Heat Transfer

Heat Exchanger Design

Calculate LMTD, thermal effectiveness, and required surface area for shell-and-tube, plate, and air-cooled exchangers per TEMA and API 660.

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Overall U typical

50–500 BTU/hr·ft²·°F

Depends on fluids and fouling; water-water ~150, oil-oil ~50.

LMTD correction

F ≥ 0.75 required

Multi-pass shells reduce effective ΔT; F < 0.75 indicates temperature cross.

TEMA standards

Class R, C, B

R = refinery (severe), C = commercial, B = chemical (light duty).

Contents

Use this guide when you need to:

  • Calculate required heat transfer area
  • Determine LMTD and apply F correction
  • Select exchanger type and configuration
  • Specify shell-tube geometry per TEMA

1. Heat Transfer Fundamentals

Heat exchangers transfer thermal energy between fluids at different temperatures. The heat transfer rate depends on three mechanisms acting in series:

Conduction

Through walls

Heat flows through tube walls separating hot and cold fluids.

Convection

Film coefficients

Hot-side hh and cold-side hc control fluid-to-wall transfer.

Fouling

Resistance buildup

Deposits reduce U over time; design includes fouling margins per TEMA.

Cross-section diagram showing thermal resistances in series through a heat exchanger tube: hot bulk fluid at 300°F, hot film resistance, hot fouling layer, tube wall, cold fouling layer, cold film resistance, and cold bulk fluid at 100°F, with temperature profile and overall U equation
Thermal resistances in series from hot fluid to cold fluid through tube wall, showing the temperature profile and heat transfer equation.

Fundamental Heat Transfer Equation

Heat Duty: Q = U × A × ΔTm Where: Q = Heat duty (BTU/hr) U = Overall heat transfer coefficient (BTU/hr·ft²·°F) A = Heat transfer area (ft²) ΔTm = Mean temperature difference (°F)

Overall Heat Transfer Coefficient (U)

U combines all resistances in series—hot-side film, tube wall, cold-side film, and fouling:

Overall U: 1/U = 1/hh + Rf,h + twall/kwall + Rf,c + 1/hc Where: hh, hc = Film coefficients (BTU/hr·ft²·°F) Rf,h, Rf,c = Fouling resistances (hr·ft²·°F/BTU) twall = Wall thickness (ft) kwall = Wall thermal conductivity (BTU/hr·ft·°F)

Typical Overall U Values

Service U Clean U Design
Water to water200–250150–200
Water to light oil80–12060–90
Light oil to light oil60–9040–60
Heavy oil to heavy oil30–5020–35
Gas to gas (no fins)10–308–25
Condensing steam to water400–600300–500

Units: BTU/hr·ft²·°F. Design U includes fouling allowance per TEMA.

Design margin: Always include fouling factors. Clean U can be 20–50% higher than design U. TEMA provides standard fouling resistances for various fluids.

2. Log Mean Temperature Difference (LMTD)

LMTD represents the effective temperature driving force when terminal temperatures vary along the exchanger length. It accounts for the logarithmic temperature profile in heat exchangers.

Side-by-side temperature profile graphs comparing counterflow (most efficient, highest average ΔT) and parallel flow (less efficient, ΔT decreases along length) heat exchangers, showing hot and cold fluid temperature curves with ΔT annotations and LMTD comparison
Temperature profiles for counterflow vs parallel flow configurations showing why counterflow achieves higher LMTD.

Counterflow Configuration

Most efficient arrangement—hot fluid enters where cold fluid exits, maximizing ΔT at both ends.

LMTD for Counterflow: LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂) Where: ΔT₁ = Th,in - Tc,out (hot end) ΔT₂ = Th,out - Tc,in (cold end) If ΔT₁ ≈ ΔT₂: use arithmetic mean LMTD ≈ (ΔT₁ + ΔT₂)/2

LMTD Correction Factor (F)

For shell-and-tube exchangers with multiple passes, actual mean ΔT is lower than pure counterflow. The F factor corrects for this:

Corrected Mean Temperature Difference: ΔTm = F × LMTDcounterflow F depends on: - Shell/tube pass configuration (1-2, 2-4, etc.) - Thermal effectiveness P = (Tc,out - Tc,in) / (Th,in - Tc,in) - Heat capacity ratio R = (Th,in - Th,out) / (Tc,out - Tc,in)
LMTD correction factor F chart for 1-2 shell and tube heat exchanger showing F vs thermal effectiveness P for R values from 0.2 to 2.0, with minimum F=0.75 design limit line and shaded temperature cross avoidance region
TEMA F correction factor chart for 1-2 shell and tube configuration. Avoid designs with F < 0.75.

