Putting the rough side up consistently eliminates the need to decide
which side to put up.
If you are shining a light onto the aluminum foil, expecting it to act
like a mirror, then by all means use the shiny side up. The shiny side
reflects light more specularly like the mirror does, the dull side is a
better diffuse reflector.
This question seems to be a "chestnut".
The dull side probably is better for sticking to food liquids during
cooking than is the shiny side.
So, depending upon what you consider "good", the answer varies.
Which is better? A chestnut or an acorn?
The common indicators of thermal performance are the absorption, total
reflection and hemispherical emissivity of the material (aluminum foil).
The spectral reflectivity of the shiny side is high, but the dull side
has almost the same reflectivity when averaged over all of the scattered
reflection directions caused by the surface roughness.
The hemispherical emissivity is likely little changed as well,
especially at the long wavelengths (2 to 8 microns) typical of the
interior temperatures of a cooking oven.
Black anodized aluminum is reported as cooking faster than shiny or dull
aluminum, and the difference there is substantial in appearance
difference with shiny or dull aluminum.
There could be a small difference between the shiny and dull sides of
aluminum foil on cooking rate. But from visual appearance, one would
tend to believe that the difference should be large. But what one sees
isn't what controlls radient and convective heat transfer.
I'm not sure why everyone is focussing on the reflectivity of the material.
This is only important in radiation mode!
Most ovens I am familiar with use SIMPLE convection and conduction to cook.
Which means that the element heats the air in the oven (conduction/convection)
the hot air heats the foil (convection), the foil heats the turkey (conduction)
and so on. Shinyness of the foil has no bearing whatsoever on conductivity.
(At least in the grand scheme of cooking!).
If you needed a shiny surface to cook, you'd never be able to make pizza.
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