How to Design a Shell & Tube Heat Exchanger: Step‑by‑Step Guide | Kern, Bell‑Delaware, TEMA

Complete Shell & Tube Heat Exchanger Design Guide | Kern Method | Bell‑Delaware | TEMA | Perry's Handbook

How to Design a Shell & Tube Heat Exchanger
A Step‑by‑Step Engineering Guide

Comprehensive design methodology based on Kern, Bell‑Delaware, NTU‑Effectiveness and TEMA standards for process engineers. All essential formulas, correlation selection logic, pressure drop and overdesign checks.

Shell and tube heat exchangers are the most widely used type of heat exchanger in the process industries, accounting for over 60% of all installations in chemical plants, refineries, and power generation. This guide explains the complete shell and tube heat exchanger design procedure following the Kern method, Bell‑Delaware method, and TEMA standards.

Industrial standards referenced: TEMA (Tubular Exchanger Manufacturers Association) 10th Edition, Kern Process Heat Transfer (1950), Perry's Chemical Engineers' Handbook 9th Edition, API 660, and ASME Section VIII Division 1.

Step 1: Collect Process & Fluid Property Data

The first step in heat exchanger sizing is gathering accurate process data. Reliable thermal design depends on accurate fluid properties evaluated at the correct temperature. Required inputs include:

Mass flow rates (kg/s) for both hot and cold fluids
Inlet and outlet temperatures (°C) for both streams
Fluid properties at mean bulk temperature: density (kg/m³), specific heat Cp (kJ/kg·°C), dynamic viscosity (Pa·s), thermal conductivity (W/m·K)
Fouling resistances (m²·°C/W) based on fluid type and service
Design pressure and temperature for mechanical design
Allowable pressure drops for both sides

Engineering note: Fluid properties should be evaluated at the mean fluid temperature (average of inlet and outlet). For phase‑change services, properties at saturation conditions are required.

Step 2: Calculate Heat Duty

The heat duty calculation determines the thermal load the exchanger must handle. The correct equation depends on the service type:

For Sensible Heating or Cooling (no phase change):

Q = m × Cp × ΔT Q = Heat duty (W or kW) m = Mass flow rate (kg/s) Cp = Specific heat capacity (J/kg·°C) ΔT = Temperature change (°C)

For Phase Change (condensation or boiling):

Q = m × λ λ = Latent heat of vaporization/condensation (J/kg)

For Subcooling (combined condensation + sensible cooling):

Q_total = Q_condensation + Q_subcooling

For manual design, the engineer must identify the service type and apply the appropriate equation. For partial condensation services, the duty must be split into latent and sensible portions.

Step 3: Select Shell‑Side and Tube‑Side Fluids

Fluid allocation is a critical design decision that affects heat transfer, pressure drop, and mechanical design. Industry guidelines per Kern and TEMA recommend:

Tube side preferred for: high‑pressure fluids (tubes are stronger than shell), corrosive fluids (allows use of corrosion‑resistant alloys for tubes only), severely fouling fluids (easier mechanical cleaning), and high‑temperature fluids (reduces shell expansion issues).
Shell side preferred for: condensing vapors (larger flow area, lower pressure drop), viscous fluids (better heat transfer on shell side with baffles), and low‑pressure, high‑volume gas streams.

Step 4: Calculate LMTD (Log Mean Temperature Difference)

The LMTD calculation provides the effective temperature driving force for heat transfer. Because the temperature difference between hot and cold fluids varies along the exchanger length, a simple arithmetic average is inaccurate.

ΔT₁ = T_h,in - T_c,out (Hot end) ΔT₂ = T_h,out - T_c,in (Cold end) LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂)

For counter‑current flow, the LMTD is always greater than for co‑current (parallel) flow, making counter‑current arrangements more thermally efficient.

If ΔT₁ and ΔT₂ are nearly equal (ratio < 1.5), the arithmetic mean temperature difference is an acceptable approximation.

Step 5: Calculate the LMTD Correction Factor (Ft)

The Ft correction factor accounts for deviation from true counter‑current flow. In multi‑pass shell and tube exchangers, the flow pattern is not purely counter‑current. Ignoring Ft can significantly underestimate the required exchanger area.

TEMA recommendation: Ft should be ≥ 0.75. Values below 0.75 indicate poor thermal design, and values below 0.5 suggest the exchanger configuration is unsuitable and should be redesigned with multiple shells or different pass arrangements.

