quenched by
external conditions) comes up from below ground, and because the
insulation severely reduces heat flow, some heat is diverted to the
foundation and some escapes to the outside.  Enough insulation and you
don't have significant frost heaving problems.  But I can't say I've
run across a model of this, which would give me a starting point.

I don't want to build a structure of consequence.  I want to build
something 3 or 4 feet high, that is maybe 2 feet wide on the inside and
not that long.  A really short greenhouse if you will, to germinate and
produce tree seedlings.  What I want to look at, is the placement of
styrofoam insulation and the exterior walls.  I am thinking of building
this from concrete block, placing 4 inch styrofoam insulation on the
exterior surfaces (except the glazing side) and filling the cores with
gravel.

Being short, there is no mortar, and hence it is by definition
unstable.  Then I can use the blocks for something else in a year or so
when the seedlings get moved "outside".

Is there a published Octave model even vaguely along this line, that I
can lean on to figure out how thick I want the walls to be, and how
much exterior insulation to apply?  I know the theoretical answer to
both is infinite (or very large).  I am looking for the economic answer.

URLs would be nice.  :-)

Have a great day!
Gord