Is there a best placement of hot hardware in a rack to maximize convection cooling for the whole rack?

To maximize convection cooling in a rack, does it make a difference whether the hottest items are at the top or bottom? If so, which produces the most cooling and why? Please limit answers to ones based on facts or industry-standard design principles rather than speculation, opinion, or personal choice.

Please note for this question I want to focus purely on the effect of the placement of the items on convection-only cooling. Please ignore other considerations, such as weight distribution or use of fans.

Basic physics: you will get the most cooling by putting the hottest units at the top and the coolest at the bottom (assuming cold air is entering at the bottom and hot air leaving at the top).

Whether it's an open rack or a closed cabinet with top and bottom openings will make a difference in the extent to which the units will act collectively. I'm assuming a cabinet.

The amount of air being drawn through the cabinet will be driven by how hot the exiting air is. Placement will affect the amount of heat that can be transferred to the air (hottest units at the top will transfer the most heat). But the amount of air isn't the main consideration, more important is how effectively you use the air.

Cooling (heat transfer), is based on temperature difference. Cold air at the bottom will remove heat from warm units on the way up and will still be cool enough to remove heat from the hot units at the top. If the hottest units were on the bottom, The cold incoming air would remove a little more heat from them. However, the heated air coming off them would do little cooling of the units above.

This principle is commonly used in industry. It's a form of countercurrent exchange, which maintains a temperature differential along the entire path.

Real racks arn't designed around natural convection based cooling. Any such assumption is bad. You'd have air trapped inside the case and more heat from any units below, and it will all melt down causing all manner of pain, woe and damnation. Hell is probably designed like this. But I'm employing hyperbole here. They'll just overheat, shut down or throttle down, and hell would seem like a nice place for a vacation.

Real racks, or most systems designed for use in any sort of constrained space used forced convection. Real racks suck in air from one side and out the other. That way, you don't need uninterrupted air flow from the top to the bottom.

So the best placement? Make sure the air intake is as cool as possible. Make sure the air exhaust isn't someone elses air intake.

If you need to design a system purely based on convection in a rack environment, either run away, or get a thermal imaging camera and experiment - that should at the very least show you where the heat is travelling, and how close your servers are to melting down.

That said - there's experiments going on with optimising data centre design for higher temperatures and more efficient cooling. These are big projects, done by governments, chipmakers and companies with large data centres, and is out of the scope of the sort of advice you get here.