Those thermal pads on the fins of the heat sink looks peculiar. I'd guess they shouldn't be placed there.
As for passively cooling a Celeron 400 - I'm skeptical, I think there should be at least some large, slow moving fan circulating air over the heat sink.

I have a celeron 433 overclocked to 500 for years only with a big heatsink, no fan in the computer exept in PSU, and i connected to 5v to be silent

There were some pretty substantial quiet coolers made by Zalman for socket A. Mendocino Celerons run in the 20-30 watt range- less than half that of the Athlon/Athlon XP CPUs that socket A coolers were designed for. That said, you'll still need at least some airflow to prevent heat building up over time.

Thanks everyone for the suggestions.
The problem is the fan itself, and I'd like to avoid it.
Could I just use the case fan? It's a fairly tall desktop case with a fan on the side. I need a maximum of 20 dB of noise.
I need to silence the computer featured in this article.

https://blog.gardensound.ca/quieting-the-lexicon-960l/

Two Noctuas were used in the article, but I'd like to try to do better. I'd like to avoid the CPU fan, which is the loudest, and perhaps find a case fan that extracts hot air well, operating at less than 20 dB.

Do you think it's impossible to achieve zero dB? Or should I settle for about 20 dB?

I did something similar with a K6-3+ in Socket 7. I have a case fan and power supply fan only. The video card is the hottest part:

I think you'll need some kind of fan, but there are quiet ones available and if you connect it to a temperature controller it can go slow when the system is idle. You could also experiment with under-volting and under-clocking the CPU to reduce power.

Thanks Nickles, perhaps a Zalmann CNPS 6000 without a fan and a Noctua in the case might work.

The processor specifications are:
Minimum/Maximum operating temperature: 5°C - 85°C

Maximum power dissipation : 23.7 Watts

Would the Zalmann fan + excellent thermal paste be enough?

There is also the option of thermal pads.

The big question with any passive cooling solution is how good the airflow in the case is. The best heatsink won't be able to work properly if the case is full of hot, stagnant air, whereas you can get away with surprisingly small heatsinks if there's a constant cool airflow straight over them (Compaq AP550 workstation comes to mind, with two Slot 1 CPUs very close together with tall thin heatsinks placed in a shroud with output fan sucking the air straight over them). Outtake fans are more important than intake, as you want to draw air out of a case, not stuff it in.

Looking at the pics in your link I'm not very impressed: there's a nice 92mm intake fan on the side of the case, but the only outtake fan seems to be in the PSU, and both are a long way away from the CPU socket. That looks like a recipie for fairly inefficient airflow over the CPU...

But remember what I said about a shroud. This could work with a passive heatsink with one condition and one modification.

Condition: the PSU fan must be able to move more air (at an acceptable sound level) than the intake fan.

Modification: make a shroud/tunnel from the intake fan directly to the heatsink, so it's blowing cold air over it. That will potentially raise the temperature of all other components, but it's the PSU fan's job to suck that hot air out of the case.

If you can fit a Zalman CNPS in here (6000 is complete overkill, a 2xxx/3xxx would be more than enough for that Celeron Mendocino) it should work perfectly, as the socket is angled so the cold air would flow over the vanes of the heatsink.

Dear dionb,
thanks for your detailed reply.

I was planning on using a passive, fanless power supply, the Seasonic PX 450 (or 500), and focusing on extracting the heat with the Noctua, mounted on the side of the case, replacing the original fan.

Do you think the Zalman CNPS can be used passively, without its fan?

Music080 wrote on Yesterday, 18:31:

Dear dionb, thanks for your detailed reply. […]
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Dear dionb,
thanks for your detailed reply.

I was planning on using a passive, fanless power supply, the Seasonic PX 450 (or 500), and focusing on extracting the heat with the Noctua, mounted on the side of the case, replacing the original fan.

Do you think the Zalman CNPS can be used passively, without its fan?

With good airflow over it: sure. But you're not getting that in this case without modification, and if you don't even want a fan in the PSU, that Noctua on the side is going to have to do some heavy (and potentially noisy) lifting, and I'm concerned it's much too far away from the CPU socket. I'd advise against it in this case, and I'd advise against the fanless PSU, as the case is designed for the PSU to actively draw hot air from around all those I/O components.

A 120W fan in a PSU can move more air at the same sound level than a 92mm fan on the side, and both working together definitely can. The system will be quieter with two fans turning slowly than one spinning faster.

Thanks for the advice Dionb.
I'll have to test it out because the case for this device is quite crowded with components.

If I understand correctly, the power supply also draws air and releases it out the back, but I don't know if they're designed to cool the inside of the case.
I think their fan is designed to cool themselves, not the case; it would be too loud to have the power to cool the inside of the case.

Even the 90mm Noctua doesn't move much air, about 45 CFM. Is 45 CFM enough?

I think the real cooling is provided by the fan on top of the processor heatsink.

No, again the biggest factor is the ambient temperature of the air flowing over the heatsink, or rather the temperature difference between it and the power source (CPU) it's supposed to cool. It's thermodynamics, but fortunaltely a pretty basic part of it.

The amount of air that needs to flow over the heatsink depends on that difference (and on the efficiency of the heatsink design). Twice the temperature difference means half the air needed, conversely, half the temperature difference means you need twice as much air. The CPU fan is just a means of getting more of that air over it, if needed.

To get a feel for the numbers, you can take the temperature values your BIOS gives you: CPU temperature and case temperature. Let's say your PC case temperature is well under control and is say 35C and you want to keep your CPU at 75C. That's a 40C difference, which will make it easy to do it with minimal airflow. But if you (like my son a while back) have a case with virtually no airflow, that temperature could be as high as 65C. You only have 10C difference then, which means you need four times as much air to keep the CPU temperature under control, which will probably mean you need that CPU fan and it will have to be blowing hard (what my son was complaining about 😉 ).

That tells you one thing: the cooler you can get the air, the less air needed, so the quieter your system will be. So particularly in your use case, controlling case temperature is the key to keeping the box quiet. And the most important way to do that is to get hot air out of the system, using the biggest (so slowest, so quietest) fan available. Yes, you can almost certainly get the CPU adequately cooled with a CPU fan, but that's the loudest option, not the quietest.

Thanks again for the fantastic explanation. I've realized that getting a 0dB, completely silent PC with a Celeron is impossible.