thermosyphon

name	thermosyphon
description	Closed two-phase thermosyphon (CTPT) — gravity-driven heat pipe (no wick), flooding/geyser/entrainment limits, boiling limit, Bond number and inclination effects, fill ratio optimization, working fluid selection (water/ammonia/methanol/CO₂/R134a), heat transfer coefficients (pool boiling at evaporator, condensation at condenser), thermal resistance network, horizontal and inclined operation, and ASHRAE/ASTM standards for thermosyphon applications.
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Closed Two-Phase Thermosyphon (CTPT) — Complete Skill

Thermosyphon Fundamentals

Operating Principle

Thermosyphon (gravity-assisted heat pipe): Sealed tube partially filled with working fluid; evaporator at bottom; condenser at top Heat in at evaporator → liquid evaporates → vapor rises → condenses at condenser → liquid falls back by gravity No wick required (gravity provides liquid return); simpler and cheaper than wick heat pipe Limitation: condenser must be above evaporator (gravity drives liquid return); cannot operate inverted

vs. Wick heat pipe: Thermosyphon: higher capacity (no wick capillary limit); gravity-dependent orientation Heat pipe with wick: operates in any orientation; lower capacity (capillary pressure limited); more expensive

Thermal Resistance Network

Overall thermal resistance: R_total = R_evap + R_vapor + R_cond + R_wall_evap + R_wall_cond R_evap = 1 / (h_evap × A_evap) [evaporator heat transfer; pool boiling or film boiling] R_cond = 1 / (h_cond × A_cond) [condenser; film condensation] R_vapor ≈ T_sat / (h_fg × ρ_v × A_cross) [negligible for well-designed units; vapor pressure drop] R_wall = t / (k_wall × A) [tube wall conduction; usually negligible]

Typical overall R: 0.01–0.2 K/W depending on size and fluid

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Working Fluid Selection

Fluid Properties and Selection

Merit number (Liquid transport factor): FOM = (σ × ρ_l × h_fg) / μ_l [higher FOM → better heat transport capacity; useful for comparing fluids] Water: FOM_100°C = 0.48 MJ/(m²·s) — extremely high; best for 50–270°C range Ammonia: excellent for −40 to +100°C; FOM comparable to water at low T; toxic Methanol: −10 to +130°C; flammable; lower FOM than water Acetone: 0–120°C; clean; moderate FOM R134a: −40 to +80°C; non-flammable; ODP = 0; lower FOM

Operating temperature ranges:

Fluid	T_min [°C]	T_max [°C]	Applications
Water	50	270	Electronics cooling, waste heat recovery
Ammonia	−60	+100	Refrigeration, building HVAC
Methanol	−10	130	Electronics, moderate T
Acetone	0	120	Moderate temp, clean
CO₂	−50	+25	Transcritical refrigeration, food
Sodium	500	1000	High temperature (nuclear, solar)
Hg	200	500	Intermediate high temperature

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Fill Ratio and Flooding Limit

Optimal Fill Ratio

Fill ratio: φ = V_liquid_fill / V_evaporator [dimensionless; or % of total tube volume] Too low (φ < φ_min): dry-out; evaporator wall superheating → deterioration Too high (φ > φ_opt): flooding; liquid fills vapor space → geyser/carryover → instability

Optimal fill ratio (practical): φ_opt ≈ 0.3–0.7 (30–70% of evaporator volume) For horizontal thermosyphon: fill ratio less critical (pool covers entire bottom) Best practice: initial fill calibration testing; start at φ = 0.5 and adjust based on performance

Flooding limit (vapor-liquid counter-flow): When vapor velocity too high → carries liquid upward → flooding → breakdown of operation Flooding criterion (Kutateladze flooding constant K_f): Q_max_flood = A_cross × h_fg × ρ_v^(1/2) × [σ × g × (ρ_l − ρ_v)]^(1/4) × K_f K_f = 0.16 (empirical; Wallis flooding); accounts for tube diameter via Bond number

Bond number: Bo = D / √(σ / (g × (ρ_l − ρ_v))) [D = tube inner diameter] For Bo > 30: flooding limit increases linearly with D (large diameter; flooding not limiting) For Bo < 30: flooding significant; use larger diameter or multiple small tubes For water at 100°C: √(σ/(g(ρ_l-ρ_v))) = √(0.058/(9.81×960)) = √(6.2×10⁻⁶) = 2.49 mm Bo = D / 2.49 mm; Bo = 30 → D_min = 75 mm (large tube needed for water thermosyphon)

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Heat Transfer Correlations

Evaporator (Pool Boiling)