P = (T_c,out - T_c,in) / (T_h,in - T_c,in) R = (T_h,in - T_h,out) / (T_c,out - T_c,in) Ft = f(R, P, shell passes, tube passes) — per TEMA equations

THE CORRECT HEAT TRANSFER EQUATION for shell‑and‑tube exchangers is:

Q = U × A × Ft × LMTD
Q = Heat duty (W) | U = Overall heat transfer coefficient (W/m²·°C)
A = Heat transfer area (m²) | Ft = LMTD correction factor | LMTD = Log mean temperature difference (°C)

Warning: Simplified equations showing Q = U × A × ΔT_m without Ft are incomplete for shell‑and‑tube exchangers and should not be used for final design.

Step 6: Select and Calculate Tube‑Side Heat Transfer Coefficient (h_i)

The tube‑side heat transfer coefficient is calculated using correlations that depend on the flow regime (Reynolds number), fluid properties (Prandtl number), and application type. The appropriate correlation must be selected manually:

Laminar Flow (Re < 2300):

Hausen correlation (recommended for developing laminar flow):

Nu = 3.66 + [0.0668(Re)(Pr)(D/L)] / [1 + 0.04((Re)(Pr)(D/L))^(2/3)] Reference: Kern Process Heat Transfer | Valid: Re < 2300

Transitional Flow (2300 ≤ Re ≤ 10000):

Gnielinski correlation (recommended for transitional and turbulent flow):

Nu = [(f/8)(Re-1000)Pr] / [1 + 12.7(f/8)^0.5(Pr^(2/3)-1)] f = (0.79 ln(Re) - 1.64)^(-2) (friction factor) Reference: Perry's Chemical Engineers' Handbook | Valid: 2300 ≤ Re ≤ 5×10^6, 0.5 < Pr < 2000

Turbulent Flow (Re > 10000):

Dittus‑Boelter correlation:

Nu = 0.023 Re^0.8 Pr^n n = 0.4 for heating | n = 0.3 for cooling Reference: Kern Process Heat Transfer / McCabe Smith | Valid: Re > 10000, 0.6 < Pr < 160, L/D > 10

For Condensation Services:

Nusselt film condensation correlation — use this instead of Dittus‑Boelter for condensation applications.

h = 0.943 [(ρ_l(ρ_l-ρ_v)gλk³) / (μLΔT)]^(1/4) Reference: Kern Process Heat Transfer

For High Viscosity Fluids:

Sieder‑Tate correlation with viscosity correction:

Nu = 0.027 Re^0.8 Pr^(1/3) (μ/μ_w)^0.14 (μ/μ_w)^0.14 = Viscosity correction factor (ratio of bulk to wall viscosity) Reference: Kern Process Heat Transfer

Step 7: Select and Calculate Shell‑Side Heat Transfer Coefficient (h_o)

The shell‑side heat transfer coefficient is more complex due to the flow patterns created by baffles. Two methods are available:

Kern Method (Preliminary Design):

Nu = 0.36 Re^0.55 Pr^0.33 (Turbulent, Re > 100) Nu = 0.9 Re^0.4 Pr^0.36 (Laminar, Re < 100) Reference: Kern Process Heat Transfer (1950)

The Kern method uses bulk fluid properties and an equivalent diameter based on tube layout. It does not account for leakage and bypass streams, making it suitable for preliminary sizing.

Bell‑Delaware Method (Advanced Design):

The Bell‑Delaware method provides more accurate results by applying five correction factors to the ideal tube bank heat transfer coefficient:

Jc — Baffle cut and spacing correction factor
Jl — Tube‑to‑baffle and shell‑to‑baffle leakage correction
Jb — Bundle bypass stream correction (accounts for flow around the tube bundle)
Jr — Laminar flow correction (accounts for heat transfer reduction at low Re)
Js — Unequal baffle spacing correction (inlet/outlet regions)

The total correction factor (typically 0.5–0.8) is multiplied by the ideal heat transfer coefficient. Bell‑Delaware generally predicts lower h_o values than Kern but is more realistic for industrial design.

Step 8: Calculate Overall Heat Transfer Coefficient (U)

The overall heat transfer coefficient combines all thermal resistances in series. The correct equation referenced to the outside tube area is:

1/U_o = d_o/(d_ih_i) + R_fi(d_o/d_i) + d_o ln(d_o/d_i)/(2k_w) + R_fo + 1/h_o Where: d_o/(d_ih_i) = Tube‑side film resistance (outside basis) R_fi(d_o/d_i) = Tube‑side fouling resistance (outside basis) d_o ln(d_o/d_i)/(2k_w) = Tube wall resistance R_fo = Shell‑side fouling resistance 1/h_o = Shell‑side film resistance

Both U_clean (without fouling) and U_dirty (with fouling) should be evaluated. The fouling impact on overall U can be significant — typically 10‑30% of total resistance in clean services and up to 50% in fouling services.

