Everything, Everywhere
Verified Specification | Standardized Formulas | Instant Precision
Secure & Private (Zero Data Retention) Free Access • No Sign-Up

Perform rigorous thermal rating and hydraulic pressure drop calculations for TEMA Type E industrial shell and tube heat exchangers using Kern's method. Solves true mean temperature difference FT × LMTD, shell crossflow mass velocity, clean and fouled overall heat transfer coefficient U, and shell/tube pressure drops.

1. Thermal Stream Parameters

2. Shell & Tube Bundle Geometry

3. Thermal Rating & Pressure Drops

Countercurrent LMTD: -- °C
TEMA FT Correction Factor: --
Effective Temperature ΔTeff: -- °C
Installed Surface Area Aext: -- m² (-- ft²)
Required Design Overall Ureq: -- W/(m²·K)
Calculated Fouled Overall Ufouled: -- W/(m²·K)
Thermal Overdesign Margin: -- % EXCESS
Shell Crossflow Velocity vs: -- m/s
Shell-Side Pressure Drop ΔPs: -- kPa (-- psi)
Tube-Side Velocity & ΔPt: -- m/s | -- kPa
TEMA Type E Shell & Tube Exchanger Cross-Sectional Geometry
[ Shell Inlet Nozzle → Impingement Plate ] → [ Transverse Segmental Baffles (B Spacing, 25% Cut) ]
→ [ Multi-Pass Tube Bundle (Nt Tubes, do × di, Pt Pitch) ] → [ Floating / Fixed Tubesheets ]
→ [ Tube-Side Channel Head with Pass Partitions ] ↔ [ Shell Outlet Nozzle ]

Mathematical Foundations & Kern's Shell-Side Derivations

Heat exchanger rating couples the basic heat transfer rate equation $Q = U cdot A cdot F_T cdot ext{LMTD}$ with Kern's hydrodynamic crossflow correlations:

1. Corrected Mean Temp Difference
$$ ext{LMTD} = rac{Delta T_1 - Delta T_2}{ln(Delta T_1 / Delta T_2)}$$ $$F_T = rac{sqrt{R^2 + 1} lnleft( rac{1-P}{1-PR} ight)}{(R-1) lnleft( rac{2 - P(R+1-sqrt{R^2+1})}{2 - P(R+1+sqrt{R^2+1})} ight)}$$ Prevents unfeasible temperature cross designs.
2. Shell Crossflow Area & Mass Velocity
$$S_m = rac{D_s cdot (P_t - d_o) cdot B}{P_t} quad [ ext{m}^2]$$ $$G_s = rac{dot{m}_{shell}}{S_m} quad [ ext{kg}/( ext{m}^2cdot ext{s})]$$ $$Re_s = rac{G_s cdot D_e}{mu_s}$$
3. Overall Heat Transfer Coefficient U
$$ rac{1}{U_{fouled}} = rac{1}{h_o} + R_{fs} + rac{d_o ln(d_o/d_i)}{2 k_{wall}} + R_{ft} rac{d_o}{d_i} + rac{1}{h_i} rac{d_o}{d_i}$$ Evaluates true fouled margin under operating cycles.
4. Shell-Side Pressure Drop ΔPs
$$Delta P_s = rac{f_s cdot G_s^2 cdot D_s cdot (N_b + 1)}{2 ho_s cdot D_e cdot (mu_s / mu_w)^{0.14}}$$ $$f_s = exp(0.576 - 0.19 ln Re_s)$$

5 Fatal Traps in Shell & Tube Exchanger Design

1. The Acoustic Resonance & Tube Vibration Destruction Trap

When high-velocity shell-side gas or vapor crosses the tube bundle, Karman vortex shedding or fluid-elastic instability can lock onto the acoustic natural frequency of the shell cavity ($f_a = c / 2 D_s$). The resulting standing acoustic wave creates deafening 130 dB sonic screams and induces violent tube bundle vibration. Tubes repeatedly hammer against baffle holes, severing tubes cleanly at baffle edges and releasing high-pressure toxic chemicals into cooling water systems. Always verify Connors instability constants and baffle spacing.

2. The Temperature Cross FT Collapse Trap

When the cold fluid outlet temperature exceeds the hot fluid outlet temperature ($T_{c,out} > T_{h,out}$), a temperature cross occurs. In a multi-pass 1-2 TEMA E shell, this causes the local temperature driving force in the cocurrent pass to reverse, heating the cold fluid backwards. The configuration factor $F_T$ drops steeply below 0.75. Novice engineers compensate by arbitrarily multiplying surface area, but the exchanger will physically never achieve the target duty. The only engineering solution is splitting the duty into two or more shells in series (TEMA F or multi-shell E).

3. High Kinetic Energy Nozzle Impingement Erosion Trap

Process fluids entering the shell inlet nozzle at high velocity carry immense kinetic energy density ($ ho v^2$). If $ ho v^2 > 2,230 ext{ kg}/( ext{m}cdot ext{s}^2)$ and no TEMA solid impingement plate or annular distribution belt is installed under the nozzle, the incoming jet strikes the top row of tubes directly. Entrained liquid droplets or particulate fines erode the 1.6 mm tube wall within months, causing catastrophic tube puncture and inter-stream cross-contamination.

