The heatsink may be fanless, but it will surely require some sort of airflow. Even without casing, unless the ambient temps are very low and some sort of constant natural breeze, I don't think it will handle the heat from most modern processors. There are also a lot of heat generating devices within a PC, i.e. motherboard, SSDs, dedicated graphic card which will need some sort of airflow. So if a fan is required, that pretty much negates the point of passive coolers. I feel one is better off buying a cooler that uses low RPM fans instead so as not to compromise performance/ cooling.
This is why I'm not enthusiastic on full-passive designs. I have a masters in engineering and spent a good 18 months learning about thermodynamics and fluid mechanics. Plus I took an optional module in acoustic engineering and one of my projects was fan blade design (did a short work-experience stint for Rolls Royce working on their turbine blades because of that). So no, I'm not an experienced expert in the field but I do know more than your average bear when it comes to fans, cooling, and noise levels.
The way I see it, human hearing has a natural cutoff, so even in an anechoic chamber, some fans are going to be inaudible. We're talking 3-blade fans at 400rpm here. Even though that sounds like a woefully weak fan, it would successfully move air across a low-density heatsink, and it would still move more air across a high density heatsink than convection alone could manage on a low-density heatsink.
What I'm saying is that it's possible to double or triple the cooling performance of any passive cooler whilst still making it
actually silent by human hearing standards. Yes, that fan is generating absolute noise, but the sound of your blood flowing through vessels that supply your cochlea is greater, and the vast bulk of the sound waves from such a slow fan are below the frequency that human hearing even functions.
The sole market for which passive cooling is valid is sealed units that have zero airflow inside. If you need to keep flammable gases or vapours away from anything that could potentially spark (like a DC motor or electrical connection) then you can't have fans and you probably can't have an open design that lets cool air in to replace the warm air.