Pool boiling heat transfer coefficient: Forster-Zuber nucleate boiling correlation: h_evap = 0.00122 × (k_l^0.79 × c_pl^0.45 × ρ_l^0.49) / (σ^0.5 × μ_l^0.29 × h_fg^0.24 × ρ_v^0.24) × ΔT_sat^0.24 × ΔP_sat^0.75 Simplified: h_evap ∝ q^0.7 for pool boiling (nucleate regime) Typical h_evap for water at 100°C: 5,000–25,000 W/m²K (depending on surface, ΔT_sat) For refrigerants: 1,000–8,000 W/m²K

Boiling limit: Critical heat flux (CHF) at evaporator: q_max = h_fg × ρ_v × [σ × g × (ρ_l − ρ_v) / ρ_v²]^(1/4) × K_Z K_Z = 0.131 (Zuber constant for flat surface); 0.149 (cylinder) For water at 100°C: q_CHF ≈ 1.5 MW/m² (theoretical; practical: 0.5–1.0 MW/m² in thermosyphon)

Condenser (Film Condensation)

Nusselt film condensation (inside vertical tube): h_cond = 0.943 × [ρ_l × (ρ_l − ρ_v) × g × h_fg × k_l³ / (μ_l × L_cond × ΔT_cond)]^(1/4) [L_cond = condenser length; ΔT_cond = T_sat − T_wall]

Or simplified: h_cond = C × (ρ_l² × g × k_l³ × h_fg / (μ_l × Q_cond/A))^(1/3) [turbulent condensation at high Q]

Modified Chato correlation for horizontal condensation: h_cond_horiz = 0.728 × [ρ_l × (ρ_l − ρ_v) × g × h_fg × k_l³ / (μ_l × D × ΔT)]^(1/4)

Typical h_cond: Water: 5,000–20,000 W/m²K; Ammonia: 4,000–15,000 W/m²K; Refrigerants: 1,500–8,000 W/m²K

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Inclination Effects

Tilted and Horizontal Operation

Inclined thermosyphon: Inclination angle θ from horizontal: 0° = horizontal; 90° = vertical (optimal for gravity return) As θ decreases below 60°: flooding limit decreases (reduced gravity component driving liquid return) Liquid return velocity: v_liq = V_vapor_condensed / (π × D × t_film) [film flow by gravity component g×sin(θ)]

Horizontal thermosyphon (θ = 0°): Pool of liquid in bottom; vapor in upper half; no flooding limit (counter-flow minor) But: stratified flow; only bottom of tube active in evaporator → reduced effective area Performance 30–50% lower than vertical (per unit area)

Best inclination: 60–90° from horizontal; 75° is practical optimum in many installations

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Applications

Application	Fluid	T_range [°C]	Q_capacity [W]	Notes
CPU heat sink	Water/methanol	40–90	50–300	Laptop/server cooling
Transformer cooling	Diala oil	60–120	10,000+	Electrical insulation required
Permafrost preservation	CO₂/NH₃	−40 to −10	100–1000	Arctic pipeline supports
Solar water heater	Water	30–90	500–5000	Domestic and commercial
Waste heat recovery	Water	60–200	50,000+	Industrial flue gas
Data center immersion	Fluorinert/HFE	40–60	5,000–50,000	2-phase immersion

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Standards and References

Standard	Scope
ASHRAE Handbook Fundamentals	Heat pipe and thermosyphon thermal properties
ASTM E1465	Measurement of thermal resistance of thin insulation
ISO 16812	Petroleum — shell and tube heat exchangers (applicable to waste heat thermosyphon)
Chi (1976) "Heat Pipe Theory and Practice"	Foundational reference
Faghri (1995) "Heat Pipe Science and Technology"	Comprehensive reference

Output

Provide: application (heat source/sink; geometry: vertical/inclined/horizontal; T_evap [°C]; T_cond [°C]; ΔT available [°C]; Q_target [W]), fluid selection (working fluid; T_range match; FOM rank; Bo number at operating T), geometry (D [mm]; L_evap [mm]; L_adiabatic [mm]; L_cond [mm]; fill ratio φ [%]), flooding limit (Q_flood from Kutateladze; K_f = 0.16; Bo = D/capillary_length; Q_flood vs. Q_target; safety margin), boiling limit (q_CHF [W/m²]; Q_CHF = q_CHF × A_evap [W]; safety margin vs. Q_target), heat transfer (h_evap from pool boiling correlation [W/m²K]; R_evap = 1/(h_evap×A_evap) [K/W]; h_cond from Nusselt [W/m²K]; R_cond [K/W]; R_total [K/W]; ΔT_total = Q × R_total [°C]), inclination (optimal angle [°]; performance factor vs. vertical [%]; g×sinθ effect on flooding), material compatibility (fluid-tube compatibility: copper+water OK; Al+ammonia OK; SS+methanol OK; avoid copper+ammonia; Al+water — oxide issue), and applicable standard (ASHRAE Fundamentals; Chi/Faghri references for detailed design; ASTM E1465 for insulation verification).