I propose you the following conjecture: is it possible to convert
directly solar energy in a mechanical form?

The conical hole discriminates the molecules of gas according as they
enter by its small or large opening.

The molecules of gas entering in hole by the
large opening have their trajectories inverted by the shocks on the
wall of hole. They quit the hole by the large opening, so their
contribution to the pressure applied on the face of the sheet metal is
the same as if the holes are absent.

I think that this phenomenon is not incompatible with the second law
of thermodynamic. These sheet metal drilled by conical holes could be
seen as a dissipative system, permitting the local apparition of
negative entropy.

I propose you the following conjecture: is it possible to convert
directly solar energy in a mechanical form?

Yes. This was theoretically shown by James Maxwell in 1871 and
experimentally proven by Pyotr Lebedev in 1899.
But the device you propose appears to be unrelated to that concept and,
in fact, doesn't appear to have anything to do with solar energy per se
but appears to be a variation on "Maxwell's Daemon".

The conical hole discriminates the molecules of gas according as they
enter by its small or large opening.

That's your claim, but your argument is faulty because it makes the
following invalid claim:

The molecules of gas entering in hole by the
large opening have their trajectories inverted by the shocks on the
wall of hole. They quit the hole by the large opening, so their
contribution to the pressure applied on the face of the sheet metal is
the same as if the holes are absent.

If the area of the small opening is A1 and the larger area is A2, then
there is an area A1 through which the molecules entering the large
opening can pass through to the other side. You are incorrect when you
say the trajectories of all the molecules entering the large hole are
inverted. So long as any can fit through area A1 then some random number
will make it to that hole. The geometry of the holes does not prevent
that from happening. I can invent an infinite number of initial particle
positions and velocities where I can get particles from the side with
the larger end of the conical holes out through the smaller end. If you
don't believe me I'll be glad to show you examples.

I think that this phenomenon is not incompatible with the second law
of thermodynamic. These sheet metal drilled by conical holes could be
seen as a dissipative system, permitting the local apparition of
negative entropy.

The proposal is a macro-sized system and the second law applies and your
mechanism will not work.

My device is related with solar energy by the fact that this energy is
responsible of the temperature of atmosphere.

The geometry of the hole is
important. The conical hole could filter the gas molecules if the
diameter of the hole near the small opening is sufficiently small in
regard of the mean free path of the gas.

I have made a simulation with Visual Basic language. This simulation
describes the comportment of a gas not in a conical hole but in a
similar form, a pyramidal hole. Although this software doesn't
consider the shocks between gas molecules, I think it can be realistic
for the simulation of a gas in the part of hole near the small opening
when the section of hole is smaller than the mean free path of the
gas.

For example, I have tested the following geometry:

- side of the square large opening: 500 nm,

- side of the square small opening: 50 nm,

- length of the pyramidal hole: 50000 nm,

- amount of launched molecules: 100000.

In this case, the area of the small opening represents 1% of the area
of the large opening so the flow of molecules entering by the small
opening represents 1% of the flow of molecules entering by the large
opening. My simulation said that only 0.3% of the molecules entering
by the large opening reach the small opening. It is an insufficient
flow to compensate the flow of gas molecules entering by the small
opening. If the simulation is sufficiently realistic, it can appear a
difference of pressure between the two faces of the sheet metal.

Your device purports, and correct me if I'm wrong, to effectively sort
molecules into molecules of high kinetic energy and low kinetic
energy, does it not?
So, lets say this was possible. You could then place your device in
the middle of a chamber filled with a gas, and end up with a higher
temperature at one side of the chamber than the other, could you not?
You could then run a heat engine off of the resulting temperature
difference. This would seem to violate the second law of
thermodynamics, so it should raise certain suspicions.

Because your mechanism isn't expending any energy, yet would allow two
halves of an otherwise closed container of gas to move to unequal
densities, your device appears to increase the energy available to do
useful work. That appears to be a fundamental violation of the laws of
thermodynamics as I understand them.

My suspicion is that if you properly account for all the real
interaction that take place, your device will not work as expected.
However, if it does work as expected, you should be prepared to
explain why it does not violate the second law of thermodynamics...

There are a host of possible reasons your simulation is yielding
incorrect results. Perhaps the volume, density, or energy distributions
of the ensemble of particles used for the two sides differ in ways you
haven't noticed. (I presume your runs were of equal length time.) Or
perhaps your test for wall collisions and subsequent bounce trajectories
is incorrect. (Also, I suspect a 2 dimensional model would suffice rather
than a 3 dimensional one.)
If the simulation is not too long and you are willing to allow it to be
publicly reviewed, I'd be happy to review it with you on this forum. If
not, I can understand.