Step 9: Calculate Required Heat Transfer Area

Using the correct heat transfer equation with Ft:

A_required = Q / (U_dirty × Ft × LMTD) A = Heat transfer area (m²)

The actual installed area is calculated from the tube count and geometry. The overdesign percentage provides margin for uncertainties:

Overdesign % = (A_installed - A_required) / A_required × 100

Industry practice typically targets 5‑20% overdesign for clean services and 10‑30% for fouling services. Overdesign above 40% may indicate an oversized exchanger.

Step 10: Select Tube Count, Diameter & Layout

Tube count is estimated from the required area and tube geometry. TEMA standards provide recommendations for:

Triangular pitch (30°): Most compact, highest heat transfer area per shell. Used for clean fluids on shell side.
Square pitch (90°): Allows mechanical cleaning of shell side. Used for fouling services.
Rotated square (45°): Compromise between compactness and cleanability.

Tube pitch ratio (pitch/tube OD) is typically 1.25 for triangular and 1.25‑1.5 for square layouts.

Step 11: Calculate Pressure Drop

Pressure drop calculations use the Darcy‑Weisbach equation with appropriate friction factors for each flow regime:

Tube‑Side Pressure Drop:

ΔP_total = ΔP_friction + ΔP_return + ΔP_{entrance/exit} ΔP_friction = 4fL N_p ρv² / (2 d_i) ΔP_return = 4 N_p ρv² / 2 (Darcy‑Weisbach based method, Reference: Kern)

Shell‑Side Pressure Drop:

Kern method or Bell‑Delaware corrected pressure drop, accounting for cross‑flow, window, and leakage losses.

Step 12: Engineering Validation & Final Design Review

The final step validates the design against industry criteria:

Velocity checks: Tube velocity should be 1‑2.5 m/s for water, 0.8‑1.5 m/s for hydrocarbons. Shell velocity typically 0.3‑1.0 m/s.
Ft ≥ 0.75: Per TEMA recommendation for efficient thermal design.
Pressure drop within allowable limits: Set by process requirements.
Overdesign 5‑40%: Provides margin while avoiding excessive oversizing.
Tube vibration check: Unsupported tube span should meet TEMA limits.

Industrial Design Guideline Tables

Recommended ranges based on TEMA standards, Kern Process Heat Transfer, and Perry's Chemical Engineers' Handbook.

Typical Velocity Ranges

Fluid Type	Tube‑Side Velocity (m/s)	Shell‑Side Velocity (m/s)
Water / Aqueous Solutions	1.0 – 2.5	0.3 – 1.0
Light Hydrocarbons	0.8 – 1.5	0.3 – 0.8
Heavy Oils / Viscous Fluids	0.3 – 0.8	0.2 – 0.5
Gases (at pressure)	5 – 15	2 – 8
Condensing Steam	—	0.5 – 2.0 (inlet)

Typical Overall U Ranges

Service	U Range (W/m²·°C)
Water – Water	800 – 1500
Water – Oil	250 – 500
Water – Gas	50 – 200
Steam – Water (Condenser)	1000 – 3000
Steam – Oil	200 – 600
Oil – Oil	100 – 300
Gas – Gas	20 – 80

Typical Fouling Resistances

Fluid	Fouling Resistance (m²·°C/W)
Clean Water (treated)	0.0001 – 0.0002
Cooling Tower Water	0.0002 – 0.0004
Light Hydrocarbons	0.0002 – 0.0004
Heavy Fuel Oil	0.0005 – 0.001
Crude Oil	0.0005 – 0.005
Steam (clean)	0.00005 – 0.0001

Baffle & Layout Recommendations

Parameter	Recommended Range
Baffle Cut	20 – 35% of shell diameter
Baffle Spacing	0.2 – 1.0 x Shell ID (min 50 mm)
Tube Pitch Ratio	1.25 – 1.5 x Tube OD
Tube Passes	1, 2, 4, or 6 (even numbers)
Maximum Unsupported Tube Span	Per TEMA Table RCB‑4.52