F Factor Guidelines

Configuration F Range Comments
True counterflow1.0Maximum effectiveness
1-2 shell & tube0.75–0.95Most common; avoid F < 0.75
2-4 shell & tube0.85–0.98Higher F but more expensive
Crossflow (air-cooled)0.70–0.90Lower due to flow pattern
Design rule: Target F ≥ 0.75. If F < 0.75, add shell passes or switch to true counterflow. Low F indicates temperature cross (cold outlet too close to hot inlet).

Example Calculation

Given: Hot oil: 250°F in → 150°F out Cold water: 80°F in → 180°F out Configuration: 1-2 shell & tube Step 1: Calculate ΔT values (counterflow basis) ΔT₁ = 250 - 180 = 70°F ΔT₂ = 150 - 80 = 70°F Step 2: Calculate LMTD Since ΔT₁ = ΔT₂: LMTD = 70°F (arithmetic mean) Step 3: Calculate P and R P = (180 - 80)/(250 - 80) = 0.588 R = (250 - 150)/(180 - 80) = 1.0 Step 4: Find F from TEMA chart For 1-2 exchanger with P=0.588, R=1.0: F ≈ 0.88 Step 5: Corrected ΔTm ΔTm = 0.88 × 70 = 61.6°F

3. Effectiveness-NTU Method

Alternative to LMTD when outlet temperatures are unknown. Essential for rating existing exchangers or iterative design optimization.

Thermal Effectiveness (ε)

Effectiveness Definition: ε = Qactual / Qmax Where: Qmax = Cmin × (Th,in - Tc,in) Cmin = minimum of (ṁ × Cp)hot or (ṁ × Cp)cold ε ranges from 0 to 1.0 (theoretical maximum)

Number of Transfer Units (NTU)

NTU Definition: NTU = U × A / Cmin NTU represents exchanger "size": - Higher NTU → larger area → higher effectiveness - Typical range: 0.5 to 5 - NTU > 4: diminishing returns on area

Heat Capacity Ratio (C*)

C* Definition: C* = Cmin / Cmax C* ranges from 0 to 1.0: - C* = 0: One fluid has phase change (condenser/reboiler) - C* = 1: Balanced exchanger (equal heat capacities)
Effectiveness-NTU chart for counterflow heat exchanger showing effectiveness vs NTU curves for C* values of 0, 0.25, 0.5, 0.75, and 1.0, with annotation showing 63% effectiveness at NTU=1 and diminishing returns beyond NTU≈3
Effectiveness-NTU relationship for counterflow configuration. Higher NTU yields diminishing returns beyond NTU ≈ 3.

Effectiveness Correlations

Counterflow

If C* < 1: ε = [1 - exp(-NTU(1-C*))] / [1 - C*·exp(-NTU(1-C*))] If C* = 1: ε = NTU / (1 + NTU)

Parallel Flow

ε = [1 - exp(-NTU(1+C*))] / (1 + C*)

Phase Change (C* = 0)

ε = 1 - exp(-NTU)

When to Use Each Method

Situation Method Reason
All 4 temperatures knownLMTDSimpler calculation
Outlet temps unknownε-NTUDirect solution
Rating existing exchangerε-NTUGiven area, find outlets
Phase change processε-NTUC* = 0 simplifies equations
LMTD vs ε-NTU: LMTD is simpler for sizing (all temps known). ε-NTU is better for rating (given area, find performance) or when outlet temps vary during optimization.

4. Shell-and-Tube Design

Shell-and-tube exchangers are the workhorse of process industries—robust, repairable, and scalable to very large duties.

Detailed cutaway diagram of 1-2 shell and tube heat exchanger showing shell side hot fluid flow, tube side cold fluid flow, segmental baffles, front channel Type A, floating head Type S, tubesheets, impingement plate, tie rods, support saddles, and triangular tube pitch pattern
Shell-and-tube heat exchanger cutaway showing 1-2 configuration with all major components labeled.

