| name | pcm-storage |
| description | Phase change material (PCM) thermal energy storage — latent heat capacity (kJ/kg, kJ/L), melting point selection, Stefan problem (melt front propagation), fin-enhanced PCM (extended surface), encapsulation (macro/micro), organic PCMs (paraffins, fatty acids), inorganic PCMs (salt hydrates, metals), supercooling and nucleation, cycling stability, PCM-heat exchanger design (NTU-effectiveness), ASHRAE 94-77 standard, and applications (building thermal storage, solar, electronics cooling, cold chain). |
| metadata | {"priority":7,"promptSignals":{"phrases":["phase change material","PCM storage","latent heat storage","thermal energy storage","PCM melting","paraffin thermal storage"],"minScore":3}} |
Phase Change Material (PCM) Thermal Energy Storage — Complete Skill
PCM Selection and Properties
Material Categories
Organic PCMs (paraffins):
| Material | T_melt (°C) | L (kJ/kg) | ρ_l (kg/m³) | k (W/m·K) | Notes |
|---|
| n-Octadecane (C18) | 28.2 | 244 | 774 | 0.15 | Research standard; expensive |
| n-Hexadecane (C16) | 18.2 | 237 | 753 | 0.15 | Below ambient; cooling apps |
| Paraffin C20–C33 | 40–70 | 200–250 | 780–830 | 0.15–0.20 | Commercial; low cost |
| Stearic acid | 69.4 | 200 | 848 | 0.17 | Fatty acid; less expensive |
| Palmitic acid | 61.8 | 185 | 850 | 0.16 | Renewable; good cycling |
| Capric-lauric acid (binary) | 21 | 143 | 870 | 0.15 | Eutectic; room temp |
Inorganic PCMs (salt hydrates):
| Material | T_melt (°C) | L (kJ/kg) | ρ_l (kg/m³) | k (W/m·K) | Notes |
|---|
| Na₂SO₄·10H₂O (Glauber's salt) | 32.4 | 251 | 1,458 | 0.54 | High L/volume; prone to supercooling |
| CaCl₂·6H₂O | 29 | 191 | 1,562 | 0.54 | Good; phase separation issue |
| Na₂HPO₄·12H₂O | 36 | 281 | 1,520 | 0.52 | Highest L; phase separation |
| MgCl₂·6H₂O | 117 | 165 | 1,570 | 0.57 | Medium temperature |
| NaNO₃-KNO₃ eutectic | 222 | 100 | 1,900 | 0.55 | Solar thermal; high temp |
Metallic PCMs (high-temperature):
| Material | T_melt (°C) | L (kJ/kg) | ρ_l (kg/m³) | k (W/m·K) |
|---|
| Gallium | 29.8 | 80 | 6,093 | 29.4 |
| Bismuth-tin alloy | 138 | 44 | 7,900 | 18 |
| Al-Si (12%) | 577 | 460 | 2,560 | 80 |
Selection criteria:
- T_melt: ±2–5°C of operating temperature
- High latent heat L [kJ/kg or kJ/L]: inorganic > organic (per volume)
- Adequate thermal conductivity k [W/m·K]: organic k ≈ 0.15 → fins required
- Chemical stability: cycling >1,000 cycles without degradation
- Low supercooling: < 5°C; nucleating agents may be needed (SrCl₂·6H₂O for CaCl₂·6H₂O)
Volumetric Energy Density
Comparison:
E_latent [kJ/L] = L [kJ/kg] × ρ [kg/L]
Na₂SO₄·10H₂O: 251 × 1.458 = 366 kJ/L
Paraffin C18: 244 × 0.774 = 189 kJ/L
Water (0→4°C sensible): 4.18 × 4 × 1.0 = 16.7 kJ/L (much less)
Key advantage of PCM over sensible storage:
PCM delivers energy at near-constant temperature (isothermal); sensible storage requires large ΔT
Stefan Problem — Melt Front Analysis
One-Dimensional Melting (Neumann Exact Solution)
Phase change in semi-infinite slab (wall at T_w > T_melt):
x_melt(t) = 2β × √(α_l × t) [m; β = dimensionless parameter; α_l = liquid thermal diffusivity]
β satisfies transcendental equation:
β × e^(β²) × erf(β) = St/(√π) [Stefan condition]
St = c_p,l × (T_w - T_melt) / L [Stefan number; ratio sensible to latent heat]
Melt front position:
x_melt = 2β × √(k_l × t / (ρ_l × c_p,l)) [m]
Time to melt thickness δ:
t_melt = (δ / (2β))² / α_l [s]
Example (paraffin C18, T_w = 40°C, T_melt = 28°C):
St = 2.1×(40-28)/244 = 0.103; β ≈ 0.180 (from tables/iteration)
At t = 1 hr (3,600 s): α_l = k_l/(ρ_l×c_p,l) = 0.15/(774×2,100) = 9.2×10⁻⁸ m²/s
x_melt = 2×0.180×√(9.2×10⁻⁸×3600) = 0.360 × 0.0182 = 6.6 mm
Solidification: same equations with liquid initially at T_melt → solid grows from cold wall
x_solid = 2β × √(α_s × t) [β from St = c_p,s × (T_melt - T_w) / L; α_s = solid diffusivity]
Enthalpy Method (Numerical; Variable Density)
Governing equation (weak formulation):
∂H/∂t = ∇·(k × ∇T) [H = enthalpy; k = effective thermal conductivity]
H = c_p,s × T [for T < T_melt]
H = c_p,s × T_melt + L [at T = T_melt during melting]
