T i m wrote:
Hi all,

I have some neat extruded ally cases for my std Raspberry Pi's and I
was about to put my new 3B+ in one and wondered, because it seems to
get the warmest of all the Pi's so far ... if the interior finish
(shiny / matt) / colour (white to matt black) would make any
difference to how efficiently the case would re-radiate the (Pi) heat?

eg, If we assume the case is sealed (it isn't but doesn't have much in
the way of airflow) then the heat coming off the Pi to the inside of
the case would be direct in the form of radiation ... and indirect by
the way of conduction from the warm air, that distributed /
transferred via convection to the inside of the case (and hence via
conduction to the outside etc).

ISTM that if you have a closed system, all that matters is the flux to the
outside. The nature of construction of the closed system will affect
distribution of heat within the system, but fundamentally it's the amount of
heat you can get rid of that matters.

Here I'm modelling the system as $hot_interior_stuff surrounded by some
kind of case shell. That shell is not convecting, because it's a solid.
There is no air convection through it, because it's sealed.

So the overall thermal resistance of the shell is:

a) absorption of heat from $stuff to shell
b) conduction of heat through shell
c) radiation of heat from shell to environment

(I'll declare convection, conduction of heat from the shell to the
environment as orthogonal for now)

I think I'd agree that a black interior would absorb more internally radiated
heat, but you'd achieve a lower resistance by conduction directly from
$stuff to the shell.

So I think you maximise by colouring it black for a) and c), but you don't
want to make b) worse by painting it. For instance, a black anodising layer
would be very thin. If that's not an option, the thinnest paint you can
find followed by scraping off interior paint to achieve a better conductive
interface might be appropriate.

So, the case has a slightly shot blasted / gold anodised finish
throughout and I was wondering if painting the inside matt black (acid
etch spray primer and matt black spray) would have any cooling
advantage at all or would it in fact actually make matters worse
because the paint would act like a thermal barrier?

I suspect the difference in absorption a) based on
interior colour is going to be outweighed by adding additional shell layers
hindering b). However you'd really need to run numbers to find out.

Theo