Heatsink Sizing: Junction-to-Ambient Rth and Natural-Convection Fin Arrays

Why the heatsink is a budget, not a single number

A power device's junction temperature isn't set by the heatsink alone — it's the last link in a chain of thermal resistances that heat has to cross to get from the silicon die to the surrounding air: junction-to-case (Rjc, fixed by the device package), case-to-sink (Rcs, set by whatever thermal interface material sits between them), and sink-to-ambient (Rsa, the heatsink itself). Each one adds a temperature rise proportional to the power flowing through it, so the useful question isn't "how good is this heatsink?" but "how much Rsa can the rest of the chain afford?"

The budget: Tj = Ta + P·(Rjc + Rcs + Rsa)

Rearranging that equation the other way answers the sizing question directly: given a maximum allowed junction temperature, the ambient temperature, the power to dissipate, and the two resistances the designer doesn't control (Rjc from the datasheet, Rcs from the chosen TIM), the maximum sink resistance the design can tolerate falls out as Rsa(required) = (Tj_max − Ta)/P − Rjc − Rcs. Any heatsink at or below that number keeps the junction in spec; anything above it doesn't, no matter how good it looks on a shelf.

Case-to-sink: a resistance you choose

Unlike Rjc (fixed by the device) or Rsa (fixed by the heatsink), Rcs is largely a design choice — it's the thermal interface material's thickness divided by its conductivity and contact area (Rcs = t/(k·A)). Thermal grease, gap pads, and graphite pads all trade off thickness, conductivity, and ease of assembly differently, and a poor TIM choice can eat a surprising chunk of the whole budget.

Sizing the sink itself: natural convection off a fin array

For a natural-convection (no fan) extruded heatsink, air rising past each fin behaves — to a good approximation — like buoyancy-driven flow along a vertical flat plate, which is where the Churchill-Chu correlation comes in: it gives the convection coefficient h from the Rayleigh number (buoyancy vs. viscosity) and Prandtl number (fluid properties) for any vertical surface, laminar or turbulent. Multiply h by the fin array's effective surface area — corrected by a fin-efficiency factor since a fin's tip runs cooler than its base — and add radiation, and the two together have to carry away the target power at some base-to-ambient temperature rise. That temperature rise, divided by the power, is Rsa.