| name | heat-exchanger |
| description | Heat exchanger design and rating — LMTD method, NTU-effectiveness method, shell-and-tube, plate, crossflow. Fouling factors, pressure drop, tube sizing, TEMA standards. |
| metadata | {"priority":7,"promptSignals":{"phrases":["heat exchanger","LMTD","NTU","shell and tube","effectiveness","heat transfer","counterflow","parallel flow"],"minScore":4}} |
Heat Exchanger Design — Complete Skill
Fundamentals
Heat duty: q = ṁ_h·c_p,h·(T_h,in - T_h,out) = ṁ_c·c_p,c·(T_c,out - T_c,in)
Heat capacity rates: C_h = ṁ_h·c_p,h, C_c = ṁ_c·c_p,c
C_min = min(C_h, C_c), C_max = max(C_h, C_c)
Capacity ratio: c = C_min/C_max
LMTD Method (Rating/Design with known temps)
q = U·A·F·ΔTLM
ΔTLM = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂)
Counterflow: ΔT₁ = T_h,in - T_c,out, ΔT₂ = T_h,out - T_c,in
Parallel flow: ΔT₁ = T_h,in - T_c,in, ΔT₂ = T_h,out - T_c,out
Correction factor F (for non-counterflow):
F = f(P, R) from charts/tables:
P = (T_c,out - T_c,in)/(T_h,in - T_c,in) [cold side effectiveness]
R = (T_h,in - T_h,out)/(T_c,out - T_c,in) = C_c/C_h
1-2 shell-and-tube: F from TEMA charts (F > 0.75 acceptable, F > 0.9 preferred)
Crossflow (both unmixed): F from standard chart
NTU-Effectiveness Method (When outlet temps unknown)
NTU = U·A/C_min
Effectiveness: ε = q/q_max = q/(C_min·(T_h,in - T_c,in))
Counterflow:
ε = (1-exp(-NTU(1-c)))/(1-c·exp(-NTU(1-c))) [c ≠ 1]
ε = NTU/(1+NTU) [c = 1]
Parallel flow:
ε = (1-exp(-NTU(1+c)))/(1+c)
Crossflow (both unmixed):
ε = 1 - exp((NTU^0.22/c)·(exp(-c·NTU^0.78) - 1))
Shell-and-tube (1 shell pass, 2 tube passes):
ε₁ = 2/(1+c+√(1+c²)·(1+exp(-NTU√(1+c²)))/(1-exp(-NTU√(1+c²))))
Condenser/Boiler (c = 0 or C_max → ∞):
ε = 1 - exp(-NTU)
NTU = -ln(1-ε)
Overall Heat Transfer Coefficient
1/U = 1/h_i + R_fi + t_w/k_w + R_fo + 1/h_o
Fouling resistances R_f (TEMA recommended):
| Fluid | R_f (m²K/W) |
|---|
| Cooling water (treated) | 0.0002 |
| Cooling water (river) | 0.0003-0.0006 |
| Steam | 0.0001 |
| Refrigerant | 0.0002 |
| Oil (light) | 0.0004 |
| Oil (heavy) | 0.0009 |
| Seawater | 0.0001-0.0002 |
Internal Convection (Tube Side)
Turbulent (Re > 10,000): Nu = 0.023·Re^0.8·Pr^n (Dittus-Boelter)
n = 0.4 (heating), n = 0.3 (cooling)
Fully developed turbulent (0.5 < Pr < 2000):
Nu = (f/8)(Re-1000)Pr / (1+12.7·√(f/8)·(Pr^(2/3)-1)) (Gnielinski)
f = (0.790·ln(Re)-1.64)^(-2) (Petukhov friction factor)
Laminar (Re < 2300):
Constant heat flux: Nu = 4.36
Constant wall temp: Nu = 3.66
Developing length: Nu = 3.66 + 0.0668(D/L)Re·Pr/(1+0.04((D/L)Re·Pr)^(2/3))
External Convection (Shell Side)
Single cylinder in crossflow:
Nu = C·Re^m·Pr^(1/3)·(Pr/Pr_s)^0.25
C, m from Zhukauskas table:
Re=40-4000: C=0.683, m=0.466
Re=4000-40000: C=0.228, m=0.731
Re=40000-400000: C=0.300, m=0.805
Bank of tubes: Use Grimison/Zhukauskas correction for N rows
Shell-and-tube — Bell-Delaware method:
h_o = h_ideal · J_c · J_l · J_b · J_s · J_r
(correction factors for baffle configuration, leakage, bypass, unequal baffle spacing)
Pressure Drop
Tube side: ΔP = (4f·L/D + Σ_K) · ρV²/2 (per tube pass)
Include entrance/exit losses: K ≈ 1.5 per pass
Shell side (simplified): ΔP_s ≈ 2f·G_s²·D_s·(N_b+1)/(ρ·D_e·φ_s)
Acceptable shell-side ΔP: < 14 kPa (2 psi) for liquids, < 1.4 kPa for gases
TEMA Standards
TEMA R: severe service (refinery)
TEMA C: general industrial
TEMA B: chemical process
Shell types: E (1 pass), F (2 pass), G (split flow), H (double split), J (divided flow), K (kettle reboiler), X (crossflow)
Plate Heat Exchanger
Chevron angle β: 45° (low ΔP, low h), 65° (high ΔP, high h)
High U values (3000-7000 W/m²K) — excellent for liquid-liquid
Cannot handle fouling > R_f = 0.0001 m²K/W
Design Procedure
- Determine q from duty
- Estimate U (initial guess from fluid type table)
- Calculate A = q/(U·F·ΔTLM) or use NTU method
- Select tube size (19mm OD or 25mm OD typical), tube length (1.83-6.1m)
- Calculate number of tubes: N_t = A/(π·D_o·L)
- Select shell diameter from TEMA tube count tables
- Calculate h_i (tube side), h_o (shell side), fouling factors → actual U
- Iterate until assumed U ≈ calculated U
Output
Provide: q [kW], U [W/m²K], A [m²], NTU, ε, ΔTLM, F, tube count, shell diameter, ΔP (tube + shell side).
