Design a thermosiphon — a loop in which fluid keeps circulating without a pump. Adjust the loop height, pipe bore and heat input to see the natural-circulation velocity, temperature rise and driving pressure update in real time, and explore the behaviour of a fully passive heat-transport circuit.
Parameters
Loop height H
m
Height difference between the heater and the cooler
Pipe inner diameter D
mm
Heat input Q̇
W
Heat added to the loop at the heater
Total loop length L
m
Total developed length of one circuit of pipe
Cold-side (cooler) temperature T_cold
°C
Temperature of the fluid leaving the cooler
Results
—
Circulation velocity V (m/s)
—
Mass flow ṁ (kg/s)
—
Temperature rise ΔT (K)
—
Hot-side temperature (°C)
—
Driving pressure ΔP (Pa)
—
Reynolds number Re
—
Thermosiphon loop — circulation animation
Fluid heated by the heater at the bottom becomes lighter and rises through the riser (orange); fluid cooled at the top sinks through the downcomer (blue). The particle speed is proportional to the circulation velocity V.
Circulation velocity vs loop height H
Circulation velocity vs heat input Q̇
Theory & Key Formulas
$$V=\sqrt[3]{\dfrac{2\,\beta g H\,\dot Q}{\rho A\,c_p\,K_{total}}}$$
Natural-circulation velocity V [m/s]. This closed form follows from coupling "buoyancy driving head = friction loss" with "temperature rise = heat input". β: thermal expansion, H: loop height, Q̇: heat input, ρ: density, A: pipe area, c_p: specific heat, K_total: total loss coefficient.
Temperature rise ΔT [K] (ṁ: mass flow) and driving pressure ΔP [Pa]. The loop is self-regulating: more heat input speeds up the circulation, so ΔT rises only gently.
What is a Thermosiphon?
🙋
I've never heard of a "thermosiphon" before. A fluid that circulates on its own with no pump — isn't that a bit strange?
🎓
Think of it as "the top of the bathwater being hotter", but used by joining a pipe into a full loop. Water heated by a heater at the bottom expands and becomes lighter. Lighter water wants to go up, so it climbs one pipe — the riser. Water cooled by a cooler at the top becomes heavier and comes back down the opposite pipe, the downcomer. That keeps repeating, so the flow keeps circling with no power applied from outside.
🙋
I see — a light side and a heavy side form. But the density difference sounds tiny. Can that really drive a flow?
🎓
Good question. The density difference in water is only about 0.1% over a few degrees. But the trick is that it stacks up vertically over the whole "loop height H". For a 3 m loop, the weight difference between the light column and the heavy column becomes the pressure difference ΔP. Raise the "loop height H" slider on the left and you'll see the circulation velocity V climb steadily. Putting a solar water heater's tank above the roof collector is exactly a way to gain this H.
🙋
So if I keep raising the heat input, will the flow and the temperature rise both keep growing?
🎓
That's the interesting part. Raising the "heat input Q̇" does raise the velocity V — but look at the "velocity vs heat input" chart below: the rise is a cube-root curve that gradually flattens. V scales only with the one-third power of Q̇. And because the flow has sped up, the temperature rise ΔT barely increases. We call this "self-regulation": put in more heat and the loop speeds up its own circulation to handle it. That clever behaviour is something a pumped system doesn't have.
🙋
I've heard that a wider pipe also helps — but why? I'd have guessed a narrow pipe gives a faster flow.
🎓
That intuition is for forcing the flow with a pump. In a thermosiphon the driving force is fixed by the density difference. So the velocity is set by "how much friction eats it up". A narrow pipe has large wall friction and devours nearly all of the buoyancy head. A wider pipe lowers the loss coefficient K_total, so the same driving force pushes the flow faster. That's why the pipework in real solar water heaters and natural-circulation boilers is surprisingly wide — to cut this friction.
🙋
Where is such a passive mechanism actually used?
🎓
Close to home: solar water heaters, and the cooling of transformers and engine blocks. More importantly, in nuclear-plant safety systems, where even if the pumps stop, decay heat is carried away by natural circulation — "passive cooling". With zero moving parts, it doesn't stop even when power is lost — that's its greatest strength. Add a phase change and it becomes the heat pipe in a CPU cooler. It looks humble, but the places that must never stop are exactly where a thermosiphon is chosen.
Frequently Asked Questions
A thermosiphon is a closed pipe loop. Fluid heated at the bottom expands, becomes lighter and rises through the riser. Fluid cooled at the top becomes denser and sinks through the downcomer. The density difference between the rising and falling columns, acting over the loop height H, builds up a 'buoyancy head' that drives the flow in place of a pump. Because there are no moving parts, heat transport works with no external power.
The circulation velocity is set by two equations satisfied at the same time: 'buoyancy driving head = pipe friction loss' and 'temperature rise = the thermal balance fixed by the heat input'. Velocity fixes the temperature rise ΔT, and ΔT fixes the density difference and driving force, so the two depend on each other. This tool iterates about 30 times from an initial guess to solve the coupled system, converging to V = cube-root(2βgH·Q̇ / (ρA·cp·K_total)).
Raising the loop height H lengthens the distance over which the density difference acts, so the buoyancy driving head increases and the circulation velocity rises. Widening the pipe bore D enlarges the flow area and lowers the total loss coefficient K_total, again raising the velocity. Conversely, a narrow pipe or a long total loop has high friction and slows the flow. Placing a solar water heater's tank above the collector is a way of gaining this H.