4. Excessive Baffle Cut Bypass Streaming (Window Short-Circuiting)

Specifying segmental baffle cuts greater than 35% diameter in an attempt to lower shell pressure drop creates massive low-velocity dead zones behind the baffles and allows 40% of the shell fluid to bypass the tube matrix through the window zones without participating in crossflow heat exchange. The effective heat transfer coefficient collapses by 50%, while the dead zones accumulate stagnant sludge and severe under-deposit pitting corrosion.

5. Tube-Side Velocity Low-Limit & Biofouling Settlement

To save pumping power, operators often throttle cooling water flows through condenser tubes. When cooling water tube-side velocity drops below 1.0 m/s (3.3 ft/s), silt, micro-algae, and zebra mussels settle out of suspension onto the inside tube surfaces. The resulting biofouling film increases thermal resistance tenfold and creates differential aeration cells that cause rapid localized microbiologically influenced corrosion (MIC) through-wall perforations.

Step-by-Step Worked Engineering Example

Application: Hydrocarbon Condensate Cooler (TEMA Type AES 1-2 Exchanger).

  • Thermal Duty: $Q = 1,850 ext{ kW}$, Hot kerosene stream cooled from $145^circ ext{C}$ to $85^circ ext{C}$ in shell.
  • Cooling Water: Heated from $30^circ ext{C}$ to $65^circ ext{C}$ in 2-pass tube bundle.
  • Exchanger Specs: Shell ID $D_s = 610 ext{ mm}$, $N_t = 368$ tubes, OD $d_o = 19.05 ext{ mm}$, ID $d_i = 15.75 ext{ mm}$, Length $L = 4.88 ext{ m}$.
  • Layout: $30^circ$ triangular pitch $P_t = 23.81 ext{ mm}$, Baffle spacing $B = 250 ext{ mm}$.

Step 1: Log Mean Temperature Difference & FT Factor:

$$Delta T_1 = T_{h,in} - T_{c,out} = 145 - 65 = 80^circ ext{C}$$ $$Delta T_2 = T_{h,out} - T_{c,in} = 85 - 30 = 55^circ ext{C}$$ $$ ext{LMTD} = rac{80 - 55}{ln(80 / 55)} = rac{25}{0.3747} = 66.72^circ ext{C}$$ $$P = rac{t_2 - t_1}{T_1 - t_1} = rac{65 - 30}{145 - 30} = rac{35}{115} = 0.3043$$ $$R = rac{T_1 - T_2}{t_2 - t_1} = rac{145 - 85}{65 - 30} = rac{60}{35} = 1.7143$$ $$ ext{Per 1-2 TEMA formula: } F_T = 0.942 implies Delta T_{eff} = 0.942 imes 66.72 = 62.85^circ ext{C}$$

Step 2: Installed Outside Heat Transfer Area:

$$A_{ext} = N_t cdot pi cdot d_o cdot L = 368 imes pi imes 0.01905 imes 4.88 = 107.51 ext{ m}^2 quad (1,157 ext{ ft}^2)$$ $$U_{required} = rac{Q}{A cdot Delta T_{eff}} = rac{1,850,000 ext{ W}}{107.51 ext{ m}^2 imes 62.85 ext{ K}} = 273.8 ext{ W}/( ext{m}^2cdot ext{K})$$

Step 3: Shell-Side Hydraulic Crossflow & Kern's Velocity:

$$S_m = rac{D_s cdot (P_t - d_o) cdot B}{P_t} = rac{0.610 imes (0.02381 - 0.01905) imes 0.250}{0.02381} = rac{0.610 imes 0.00476 imes 0.250}{0.02381} = 0.0305 ext{ m}^2$$ $$ ext{Hot kerosene mass flow: } dot{m}_h = rac{Q}{c_p Delta T_h} = rac{1850}{2.15 imes 60} = 14.34 ext{ kg/s}$$ $$G_s = rac{14.34 ext{ kg/s}}{0.0305 ext{ m}^2} = 470.2 ext{ kg}/( ext{m}^2cdot ext{s}) implies v_s = rac{470.2}{790} = 0.595 ext{ m/s}$$

Step 4: Heat Transfer Coefficients & Fouled Overdesign:

$$ ext{Shell-side film: } h_o = 680 ext{ W}/( ext{m}^2cdot ext{K}), quad ext{Tube-side film: } h_i = 3,450 ext{ W}/( ext{m}^2cdot ext{K})$$ $$ rac{1}{U_f} = rac{1}{680} + 0.00035 + rac{0.01905 ln(19.05/15.75)}{2 imes 16} + 0.00020left( rac{19.05}{15.75} ight) + rac{1}{3450}left( rac{19.05}{15.75} ight)$$ $$ rac{1}{U_f} = 0.001471 + 0.000350 + 0.000113 + 0.000242 + 0.000350 = 0.002526 implies U_f = 395.9 ext{ W}/( ext{m}^2cdot ext{K})$$ $$mathbf{ ext{Overdesign Margin} = rac{395.9 - 273.8}{273.8} imes 100% = +44.6% implies ext{ extbf{Safe Margin for Long Production Cycles}}}$$

Frequently Asked Questions

What is the difference between Kern's method and the Bell-Delaware method for shell-side rating? +
Why must the Log Mean Temperature Difference (LMTD) be corrected by the FT factor? +
What are the trade-offs between triangular (30°) and square (90° or 45°) tube pitch layouts? +
When is a TEMA impingement plate required at the shell inlet nozzle? +
What is the allowable shell-side and tube-side pressure drop in industrial design? +
Sponsored Utility
While You're Here
Sponsored Recommendations
Advertisement