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Cheatsheet: Heat Exchangers
1. Heat Exchanger Types and Configurations
1.1 Classification by Construction
| Type | Description |
|---|---|
| Double-Pipe | One pipe inside another; simplest configuration; used for small capacity applications |
| Shell-and-Tube | Tubes inside a cylindrical shell; most common industrial type; one fluid in tubes, other in shell |
| Plate | Corrugated plates stacked with gaskets; compact design; high heat transfer coefficients |
| Plate-and-Frame | Gasketed plates in frame; easy to clean and expand |
| Plate-Fin | Fins between plates; used in cryogenic and aerospace applications |
| Spiral | Two concentric spiral channels; self-cleaning for fouling fluids |
| Air-Cooled (Finned-Tube) | Tubes with external fins; air as cooling medium; used where water is scarce |
1.2 Flow Arrangements
| Arrangement | Characteristics |
|---|---|
| Parallel Flow | Both fluids enter same end; outlet temperature of cold fluid cannot exceed hot fluid outlet; lower effectiveness |
| Counterflow | Fluids enter opposite ends; most efficient; cold fluid outlet can exceed hot fluid outlet; maximum ΔT utilization |
| Crossflow | Fluids flow perpendicular; both fluids unmixed, one mixed/one unmixed, or both mixed configurations |
| Multi-Pass | Shell-and-tube with multiple tube passes; improves heat transfer; designated as 1-2, 2-4, etc. (shell passes-tube passes) |
1.3 Shell-and-Tube Components
- TEMA Designations: Three-letter code (Front End-Shell Type-Rear End)
- Baffles: Direct shell-side flow across tubes; segmental (25-35% cut) most common; spacing: 0.2-1.0 × shell diameter
- Tube Arrangement: Square pitch (90°) for easy cleaning; triangular pitch (30° or 60°) for higher heat transfer
- Tube Sheets: Support tubes at shell ends; tubes can be welded, roller-expanded, or both
- Expansion Joint: Accommodates differential thermal expansion between shell and tubes
2. Heat Transfer Analysis Methods
2.1 Overall Heat Transfer Equation
| Equation | Variables |
|---|---|
| Q = UA ΔTlm | Q = heat transfer rate (W or Btu/hr); U = overall heat transfer coefficient (W/m²·K or Btu/hr·ft²·°F); A = heat transfer area (m² or ft²); ΔTlm = log mean temperature difference |
| Q = ṁh cp,h (Th,in - Th,out) | ṁ = mass flow rate; cp = specific heat; T = temperature; subscript h = hot fluid |
| Q = ṁc cp,c (Tc,out - Tc,in) | subscript c = cold fluid |
2.2 Log Mean Temperature Difference (LMTD)
| Configuration | Formula |
|---|---|
| Counterflow & Parallel Flow | ΔTlm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2) |
| Counterflow | ΔT1 = Th,in - Tc,out; ΔT2 = Th,out - Tc,in |
| Parallel Flow | ΔT1 = Th,in - Tc,in; ΔT2 = Th,out - Tc,out |
| Other Configurations | ΔTm = F × ΔTlm,cf where F = correction factor, ΔTlm,cf = counterflow LMTD |
2.2.1 LMTD Correction Factor
- F Factor: Accounts for deviation from pure counterflow; obtained from charts based on P and R
- P Parameter: P = (Tc,out - Tc,in) / (Th,in - Tc,in) (temperature effectiveness)
- R Parameter: R = (Th,in - Th,out) / (Tc,out - Tc,in) = (ṁcp)c / (ṁcp)h (heat capacity rate ratio)
- Design Criterion: F ≥ 0.75 for acceptable design; F < 0.75="" requires="">
2.3 Effectiveness-NTU Method
| Parameter | Definition |
|---|---|
| Effectiveness (ε) | ε = Qactual / Qmax = (actual heat transfer) / (maximum possible heat transfer) |
| Qmax | Qmax = Cmin (Th,in - Tc,in) where Cmin = smaller of (ṁcp)h or (ṁcp)c |
| NTU | NTU = UA / Cmin (Number of Transfer Units) |
| Capacity Ratio (Cr) | Cr = Cmin / Cmax where 0 ≤ Cr ≤ 1 |
2.3.1 Effectiveness Relations
| Configuration | Effectiveness Formula |
|---|---|
| Parallel Flow | ε = [1 - exp(-NTU(1 + Cr))] / (1 + Cr) |
| Counterflow | ε = [1 - exp(-NTU(1 - Cr))] / [1 - Cr exp(-NTU(1 - Cr))] for Cr < 1;="" ε="NTU" (1="" +="" ntu)="" for="">r = 1 |
