heat-pipe

name	heat-pipe
description	Heat pipes and vapor chambers — capillary limit, wick structures, operating limits (sonic, entrainment, boiling, flooding), thermal resistance, loop heat pipes, two-phase cooling.
metadata	{"priority":7,"promptSignals":{"phrases":["heat pipe","vapor chamber","capillary","wick","loop heat pipe","LHP","two-phase heat","heat pipe limit","evaporator condenser"],"minScore":3}}

Heat Pipes & Vapor Chambers — Complete Skill

Operating Principle

Heat pipe cycle:

1. Evaporator: heat input → liquid evaporates → vapor pressure rises
2. Adiabatic section: vapor flows from evaporator to condenser (pressure gradient)
3. Condenser: heat rejected → vapor condenses → liquid
4. Return: liquid wicked back to evaporator by capillary pressure

Driving force: capillary pressure ΔP_cap = 2σ/r_eff (surface tension / effective pore radius) Must overcome: vapor pressure drop + liquid pressure drop + gravity

Capillary Limit (Primary Operating Limit)

Capillary Pressure

Maximum capillary pressure: ΔP_cap,max = 2σ/r_eff σ = fluid surface tension [N/m] r_eff = effective pore radius of wick [m]

Effective pore radius by wick type: Sintered powder: r_eff = 0.41 × r_particle (approximately) Screen mesh: r_eff = 1/(2N) where N = mesh number [wires/m] Groove: r_eff = w/2 (groove half-width)

Capillary limit (balance equation): ΔP_cap,max ≥ ΔP_l + ΔP_v + ΔP_g ΔP_l = liquid pressure drop in wick ΔP_v = vapor pressure drop in vapor core ΔP_g = gravitational head = ρ_l × g × L × sin(ψ) (ψ = tilt angle from horizontal) Positive if condenser above evaporator (assists); negative if evaporator above (adverse)

Liquid Pressure Drop

ΔP_l = (μ_l × L_eff × Q) / (K × A_w × ρ_l × h_fg) K = wick permeability [m²] A_w = wick cross-section area [m²] h_fg = latent heat of vaporization [J/kg] L_eff = effective length = L_evap/2 + L_adiabatic + L_condenser/2

Wick permeability by type: Sintered: K = r_particle² × (ε)³ / [37.5 × (1-ε)²] (Carman-Kozeny) Screen mesh: K = d_wire²ε³ / [122(1-ε)²] Groove (rectangular): K = w²(2h+w) / (4×f_Re×ν_l) (per groove, Hagen-Poiseuille) Typical K: sintered Cu 10⁻¹² to 10⁻¹⁰ m²; grooved 10⁻¹⁰ to 10⁻⁸ m²

Vapor Pressure Drop

For low-temperature range (Ma << 1): ΔP_v = (8μ_v × L_eff × Q) / (π r_v⁴ × ρ_v × h_fg) r_v = vapor core radius

Vapor figure of merit: F_v = ρ_v × h_fg × σ / μ_v (higher = better vapor transport) Liquid figure of merit: F_l = ρ_l × h_fg × K × σ / (μ_l × r_eff) (for wick transport)

Other Operating Limits

Sonic Limit

Vapor velocity becomes sonic at evaporator exit → choked flow → fixed Q Q_sonic = A_v × (ρ_v × P_v × h_fg²) / (2T_v × R_v)^(1/2) / (γ_v × R_g)^(1/2) Most relevant for liquid metal heat pipes at startup

Entrainment Limit

High vapor velocity → shear drags liquid droplets from wick surface → liquid depletion Q_entrainment = A_v × h_fg × √(σ × ρ_v / (2π r_h)) r_h = hydraulic radius of wick surface element

Boiling Limit

Nucleate boiling inside wick → vapor bubbles block liquid flow Q_boiling = 4π k_eff L T_v / h_fg ρ_v ln(r_i/r_v) × (2σ/r_n - ΔP_cap) k_eff = effective thermal conductivity of saturated wick Boiling limit particularly important for groove wicks and high heat flux

