plate-hx

name	plate-hx
description	Plate heat exchanger (PHX) design — corrugated plate geometry (chevron angle β, mean channel gap), NTU-effectiveness method, pressure drop (friction factor, equivalent diameter), fouling factor, gasketed vs. brazed vs. welded PHX, LMTD correction F-factor, port sizing, thermal performance (NTU, ε, UA calculation), TEMA/ASME standards for PHX, and industrial applications (dairy, HVAC, refinery).
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Plate Heat Exchanger Design — Complete Skill

Geometry and Configuration

Corrugated Plate Geometry

Chevron (herringbone) corrugation: β = chevron angle: angle of corrugation ridges relative to flow direction β = 30° (low angle, "L" plates): low pressure drop, lower heat transfer β = 60° (high angle, "H" plates): high heat transfer, higher pressure drop β = 45°: intermediate; most common compromise

Mean channel gap (gap between adjacent plates): b = corrugation depth: typically 2–6 mm D_h = hydraulic diameter = 2b [for parallel plate channel; D_h = 4 × area / wetted perimeter ≈ 2b] Enlargement factor φ = actual corrugated area / projected area = 1.1–1.3 (depends on β and pitch)

Effective surface area per plate: A_plate_eff = L × W × φ [L = plate length; W = plate width; φ = enlargement factor]

Number of channels: N_channels = (N_plates - 1) / 2 [for single-pass counter-current; alternating hot/cold] Hot side: (N_plates - 1)/2 channels; Cold side: (N_plates - 1)/2 channels

Flow Arrangements

Counter-current (most common): Maximum driving force; F-factor = 1.0 (no correction needed to LMTD) Requires: hot in one port, cold in opposite diagonal port

Co-current (parallel flow): Lower effectiveness; F-factor < 1; rarely used

Multi-pass: Hot or cold side divided into multiple passes → increases contact length → higher effectiveness U-turn flow: requires special port design; F-factor correction needed

Heat Transfer Calculation

Overall Heat Transfer Coefficient (U)

U for plate HX: 1/U = 1/h_hot + (t_plate / k_plate) + 1/h_cold + R_f_hot + R_f_cold h_hot, h_cold = local film heat transfer coefficients [W/(m²·K)] t_plate = plate thickness [m]; k_plate = thermal conductivity [W/(m·K)]; stainless steel: k = 16–20 W/(m·K) R_f = fouling resistance [(m²·K)/W]

Typical U values:

Service	U [W/(m²·K)]
Water-water	3,500–7,500
Steam-water	3,000–6,000
Light oil-water	800–2,500
Heavy oil-water	200–800
Gas-water	100–400
Refrigerant-water	1,500–4,000

Film Heat Transfer Coefficient (h)

Correlation for corrugated plate HX (Martin 1996): Nu = c_q × (Re_q^q × Pr^(1/3)) × (η/η_w)^0.14 For β = 45°: c_q = 0.40, q = 0.73 (turbulent Re > 10) For β = 30°: c_q = 0.17, q = 0.66 For β = 60°: c_q = 0.72, q = 0.59

Reynolds number: Re = ṁ_ch × D_h / (μ × A_ch) [ṁ_ch = mass flow per channel; A_ch = channel cross-section = b × W] Or Re = G × D_h / μ [G = mass flux = ṁ_ch / A_ch]

Turbulent flow onset: Re_transition ≈ 10–200 for corrugated plates (much lower than smooth tubes → turbulent at very low Re) PHX advantage: high h even at low flow velocity → compact

h from Nu: h = Nu × k_fluid / D_h [W/(m²·K)]

NTU-Effectiveness Method

Number of Transfer Units (NTU): NTU = U × A_total / C_min [A_total = effective area = N_plates × A_plate; C = ṁ × c_p; C_min = smaller]

Effectiveness ε: Counter-current flow: ε = (1 - exp(-NTU(1-C*))) / (1 - C* × exp(-NTU(1-C*))) [C* = C_min/C_max < 1] For C* = 1 (balanced flow): ε = NTU / (1 + NTU)

Heat duty from effectiveness: Q = ε × C_min × (T_hot_in - T_cold_in) [W] Exit temperatures: T_hot_out = T_hot_in - Q / C_hot T_cold_out = T_cold_in + Q / C_cold

Required NTU from duty: NTU = -ln[(ε - 1)/(ε × C* - 1)] / (1 - C*) [for C* ≠ 1; solved from desired ε] Or equivalently: NTU = LMTD_basis approach below

LMTD Method

Log Mean Temperature Difference: LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂) ΔT₁ = T_hot_in - T_cold_out; ΔT₂ = T_hot_out - T_cold_in [counter-current]

F-factor correction (multi-pass): LMTD_effective = F × LMTD_counter [F = 1.0 for pure counter-current; < 1 for multi-pass or co-current] F from R = (T_hot_in - T_hot_out)/(T_cold_out - T_cold_in) and P = (T_cold_out - T_cold_in)/(T_hot_in - T_cold_in)

Required area: Q = U × A × LMTD_eff → A_required = Q / (U × LMTD_eff) Number of plates: N_plates = A_required / A_plate + 2 (end plates); round up to even number + 1