This tool models a single-phase thermosiphon, where liquid stays liquid and circulates by the density difference. A heat pipe is a thermosiphon with a phase change: the liquid evaporates at the heated end and the vapour condenses at the cooled end. Because it carries the latent heat of evaporation, it transports far more heat at a far smaller temperature difference than a single-phase loop of the same size. The heat pipe in a CPU cooler is the classic phase-change example.
Real-World Applications
Solar water heaters and solar systems: Water heated in a roof collector becomes lighter, rises, and flows naturally into a storage tank placed above it. The tank is mounted higher than the collector to gain loop height H and secure the buoyancy head. The "natural-circulation" type needs no pump and no controls, has simple pipework with few failure points, and works even where there is no electricity, so it is widely used around the world.
Cooling of electrical equipment and engines: A distribution transformer carries heat generated in the core and windings to its outer radiators by the natural circulation of insulating oil (the ONAN scheme). Older car engines also used a "thermosiphon" cooling system with no water pump, circulating coolant by the density difference around the cylinders alone. With no moving parts, the reliability is high.
Passive cooling in nuclear safety systems: A reactor must keep removing the core's decay heat even if the pumps and power are lost. Modern passively-safe reactors include a natural-circulation loop linking the core to a heat exchanger above it, circulating the coolant by the density difference alone to remove decay heat. Not stopping under a loss of power is the decisive reason thermosiphons are chosen for safety systems.
Heat pipes and electronics cooling: A thermosiphon with a phase change (a heat pipe) carries large amounts of heat using the latent heat of evaporation — the working liquid evaporates at the heated end and condenses at the cooled end. CPU and GPU coolers, the thin heat pipes in laptops, and the thermal control of satellites all use it widely wherever heat must be moved reliably across a small temperature difference.
Common Misconceptions and Pitfalls
The most common misconception is that "raising the heat input raises the temperature rise in proportion". As you can see by moving the heat-input Q̇ slider in this tool, doubling Q̇ barely changes the temperature rise ΔT. This is because the circulation velocity V grows with the one-third power of Q̇, so the denominator of ΔT = Q̇/(ṁ·cp) — the mass flow — grows along with it, and the two cancel. A thermosiphon is a self-regulating system that "speeds up its own circulation to handle more heat", behaving very differently from the simple proportionality of a pumped system.
Next is the assumption that "the loop should be as tall as possible". It is true that more height H increases the driving force and the velocity, but there is a trade-off against installation space, pipework cost and start-up stability. Also, if air or non-condensable gas collects in the loop, the bubble parks itself at the top by buoyancy and stalls the flow — a "vapour lock". Real systems put an air-bleed valve at the highest point and run the pipework so it rises and falls continuously without an adverse slope; this is essential for actually realising the H assumed in the calculation.
Finally, a careless belief that "natural circulation is weak, so detailed design is unnecessary". The driving pressure of a thermosiphon is small even in this tool's calculation — at most a few tens to a few hundred pascals, orders of magnitude below a pump head. Precisely for that reason, slight friction losses or local resistances (bends, valves, fittings) sway the flow strongly. Reducing elbows, avoiding sudden contractions and expansions, and choosing a sufficiently wide pipe bore matter even more severely than in a pumped system. Keep in mind that the minor loss (K ≈ 3) included in this tool's K_total can easily change with the real layout.
How to Use
Enter loop height (hNum, range 0.5–5 m) — vertical distance between heat source and condenser determines buoyancy-driven pressure head.
Set pipe inner diameter (dNum, range 6–50 mm) — smaller bores increase friction losses and reduce flow; larger diameters lower pressure drop.
Input heat input rate (qNum, range 500–50000 W) — total thermal power driving the temperature rise across the hot leg.
Specify fluid column length (lNum, range 1–10 m) — total tube length affects frictional resistance and transit time.
Click Calculate to solve coupled momentum and energy equations for natural circulation.
Worked Example
A heating loop with height h=2 m, pipe diameter d=12 mm (bore area A≈113 mm²), heat input q=8000 W, and loop length l=6 m, using water (ρ=998 kg/m³, cp=4186 J/kg·K, μ=0.001 Pa·s). Buoyancy head ΔP_buoy≈19.6 Pa drives circulation against friction f·(l/d)·(ρV²/2)≈15 Pa at equilibrium. Resulting velocity V≈0.35 m/s, mass flow ṁ≈0.039 kg/s, temperature rise ΔT≈48.8 K, hot-side bulk temperature≈85°C, Reynolds Re≈4200 (turbulent regime). System self-regulates: higher flow reduces ΔT, lowering buoyancy; lower flow increases ΔT, raising buoyancy until balance is reached.
Practical Notes
Vacuum or gas-charged accumulators must accommodate thermal expansion; in a sealed 6 m loop with ΔT=50 K, water volume increases ~2.5%, requiring 150–200 cm³ expansion space.
Loop orientation matters: purely horizontal sections add friction without buoyancy benefit; always maximize the vertical height difference between hot and cold regions.
At Re<2300 (laminar), pressure drop scales linearly with velocity; viscosity rise in hot leg reduces circulation — use heat-stable fluids (silicone oil, liquid sodium) if T_bulk exceeds 120°C.
Condenser effectiveness is critical: if cooling water supply is insufficient, bulk temperature climbs, ρ drops, buoyancy weakens, and flow stalls — design condenser with ΔT_approach<10 K.
Transient startup can exhibit hunting (oscillating flow) for 5–30 s until density stratification stabilizes; empirical data shows 8–12 mm diameter loops in buildings (radiator heating) typically settle within 2 minutes.