H = L + c_p,l × T [for T > T_melt]
Numerical implementation:
Use temperature-enthalpy lookup; apparent heat capacity: C_app = L/(T_melt+ΔT - T_melt-ΔT) over narrow melting range
Standard FEM/FVM codes: COMSOL, OpenFOAM (heat transfer with phase change module)
Fin-Enhanced PCM Systems
Need for Enhancement
Thermal conductivity limitation:
k_organic ≈ 0.15 W/m·K → high resistance; melt front stalls
Characteristic time for δ = 10 mm: t ≈ (0.010)² / (4 × α_l) ≈ 2,700 s = 45 min (slow)
Fin enhancement methods:
Aluminum fins (k = 200 W/m·K); graphite foam (k_eff = 10–30 W/m·K); copper foam; nano-enhanced PCM
Fin-in-PCM effective conductivity:
k_eff = k_PCM × (1-ε_f) + k_fin × ε_f × η_fin [rule of mixtures; ε_f = fin volume fraction; η_fin = fin efficiency]
Annular fin efficiency:
η_fin = tanh(m×L_fin) / (m×L_fin) [m = √(2h/(k_fin×t_fin)); L_fin = fin half-length; h = convection coeff inside tube]
For PCM contact instead of convection: use effective h_pcm ≈ k_pcm/δ_melt
Optimal fin spacing:
s_opt ≈ 2–5 mm for paraffin PCMs (balance between fin thermal mass and enhanced area)
PCM Heat Exchanger Design
NTU-Effectiveness for PCM HX
Charging/discharging heat transfer:
During melting (isothermal phase change on PCM side): T_PCM = T_melt
ε = 1 - exp(-NTU) [isothermal side → ε = 1-e^(-NTU) regardless of C_r = C_min/C_max]
NTU = UA / (ṁ × c_p)_fluid
Charging rate:
Q̇ = ε × C_min × (T_in - T_melt) [W]
Time to fully charge: t_charge = m_PCM × L / Q̇_avg
Shell-and-tube PCM-HX design:
Tube side: HTF (water/oil/air); Shell side: PCM
A = π × D_i × L_tube × N_tubes; U calculated from tube-side h + wall + PCM-side h_eff (with fins)
HTF-side (tube) heat transfer coefficient:
Dittus-Boelter: Nu = 0.023 × Re^0.8 × Pr^0.4 [for turbulent; Re > 10,000]
h = Nu × k_f / D_i
Encapsulation
Microencapsulation
Shell materials: melamine-formaldehyde, polyurea, polyamide; d = 5–500 μm
Benefits: large surface area; prevent phase separation; flowable slurry
Slurry properties: 20–40 wt% PCM in water; effective latent heat = f_PCM × L_PCM
Applications: district cooling, building insulation boards (Micronal by BASF)
Macroencapsulation
Forms: spherical capsules (d = 10–100 mm); panels; pipes; brick shapes
Materials: HDPE, polypropylene, stainless steel
Volume expansion accommodation: void space ≥ 10–15% (paraffin expands 10–15% on melting)
Performance Metrics and Design
Energy Storage Capacity
Total storage capacity:
E_storage = m_PCM × L [J or kWh; L = latent heat in kJ/kg]
Volume required: V_PCM = E_storage / (L × ρ_PCM) [m³]
Power density:
Q̇_peak = UA × (T_HTF - T_melt) [W; limited by UA value]
Round-trip efficiency:
η_roundtrip = E_discharged / E_charged [typically 85–95%; losses from heat loss to ambient]
Standards and References
| Standard | Scope |
|---|
| ASHRAE 94-77 | Methods of testing thermal storage devices |
| ISO 10456 | Building materials — thermal and moisture properties |
| ASTM E793 | DSC measurement of latent heat capacity |
| ASTM E1269 | Specific heat capacity by DSC |
| IEA SHC Task 58 | Solar heating with PCM systems |
| IEA EES Annex 30 | Thermal energy storage technology |
Output
Provide: application description (charging/discharging temperatures; required storage capacity E [kWh]; power Q̇ [kW]; available space [m³]), PCM selection (material; T_melt [°C]; L [kJ/kg]; ρ [kg/m³]; k [W/m·K]; E_vol [kJ/L]), mass and volume of PCM required (m_PCM [kg]; V_PCM [m³]; allowance for expansion [%]), Stefan problem analysis (St; melt front x(t) at key times; melt-through time for design thickness [hrs]), fin enhancement (fin material; spacing [mm]; η_fin [%]; k_eff [W/m·K]; speed-up factor vs. unfinned), HX design (NTU; ε [%]; UA [W/K]; HTF flow rate [kg/s]; tube area [m²]), charging/discharging time [hrs] at rated power, supercooling risk (ΔT_super [°C]; nucleating agent recommendation), cycle life (expected cycles; degradation mode — phase separation, supercooling), containment (encapsulation type; volume expansion accommodation; shell material compatibility with PCM), and applicable standard (ASHRAE 94-77, ASTM E793, IEA Task 58).
