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Heat Transfer Simulator

Fin Array Simulator — Heat Sink Total Heat Transfer

Visualize the total heat transfer and overall surface efficiency of a heat sink with N straight rectangular fins. Vary fin height, count, conductivity and convection coefficient to learn CPU cooler design fundamentals.

Parameters
Convection coefficient h
W/m²·K
Fin material conductivity k
W/m·K
Fin height L
mm
Number of fins N
fins

Base dimensions W = D = 100 mm, fin thickness t = 2 mm, base-to-ambient temperature difference ΔT = 50 K are assumed.

Results
—
Fin parameter m
—
Fin efficiency η_f
—
Overall efficiency η_o
—
Total heat transfer Q
Heat sink side view and fin efficiency curve

Left: side view with N fins standing on the base / Right: tanh(x)/x fin efficiency curve (yellow dot = current m·Lc)

Theory & Key Formulas

Fin parameter for a straight rectangular fin (thin-fin, adiabatic-tip approximation). h = convection coefficient, k = fin conductivity, t = fin thickness:

$$m = \sqrt{\frac{2h}{k\,t}}$$

Fin efficiency. Lc = L + t/2 is the corrected fin length:

$$\eta_f = \frac{\tanh(m\,L_c)}{m\,L_c}$$

Overall surface efficiency. N = number of fins, A_f = single-fin area, A_total = N·A_f + (A_b − N·t·D):

$$\eta_o = 1 - \frac{N\,A_f}{A_\text{total}}(1 - \eta_f)$$

Total heat transfer. T_b = base temperature, T_∞ = ambient:

$$Q = \eta_o\,h\,A_\text{total}\,(T_b - T_\infty)$$

The smaller m·Lc (large k, short L), the closer the fin efficiency is to 1. Increasing N grows A_total and Q, but real designs must also account for the airflow penalty.

What is the Fin Array Simulator?

🙋
Why are CPU coolers always covered in those finned fences? Wouldn't a solid block of metal work just as well?
🎓
Good question. Heat dissipation roughly equals area × convection coefficient × temperature difference, so you want as much surface contact with air as possible. Standing fins up multiplies the area more than ten-fold for the same volume. Slide "Number of fins N" from 5 to 50 in the simulator and watch the total heat transfer Q climb.
🙋
So is more fins always better?
🎓
Here's the catch: tighter fins choke airflow, which lowers the real h. Plus, "fin efficiency η_f" tells you the tip is colder than the base, so a long fin doesn't dissipate at full base temperature. Push h to 200 and L to 100 mm — you'll see η_f drop below 80 %. That's the sign of an overspec'd fin doing very little near its tip.
🙋
Then shorter fins should be more efficient?
🎓
Exactly. With $m=\sqrt{2h/(kt)}$ and $\eta_f=\tanh(mL_c)/(mL_c)$, the smaller m·Lc, the closer η_f gets to 1. High-conductivity copper or aluminium with short, thick fins maximizes efficiency. But shortening fins also shrinks area, so total Q goes down. Efficiency vs. total dissipation is the heart of heat-sink design.
🙋
There's a yellow dot on the right plot — what does it mean?
🎓
It tracks where your current design sits on the tanh(x)/x curve. Small x = "short, efficient fins" (left, near 1); large x = "long, tip-cooled fins" (right, dropping). A common rule is to keep m·Lc between 1 and 2. Drop k to 10 (about plastic) and the dot jumps right while efficiency collapses — that's why material choice matters so much.

Frequently Asked Questions

A useful rule of thumb is to keep m·Lc between 1 and 2, which holds fin efficiency around 60–90 %. For aluminium (k = 200) with t = 2 mm and h = 50 W/m²·K, the sweet spot is L ≈ 30–50 mm; longer fins waste material as the tip stays cold. In practice, board space, fan capability and cost set the bounds, and optimization tools balance overall surface efficiency against pressure drop.
Copper has roughly twice the conductivity of aluminium (k ≈ 400 vs 200), but it is also about twice as dense and considerably more expensive. Pushing k from 200 to 400 in the simulator only nudges fin efficiency up a few percent. Most consumer hardware sticks with aluminium and uses a copper base or copper inlay where the heat is most concentrated. All-copper sinks appear in extreme-density power modules.
It uses the classical analytical solution for a single fin (thin, adiabatic tip, 1D conduction) — a first-pass estimate. Real systems are influenced by fin-to-fin thermal interaction, boundary-layer development, radiation and base spreading, so a ±20 % deviation is realistic. Detailed evaluation needs CFD with conjugate heat transfer or experiment, but this tool is great for sensitivity studies and early-stage trade-offs.
Straight (plate) fins favour directional forced convection where the airflow path is fixed, while pin fins (cylinders or square posts) handle airflow from any direction. CPU coolers and server racks lean toward straight fins; LED bulbs and large natural-convection systems often pick pins. This tool models the former, but pin fins fit the same framework with a different shape factor.

Real-world Applications

CPU and GPU coolers: The chips at the heart of PCs and servers dissipate tens to hundreds of watts. Heat-pipe + aluminium-fin + axial-fan stacks are the standard, and the calculation here serves as a first design pass: derive R_th = ΔT/Q from junction limits and back-solve fin geometry. When air cooling tops out, water blocks plus radiators (themselves fin arrays) take over.

Power electronics: EV inverters, PV inverters and industrial servo drives cool IGBT and SiC modules with finned heat sinks. Because power density is extreme, copper bases with skived fins under forced air, or liquid cold plates, become necessary.

Consumer electronics and natural convection: TV back panels, audio amplifier heat sinks and LED luminaires all rely on natural convection. With h around 5–15 W/m²·K, large surface area is mandatory — fins often double as visual design elements. Drop the h slider to 10 in the simulator and Q falls by an order of magnitude for the same shape.

Air-cooled engines: Vintage motorcycle and aircraft cylinders are cast with thin, long fins. Vehicle motion drives forced convection, and the same theory determines the geometry. Modern cars use water cooling, but the radiator core itself is just a compact fin array.

Common Misconceptions and Caveats

The most common misunderstanding is assuming that more fins always means more heat dissipation. Because the tool fixes h, increasing N monotonically grows A_total and Q. Real systems hit the opposite limit: tighter fins narrow the gap, choke airflow, and h itself drops. Natural convection generally needs at least 2–3 mm of pitch — closer than that can be worse than no fin at all. Treat the simulator output as the upper bound under "ideal airflow" conditions.

Next, do not confuse fin efficiency η_f with overall surface efficiency η_o. η_f rates a single fin in isolation, while η_o evaluates the whole heat sink (fin array plus exposed base). The exposed base sits at the root temperature, so η_o is normally higher: with the default settings the tool reports η_f = 92.7 % and η_o = 93.0 %. Always multiply Q by η_o, not η_f, or you will under-predict performance. Many design reports muddle these two — define them clearly in your own work.

Finally, this tool only handles the fin-array stage of the thermal path, not the full system. From a real die to ambient air, the heat passes through junction-to-case resistance, TIM, base, fins and finally air — each adds a series resistance. The simulator captures the last fin-to-air step only. TIM contact alone can absorb 20–30 % of the temperature budget, making it as critical as fin geometry itself.

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