Kern Method vs Bell‑Delaware Method — Comparison

Feature	Kern Method	Bell‑Delaware Method
Complexity	Simple, hand‑calculation friendly	Complex, requires computer
Accuracy	Moderate (±30% for h_o)	Good (±15% for h_o)
Leakage streams	Not accounted for	Accounted for (Jl factor)
Bypass streams	Not accounted for	Accounted for (Jb factor)
Baffle cut effect	Simplified	Detailed (Jc factor)
Best use case	Preliminary sizing, education	Final design, detailed engineering
Reference	Kern (1950)	Delaware Project / Perry's Handbook

NTU‑Effectiveness Method

The NTU‑Effectiveness method is an alternative to the LMTD method, particularly useful when outlet temperatures are unknown. It is based on the heat exchanger effectiveness (ε), which is the ratio of actual heat transfer to the maximum possible heat transfer.

NTU = U × A / C_min ε = Q / Q_max C_r = C_min / C_max (Heat capacity ratio) For counter‑flow: ε = [1 - exp(-NTU(1-C_r))] / [1 - C_r exp(-NTU(1-C_r))] For parallel flow: ε = [1 - exp(-NTU(1+C_r))] / [1 + C_r] Reference: Incropera / Perry's Handbook

The NTU method is widely used in heat exchanger simulation and rating programs. When both outlet temperatures are unknown, an iterative solution may be required.

Frequently Asked Questions — Shell & Tube Heat Exchanger Design

What is LMTD in heat exchanger design?

LMTD (Log Mean Temperature Difference) is the effective temperature driving force for heat transfer in a heat exchanger. It accounts for the fact that the temperature difference between hot and cold fluids varies along the exchanger length. The formula is LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂), where ΔT₁ and ΔT₂ are the terminal temperature differences.

What is the Ft correction factor?

Ft is the LMTD correction factor that accounts for deviation from true counter‑current flow in multi‑pass shell and tube exchangers. Ft is always ≤ 1.0. TEMA recommends Ft ≥ 0.75 for efficient design. Values below 0.5 indicate the configuration is unsuitable and should be redesigned.

What is a good overall heat transfer coefficient?

Typical U values depend on the service: Water‑Water: 800‑1500 W/m²·°C, Water‑Oil: 250‑500 W/m²·°C, Steam‑Water condenser: 1000‑3000 W/m²·°C, Gas‑Gas: 20‑80 W/m²·°C. Both clean and dirty U values should be considered, with a resistance breakdown to identify the dominant term.

What is the Bell‑Delaware method?

The Bell‑Delaware method is an advanced shell‑side heat transfer and pressure drop calculation method that accounts for leakage and bypass streams using five correction factors: Jc (baffle cut), Jl (leakage), Jb (bundle bypass), Jr (laminar), and Js (unequal spacing). It is more accurate than the Kern method for final design.

Why is Reynolds number important in heat exchanger design?

Reynolds number determines the flow regime (laminar: Re < 2300, transitional: 2300‑10000, turbulent: Re > 10000). Turbulent flow provides significantly better heat transfer than laminar flow. The appropriate heat transfer correlation must be selected based on the Reynolds number.

What is fouling factor in heat exchangers?

Fouling factor (R_f) accounts for the additional thermal resistance caused by deposit formation on heat transfer surfaces. Typical values range from 0.0001 m²·°C/W for clean fluids to 0.005 m²·°C/W for heavy crude oil. Fouling can account for 10‑50% of total thermal resistance.

Design Disclaimer: The design methodology described in this guide is for educational and preliminary design purposes. Final industrial design should be verified using specialized software such as HTRI Xchanger Suite, Aspen EDR, or equivalent, with full compliance with ASME Section VIII, TEMA standards, and project‑specific specifications. Correlations have known limitations, particularly near critical conditions, for highly viscous fluids, or multi‑component phase change. Always consult a qualified process engineer for final design verification.

Engineering References & Methodology

Primary Design References:

Process Heat Transfer — D.Q. Kern (1950)
Perry's Chemical Engineers' Handbook, 9th Edition, Section 11
Unit Operations of Chemical Engineering — McCabe, Smith, Harriott (7th Ed.)
TEMA Standards, 10th Edition, Sections 5‑7

Supplementary References:

API 660 — Shell‑and‑Tube Heat Exchangers, 9th Ed.
ASME Boiler & Pressure Vessel Code, Section VIII, Div. 1 (UHX)
Heat Exchanger Design Handbook — Kuppan (2000)
Bell‑Delaware Method — Delaware Project, Univ. of Delaware
Fundamentals of Heat and Mass Transfer — Incropera & DeWitt