| name | shell-tube-hx |
| description | Shell-and-tube heat exchanger design — TEMA types, LMTD correction, NTU-effectiveness, tube sizing, baffle spacing, pressure drop (Bell-Delaware), fouling, ASME VIII. |
| metadata | {"priority":8,"promptSignals":{"phrases":["shell and tube","shell tube heat exchanger","TEMA","heat exchanger design","LMTD correction","NTU effectiveness","baffle spacing"],"minScore":3}} |
Shell-and-Tube Heat Exchanger Design — Complete Skill
TEMA Classifications
| Type | Fixed TS | Floating Head | U-tube | Notes |
|---|
| TEMA E | Most common | No | No | Simple; single shell pass |
| TEMA F | — | — | — | Two shell passes; F-factor issue |
| TEMA G | Split flow | — | — | Horizontal condensers/vaporizers |
| TEMA H | Double split | — | — | Low pressure drop |
| TEMA J | Divided flow | — | — | Low shell-side ΔP |
TEMA standards: R (petroleum refining), C (commercial), B (chemical)
LMTD Method
Log Mean Temperature Difference:
LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)
For counter-current: ΔT₁ = T_h,in - T_c,out; ΔT₂ = T_h,out - T_c,in
Correction factor F:
Q = U × A × F × LMTD (for multi-pass configurations)
F from TEMA charts based on R and S:
R = (T₁ - T₂) / (t₂ - t₁) (hot-side range / cold-side range)
S = (t₂ - t₁) / (T₁ - t₁) (temperature effectiveness = cold-side gain / max possible)
Rule: F ≥ 0.75 (avoid low F → large surface penalty)
1-2 STHE (1 shell, 2 tube passes): F chart from TEMA
NTU-Effectiveness Method
Effectiveness: ε = Q / Q_max where Q_max = C_min × (T_h,in - T_c,in)
C_min = min(ṁ c_p) of two streams
NTU: NTU = UA / C_min
Counter-current HX:
ε = [1 - exp(-NTU(1-C_r))] / [1 - C_r exp(-NTU(1-C_r))] (for C_r ≠ 1)
ε = NTU/(NTU+1) (for C_r = 1, equal capacity rates)
C_r = C_min/C_max
For condensers/evaporators: C_r = 0 → ε = 1 - e^(-NTU)
Overall Heat Transfer Coefficient
1/U = 1/h_o + R_fo + (t_w/k_w) + R_fi + 1/h_i
h_o = shell-side coefficient; h_i = tube-side (×A_o/A_i if different areas)
R_fo, R_fi = fouling resistances (TEMA Table RGP-T-2.4)
Typical fouling factors:
Cooling water (river): R_f = 0.0002 m²K/W
Treated cooling water: R_f = 0.0001 m²K/W
Crude oil: R_f = 0.0004–0.0009 m²K/W
Steam (clean): R_f = 0.0001 m²K/W
Tube-Side Coefficient (Dittus-Boelter)
h_i = (k/D_i) × Nu
Nu = 0.023 Re^0.8 Pr^n (n=0.4 heating, n=0.3 cooling)
Re = ρ v D_i / μ; valid for Re > 10,000, L/D > 10
Tube-side pressure drop:
ΔP_tube = [f × L × N_passes / D_i + 4 N_passes (inlet+exit)] × ρ v² / 2
f = 0.316/Re^0.25 (Blasius); 0.0014 + 0.125/Re^0.32 (Filonenko)
Shell-Side Coefficient (Bell-Delaware Method)
More accurate than Kern method:
h_o = h_ideal × J_c × J_l × J_b × J_s × J_r
h_ideal: from ideal tube bank correlations (colburn j-factor)
J_c = baffle cut correction; J_l = leakage correction; J_b = bypass correction; J_s = unequal spacing; J_r = laminar correction
Simplified (Kern): Nu_shell = 0.36 Re_shell^0.55 Pr^0.33 (μ/μ_w)^0.14
D_e = equivalent diameter based on tube pitch layout
Tube Layout and Pitch
Triangular (30°): highest packing; better h; harder to clean
Square (90°): lower h; easy cleaning (straight lanes); use for fouling services
Rotated square (45°): compromise
Tube pitch: P_t = 1.25 D_o (minimum); 1.33 D_o preferred
Tube OD standard sizes: 3/4" (19.05 mm), 1" (25.4 mm), 1.25", 1.5"; or metric 16, 20, 25, 32 mm
Baffle Design
Segmental baffle: most common; cut = 20–25% of shell ID
Double segmental: lower ΔP; more baffles for same support
Disk-and-donut: very low ΔP; used in large condensers
Baffle spacing B: typically 0.2–1.0 × D_shell
Closer → higher h, higher ΔP; farther → opposite
B_min: tube unsupported length limit (TEMA vibration)
Shell-Side Pressure Drop (Bell-Delaware)
ΔP_shell = ΔP_cross + ΔP_window + ΔP_end
(Each segment from correlations; typically 30–70% of allowable for design)
Nozzle Sizing
Shell nozzle velocity: ≤ 3 m/s liquid; ≤ 30 m/s gas
Tube nozzle: ≤ 2 m/s liquid
ASME VIII Requirements
Shell design pressure + temperature → wall thickness from UG-27
Tube design per UA-5; tube sheets per UHX
Nozzle reinforcement per UG-37
Design Procedure
- Determine Q from energy balance; calculate LMTD and F
- Estimate U (initial guess); size A = Q/(U×F×LMTD)
- Select tube size, length, number; compute tube layout
- Calculate h_i (tube side); calculate h_o (Bell-Delaware)
- Update U; iterate until converged
- Check ΔP tube and shell vs. allowable
- Specify baffles, nozzles; verify TEMA Class
Output
Provide: shell ID [mm], tube count n_t, tube OD×length [mm], tube passes, baffle spacing [mm], U [W/m²K], A_required [m²] vs. A_provided, ΔP_tube and ΔP_shell [kPa], F factor, fouling allowance, TEMA class.
