# [ExI] If you follow the developments with Tabby's star . .

Anders anders at aleph.se
Mon Sep 19 10:27:19 UTC 2016

```Hmm, it sounds like a radiosity/radiometry problem. "Given a frustrum
with incident energy I1 on the top, perfectly reflecting walls, and a
bottom at 3K, give the equilibrium temperature distribution."

https://www.doc.ic.ac.uk/~dfg/graphics/graphics2009/GraphicsHandout06.pdf
(much recent work has happened in computer graphics rather than in heat
transfer)

So we need to subdivide the walls into small patches, calculate form
factors, and solve a big linear equation system. Seems totally doable,
except that being lazy I wish there was a Matlab toolbox for it (HOT is
just for thermodynamics). I see there are python libraries for it.

On 2016-09-18 16:51, spike wrote:
>
> -----Original Message-----
> From: extropy-chat [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf
> Of Keith Henson
> Sent: Sunday, September 18, 2016 8:08 AM
> To: ExI chat list <extropy-chat at lists.extropy.org>
> Subject: Re: [ExI] If you follow the developments with Tabby's star . .
>
> On Sat, Sep 17, 2016 at 12:49 PM, Anders <anders at aleph.se> wrote:
>
>>> ... Let's see if I get the basic argument: you have a shell of radius R.
>> The luminosity L is absorbed, and in the standard model assumed to all...
>>> ...extra IR now is radiated all over the place. So this gives L/(32 pi^2
>> R^4 )extra input of heating per square meter. That doesn't *seem* too
>
>> ...If it is really a shell, then radiation to the inside will be in net
> equilibrium.  Only the outside will radiate the energy from the star...So if
> we continue to find no excess IR from this star, it's supportive of certain
> classes of space industrial objects that radiate heat directionally...Keith
> _______________________________________________
>
>
> Anders and Keith, there is an approach I have been struggling with, which
> uses Bessel functions, but I need some adult supervision if someone here can
> offer it, or knows someone who can, specifically someone with access to idle
> graduate students armed with Matlab and such.
>
> Assume a sunlike star and assume away all planets and debris (I am not a
> mathematician, but I sometimes act like one when it is time to assume away
> planets and debris.)
>
> OK now assume a 1 square meter reference plane perpendicular to a line from
> the center of the square meter thru the center of the star.  Out at 1 AU,
> there are nearly half a mole such meter squares, so it shouldn't be hard to
> imagine picking one.
>
> OK now imagine a kind of truncated square based pyramid (frustum) opening
> outward from there, such that the included angle formed by lines to the
> center of the star remains constant.  Imagine the pyramid going out 5 AU so
> that the frustum base is 5 meters on a side.
>
> We now need only calculate the heat load on that small end square meter base
> (which is about 1400 W) and the heat emission at the 25 m^2 big end out into
> 3K space.  The heat load thru the sides of the frustum is irrelevant, since
> the heat going in vs the heat going out is identical along the entire face
> always and forever amen.  That simplifies the model to heat in at the small
> end, and heat load out the big end, ja?  Are we ready to Bessel?
>
> OK, with that model, and some clever Matlab coding (I no longer have access
> to Matlab, oy) we should be able to create thermal distributions along the
> length of that frustum.
>
> I did that using uniform distributions and discovered that my Bessel
> functions predict we overheat inboard if we extract too much energy from
> that mass distribution (of MBrain nodes) within the Frustum.
>
> If the mass distribution of MBrain nodes within the frustum is sufficiently
> low, most of the energy passes thru, and the temperature distribution stays
> good.  But if the mass distribution is high, the inboard part overheats.  At
> some point, there is a uniform mass distribution along the length of the
> frustum in which the peak temperature is a nice balmy 300K.  I propose we
> call this mass distribution the Bradbury density.  Or we could call it the
> Bradbury300 density, so we can calculate a new density for Bradbury350 and
> so on.
>
> The Bradbury density assumes no directional reflection, so all the energy
> has to come in the 1 meter square reference plane at 1 AU and be emitted
> from the 5 meter square 5 AU plane.
>
> We could of course use other numbers.  I propose a name for peak
> temperatures designated as inner diameter in AU, dash, outer diameter in AU,
> Bradbury, peak temperature in Kelvin.
>
> The above thought experiment assumes no low-entropy reflection and the peak
> temperature would be called:
>
>
> I propose this name because had Robert lived, he would have embraced this
> notion, assuming I invested several hours arguing with him over it (he
> didn't do MBrain thermal models much and didn't cotton to them, but he liked
> my doing them.)
>
> spike
>
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--
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University

```