TEMA Nomenclature

Exchangers are designated by three letters: Front Head - Shell Type - Rear Head

Position Code Description
Front HeadAChannel with removable cover
BBonnet (integral cover)
NChannel with removable cover & tubesheet
Shell TypeEOne-pass shell (most common)
FTwo-pass shell (longitudinal baffle)
JDivided flow
XCrossflow
Rear HeadL, M, NFixed tubesheet types
S, TFloating head types
UU-tube bundle

Example: AES = Channel with removable cover, one-pass shell, floating head (most common for refinery service).

Three-panel comparison of TEMA heat exchanger configurations: BEM fixed tubesheet (lowest cost, limited thermal expansion), BEU U-tube bundle (handles expansion, one tubesheet), and AES floating head (handles expansion, fully cleanable, most expensive), with pros, cons, and applications for each
Common TEMA configurations showing fixed tubesheet, U-tube, and floating head designs with selection criteria.

Key Design Parameters

Parameter Typical Values Notes
Tube OD¾" or 1"¾" most common; 1" for fouling
Tube wallBWG 12, 14, 16Thicker for high P or corrosion
Tube length8, 12, 16, 20 ftLonger = more area, harder to clean
Pitch1.25 × ODTriangular for high h; square for cleaning
Baffle spacing0.2–1.0 × shell IDCloser = higher h, higher ΔP
Baffle cut20–35% of shell ID25% typical; affects flow pattern

Fluid Allocation Guidelines

Tube Side

Place here:

Corrosive fluids (alloy tubes cheaper), high-pressure fluids, fouling fluids (easier to clean), cooling water.

Shell Side

Place here:

Low-pressure fluids, viscous fluids (need turbulence), condensing vapors, fluids needing large flow area.

TEMA Mechanical Design Classes

Class Application Features
RRefinery / SevereHeaviest construction; high T/P; full ASME VIII Div 1
CCommercial / ModerateGeneral process; lower cost than R
BChemical / LightLeast severe; lowest cost; often fixed tubesheet
Material selection: Carbon steel for clean services. Stainless 304/316 for corrosion. Titanium or high alloys for severe corrosion (sour gas, chlorides). Shell material must resist shell-side fluid.

5. Exchanger Types & Selection

Shell-and-Tube

Advantages

Proven workhorse

Handles high P/T, large duties, mechanically cleanable, repairable.

Disadvantages

Large footprint

Bulky, heavy, higher cost per ft² than plate types.

Best for

Refinery / gas plants

High P (>300 psi), high T (>400°F), large Q (>10 MMBtu/hr).

Plate Heat Exchangers

Advantages

Compact, high U

U = 800–2000; 3–5× more compact; easy to expand capacity.

Disadvantages

Limited P/T, fouling

Max ~300 psi, 350°F; gaskets; narrow channels foul easily.

Best for

Clean liquid services

HVAC, food/pharma, moderate P/T, tight space.

Air-Cooled Exchangers (Fin-Fan)

Advantages

No cooling water

Eliminates cooling tower, water treatment, blowdown.

Disadvantages

Weather dependent

Cannot cool below ambient + 15–20°F; large footprint.

Best for

Remote / arid sites

No water available; compressor aftercoolers; overhead condensers.

Selection Criteria Summary

Application Recommended Type Reason
Gas-gasShell-tube (finned) or plate-finLow h requires extended surface
Gas-liquidShell-tube or air-cooledShell-tube for high P
Liquid-liquid (clean)Plate or shell-tubePlate if P/T permit
Liquid-liquid (fouling)Shell-tube (square pitch)Mechanical cleaning access
High pressure (>500 psi)Shell-tube or double-pipeThick-wall tubes cheaper than plates
Phase change (condensing)Shell-tube (vapor shell side)Large flow area; gravity drainage
Remote / no waterAir-cooledEliminates water infrastructure

Fouling Mitigation

  • Design velocity: Tube-side ≥ 3 ft/s for liquids to minimize deposits
  • Square pitch: Allows mechanical cleaning between tubes
  • Removable bundle: TEMA types with pullable bundles (AES, BEU)
  • Oversurface: Add 10–20% excess area to maintain duty as fouling builds
Cost comparison: Plate exchangers have lowest $/ft² but limited P/T. Shell-tube handles extreme conditions but costs more. Air-cooled has highest capital but lowest operating cost when water is scarce.

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