Cold Plate Design Explained — Channel Heat Transfer, Pressure Drop & Rth

A cold plate is a pipe you can machine into any shape

A liquid cold plate is a metal block with a coolant channel milled into it: the heat-generating parts bolt to one face, coolant runs through the channel, and the two never touch. Design comes down to two competing numbers. The thermal resistance tells you how hot the mounting face runs for a given heat load — you want it low. The pressure droptells you how hard the pump has to push to keep the coolant moving — you want that low too. Push the channel smaller and faster to cut the thermal resistance and the pressure drop shoots up; the whole job is finding the balance.

Why a rectangular channel isn't a round pipe

Milled channels are rectangular, not round, and that changes the physics in a way that's easy to get wrong. For a round pipe in slow (laminar) flow, the friction factor is exactly f = 64/Re. For a rectangular channel it isn't 64 at all — the Poiseuille number f·Re ranges from about 57 for a square channel up to 96 for a very wide, thin one (the parallel-plate limit). The heat transfer shifts the same way: the laminar Nusselt number (which sets the heat-transfer coefficient h = Nu·k/Dh) is about 3.6 for a square channel and climbs toward 8.2 as the channel gets thin. This calculator uses the Shah & London polynomials that capture that aspect-ratio dependence exactly, keyed off the channel's width-to-height ratio, rather than borrowing the round-pipe numbers.

The bends are not free

A serpentine cold plate turns the flow around many times, and every turn costs pressure. Each 45°, 90° or 180° bend adds a minor loss K·(ρv²/2) on top of the straight-section friction — and on a compact plate with tight U-turns those bends can rival the straight-run losses. The K values depend heavily on how sharp the corner is: a square-milled 180° U-turn loses far more than a generously radiused one. The values here (roughly 0.3, 1.1 and 2.0 for 45°, 90° and 180°) are representative of sharp milled bends; radiused or vaned turns are lower.

From heat-transfer coefficient to a base temperature, and the fin-efficiency caveat

How the convective, caloric and conduction resistances stack up to a base temperature, why tall channels don't deliver all the area they seem to, and a cold-plate design checklist.

Three resistances in series

The temperature rise from the coolant inlet to the mounting face is the heat load times a thermal resistance, and that resistance is really three effects stacked up. The convective resistance R_conv = 1/(h·A) is the film between the channel wall and the fluid — more wetted area or a higher heat-transfer coefficient lowers it. The caloric resistance 1/(2·ṁ·cp) accounts for the coolant simply heating up as it collects the load: with too little flow the outlet runs hot and drags the whole plate up with it (the factor of two is because the average fluid sits halfway between inlet and outlet). Finally, if the power module mounts on a base of some thickness, a conduction resistance t/(k·A) carries the heat down to the channel. Add them and multiply by the heat load to get the base temperature above the inlet coolant.

The fin-efficiency caveat

There's an optimism baked into the simple picture worth being honest about. When you count the full wetted perimeter of a channel as heat-transfer area, you're implicitly assuming the side and top walls are as effective as the heated base wall. They aren't — they act as fins, and a tall thin wall gets cooler toward its tip, so it moves less heat per unit area than the base does. Ignoring that fin efficiency over-estimates the conductance and makes the plate look a little better than it is, especially for deep channels. That's why the result here is a first-order estimate: good for comparing channel layouts and catching a design that's obviously under- or over-cooled, but worth confirming with CFD or a bench test before it's final.

Cold-plate design checklist

Set the flow rate from the heat load and the coolant temperature rise you'll tolerate — the caloric resistance alone puts a floor on how cold the plate can be.
Favour wider, shallower channels for heat transfer, but watch the pressure drop climb as you shrink the cross-section.
Keep channel velocity in a sensible band (roughly 0.5–2 m/s for water/glycol): too slow and the heat-transfer coefficient collapses, too fast and the pump work and erosion climb.
Count the bends — a many-pass serpentine trades pressure drop for a longer wetted path; sometimes several parallel channels beat one long serpentine.
Check both outputs together: a plate that hits its temperature target but needs a 2-bar pump may lose to a slightly warmer design that runs on a fraction of the pump power.

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Cold Plate Design: Rectangular-Channel Heat Transfer and Pressure Drop