Pressure Drop

Channel Pressure Drop

Friction factor (Martin correlation): f = [cos β / (0.045 tan β + 0.09 sin β + f_0 / cos β) + (1 - cos β)/√(0.5(3.8 - sin β))]^(-1/2) Simplified: f ≈ K_p / Re^n [K_p, n from manufacturer data or table by β] For β = 45°, turbulent: f ≈ 0.60 / Re^0.20 (Kays & London data)

Port pressure drop: ΔP_port = 1.3 × G_port² / (2ρ) [port connections add ~1.3 velocity heads each; G_port = mass flux in port nozzle]

Channel pressure drop: ΔP_channel = 4f × (L/D_h) × G_ch² / (2ρ) × φ [friction in corrugated channel; φ accounts for enlargement]

Total pressure drop: ΔP_total = N_passes × ΔP_channel + 2 × ΔP_port [both port losses counted for each pass] Typical ΔP: 20–100 kPa per fluid side; more for high-viscosity or high-velocity applications

Port Sizing

Port diameter D_port: V_port = ṁ / (ρ × π × D_port² / 4) ≤ 6 m/s liquid; ≤ 40 m/s gas [typical maximum velocity] D_port = √(4ṁ / (ρ × π × V_max)) Standardized: D_port = 25, 40, 50, 65, 80, 100, 125, 150 mm (typical flanges)

Fouling and Cleaning

Fouling Resistance

TEMA fouling resistances (R_f) for PHX: R_f_clean_water: 0.0002 m²K/W (PHX = 1/3 of shell-tube TEMA value; more turbulent) R_f_sea_water: 0.0001 m²K/W R_f_light_oil: 0.0002 m²K/W R_f_river_water: 0.0003–0.0006 m²K/W R_f_heavily_fouling: 0.001 m²K/W (must use wide-gap plates)

PHX fouling advantage: High turbulence (Re → turbulent at Re ~ 10) suppresses fouling formation High wall shear stress: τ_w = f × ρ × u² / 2 → higher than shell-and-tube → self-cleaning tendency

Cleaning-in-Place (CIP): Gasketed PHX: disassembly for mechanical cleaning (unique PHX advantage — plates accessible) CIP chemicals: NaOH 2% (organic fouling); HNO₃ 1% (mineral/scale); EDTA for hard deposits Cleaning interval: 6–24 months depending on service; more frequent for dairy (weekly)

Wide-Gap Plates

For fibrous or particulate slurries: Special wide-gap plates: b = 7–10 mm (vs. 3–5 mm standard) → allows solids passage Semi-welded PHX: alternate welded pairs + gasket between pairs → handle corrosive fluids on one side

PHX Types

Gasketed Plate HX

Construction: Metal frame + pressure plates (head + follower); plates hung on carrying bar Gaskets: EPDM (water, steam to 160°C), NBR (oil), HNBR (high-temp oils), Viton (chemicals), PTFE encapsulated Max design conditions: P ≤ 2.5 MPa; T = -35 to +180°C (gasket dependent)

ASME/TEMA compliance: ASME VIII Div. 1 Section UHX: design of plate heat exchangers Pressure rating from gasket limitation (not plate thickness); plate S_y at T API 662 Pt. 1: petroleum industry gasketed PHX

Brazed Plate HX (BPHE)

No gaskets; brazing with Cu or Ni filler: Max conditions: Cu-brazed: P ≤ 4.0 MPa; T = -170 to +200°C; no ammonia (Cu corrosion) Ni-brazed: P ≤ 4 MPa; T = -170 to +550°C; compatible with ammonia Applications: refrigeration (evaporator/condenser), hydronic heating, solar thermal Compact; no gasket maintenance; cannot be disassembled

Welded/Semi-Welded PHX

Fully welded: no gaskets; high-pressure and high-temperature; corrosive fluids P ≤ 6–10 MPa; T ≤ 350°C Semi-welded: one side welded (corrosive), other side gasketed (utility) Applications: chemical reactors, ammonia refrigeration (semi-welded)

Standards and References

Standard	Scope
ASME VIII Div. 1 UHX	Plate heat exchanger pressure vessel design
API 662 Pt. 1	Gasketed PHX for petroleum
TEMA	Shell-and-tube standards (referenced for fouling factors)
ISO 5131	PHX terminology
EN 14222	Stainless steel shell-and-tube and plate HX
Martin (1996) IJHMT	Corrugated plate HX correlation

Output

Provide: service (fluid names; hot/cold), inlet/outlet temperatures (T_hot_in, T_hot_out, T_cold_in, T_cold_out [°C]), mass flow rates ṁ_hot, ṁ_cold [kg/s], heat duty Q [kW], LMTD [°C] (counter-current; F-factor if multi-pass), fouling resistances R_f_hot and R_f_cold [(m²·K)/W], U estimated (clean and fouled [W/(m²·K)]), required area A [m²], plate type (chevron β [°]; b [mm]; A_plate [m²]), number of plates N_plates, channel Re (hot and cold sides; verify turbulent), h_hot and h_cold [W/(m²·K)] from Martin correlation, pressure drop ΔP_hot and ΔP_cold [kPa], port diameter D_port [mm], PHX type (gasketed/brazed/welded) with gasket material, design pressure and temperature vs. limits, NTU and effectiveness ε, and applicable standard (ASME VIII UHX, API 662, Martin 1996).