Flooding Limit (Gravity-Assisted, Thermosyphon)

Countercurrent liquid and vapor → flooding (liquid held up) Q_flood = A_v × h_fg × [g σ ρ_l (ρ_l-ρ_v)/ρ_v²]^(1/4) × constant

Thermal Resistance Model

Equivalent Resistance Network

R_total = R_evap + R_wick,evap + R_vapor + R_wick,cond + R_cond

Evaporator contact (conduction through wall): R_wall = t_wall / (k_wall × A_evap)

Wick thermal resistance: R_wick = t_wick / (k_eff × A_wick) k_eff (saturated screen wick): k_eff = k_l × [(k_l + k_s) - (1-ε)(k_l-k_s)] / [(k_l+k_s)+(1-ε)(k_l-k_s)] ε = wick porosity; k_s = wick solid conductivity; k_l = liquid conductivity

Vapor space thermal resistance (very low for non-extreme conditions): R_vapor ≈ T_v / (h_fg × ρ_v × A_v × Δv × ...) ≈ negligible for most applications

Overall (rule of thumb): R_total = 0.05 - 0.5°C/W (typical Cu-water, 20cm long)

Working Fluid Selection

Figure of Merit (Liquid Transport Factor)

N_l = ρ_l × σ × h_fg / μ_l [W/m²] Higher = better heat transport capacity

Fluids and temperature ranges:

Fluid	Range [°C]	N_l [W/m²]	Notes
Cryogens (N₂, NH₃)	-196 to -33	Moderate	Cryocooling
Ammonia	-70 to 100	3×10¹⁰	Excellent, toxic
Water	30 to 200	4×10¹⁰	Best for electronics
Methanol	-45 to 120	1×10¹⁰	Low temp option
Acetone	-80 to 120	8×10⁹	Al compatible
Mercury	200 to 600	4×10¹¹	High temp, toxic
Sodium	400 to 1100	3×10¹²	Nuclear, aerospace

Material Compatibility

Cu-Water: standard electronics (most common) Al-Ammonia: space applications, lightweight SS-Water: allowed but lower thermal conductivity wall Incompatible: Al-Water (hydrogen generation), Cu-Acetone (corrosion)

Vapor Chamber

Design Characteristics

Flat plate heat pipe (2D spreading in XY plane) Thicknesses: 2-6 mm total (electronics); up to 15mm (power electronics) Effective conductivity: 10,000-50,000 W/mK (vs. 400 for Cu) — in-plane spreading

Application: CPU cooling, LED arrays, power electronics with multiple heat sources Advantage over heat spreader: same or less weight, much higher effective conductivity

Sintered vs. Mesh Wick in Vapor Chamber

Sintered Cu: high capillary pressure, works against gravity; harder to fabricate Mesh/Screen: easier fabrication; gravity dependent (must assist or horizontal) Grooved: directional; best with gravity assist

Loop Heat Pipe (LHP)

Principle

Separate liquid and vapor lines; compensation chamber controls operating temperature Evaporator: porous wick, fine pore (sintered Ni or Ti), small core Condenser: parallel tubes or flat plate, remote from evaporator (up to 10m) Startup: subcooling in compensation chamber must collapse to start circulation

Advantages over conventional heat pipe:

• Flexible tubing (remote evaporator → condenser)
• Works against gravity
• Lighter wick (only at evaporator)
• Used in: spacecraft thermal control (ISS, satellites), laptops (LG Gram)

Thermal resistance: R_LHP ≈ 0.02-0.2°C/W (depends on condenser) Operating range: -40 to 120°C (ammonia); 20-120°C (water)

Output

Provide: heat transport capacity Q_max [W] at capillary limit, dominant limit identified (capillary/sonic/entrainment/boiling), thermal resistance R_total [°C/W], T_evaporator - T_condenser [°C], fluid selection recommendation, wick permeability K [m²], tilt sensitivity assessment (gravity assist/adverse).