| Condenser/Evaporator (Cr = 0) | ε = 1 - exp(-NTU) |
| Shell-and-Tube (1-2 TEMA E) | ε = 2{1 + Cr + (1 + Cr²)0.5 × [(1 + exp(-NTU(1 + Cr²)0.5)) / (1 - exp(-NTU(1 + Cr²)0.5))]}-1 |
2.4 Overall Heat Transfer Coefficient
| Equation | Description |
|---|---|
| 1/U = 1/hi + Rf,i + Rwall + Rf,o + 1/ho | Total thermal resistance; h = convection coefficient; Rf = fouling resistance; Rwall = wall conduction resistance |
| Rwall = t/k (flat) | t = wall thickness; k = thermal conductivity |
| Rwall = ln(ro/ri)/(2πLk) (cylindrical) | ro, ri = outer and inner radii; L = length |
| 1/(UA) = 1/(hiAi) + Rf,i/Ai + Rwall + Rf,o/Ao + 1/(hoAo) | For tubes with different inside/outside areas |
2.4.1 Fouling Resistances
- Definition: Additional thermal resistance from deposits on heat transfer surfaces
- Units: m²·K/W or hr·ft²·°F/Btu
- Distilled Water: Rf = 0.0001 m²·K/W
- Seawater: Rf = 0.0001-0.0002 m²·K/W
- Treated Cooling Water: Rf = 0.0002 m²·K/W
- River Water: Rf = 0.0002-0.0004 m²·K/W
- Fuel Oil: Rf = 0.0009 m²·K/W
- Steam (non-oil bearing): Rf = 0.00009 m²·K/W
- Design Practice: Include fouling factors in U calculation; increases required area
3. Heat Transfer Coefficients and Correlations
3.1 Dimensionless Numbers
| Number | Formula |
|---|---|
| Reynolds (Re) | Re = ρVD/μ = VD/ν where ρ = density, V = velocity, D = characteristic length, μ = dynamic viscosity, ν = kinematic viscosity |
| Prandtl (Pr) | Pr = cpμ/k = ν/α where α = thermal diffusivity = k/(ρcp) |
| Nusselt (Nu) | Nu = hD/k where h = convection coefficient, k = fluid thermal conductivity |
| Grashof (Gr) | Gr = gβΔTL³/ν² where g = gravity, β = thermal expansion coefficient, L = characteristic length |
| Rayleigh (Ra) | Ra = Gr × Pr |
3.2 Internal Flow Correlations (Tube Side)
3.2.1 Turbulent Flow in Tubes (Re > 10,000)
- Dittus-Boelter: Nu = 0.023 Re0.8 Prn where n = 0.4 (heating fluid), n = 0.3 (cooling fluid); valid for 0.7 ≤ Pr ≤ 160, L/D ≥ 10
- Sieder-Tate: Nu = 0.027 Re0.8 Pr1/3 (μ/μw)0.14 where μw = viscosity at wall temperature; valid for 0.7 ≤ Pr ≤ 16,700
- Gnielinski: Nu = [(f/8)(Re-1000)Pr] / [1 + 12.7(f/8)0.5(Pr2/3-1)] where f = friction factor; valid for 3000 ≤ Re ≤ 5×10⁶, 0.5 ≤ Pr ≤ 2000
- Friction Factor (smooth tubes): f = (0.79 ln Re - 1.64)-2 (Petukhov)
3.2.2 Laminar Flow in Tubes (Re <>
- Fully Developed, Constant Surface Temperature: Nu = 3.66
- Fully Developed, Constant Heat Flux: Nu = 4.36
- Developing Flow: Nu = 1.86 (Re Pr D/L)1/3 (μ/μw)0.14 for thermal entrance region
3.3 External Flow Correlations (Shell Side)
3.3.1 Flow Across Tube Banks
- Zukauskas Correlation: NuD = C ReD,maxm Pr0.36 (Pr/Prs)1/4 where subscript s = surface temperature
- ReD,max: Based on maximum velocity through minimum flow area
- Constants: C and m depend on Re and tube arrangement (staggered vs. inline)
- Inline Arrangement: Re < 100:="" c="0.9," m="0.4;" 100-1000:="" c="0.52," m="0.5;" 1000-200,000:="" c="0.27," m="0.63;">200,000: C=0.033, m=0.8
- Correction for Tube Rows: Apply row correction factor for NL < 20="">
3.3.2 Shell-Side Correlations
- Delaware Method: Accounts for baffle leakage and bypass streams; h = hideal × Jc × Jl × Jb × Js × Jr where J = correction factors
- Bell-Delaware Method: More detailed; considers baffle geometry, clearances, and bypass effects
- Kern Method: Simplified approach; h = (jH × cp × G × Pr-2/3) where G = mass velocity, jH = Colburn j-factor
3.4 Condensation and Boiling
3.4.1 Film Condensation (Vertical Surface)
- Nusselt Theory: h = 0.943 [ρL(ρL-ρv)ghfgkL³ / (μLΔTL)]1/4 where hfg = latent heat, subscripts L,v = liquid, vapor
- Horizontal Tube: h = 0.729 [ρL(ρL-ρv)ghfgkL³ / (μLΔTD)]1/4 where D = tube diameter
- Modified Latent Heat: hfg' = hfg + 0.68 cp,L ΔT for improved accuracy
3.4.2 Pool Boiling
- Rohsenow Correlation: q/A = μL hfg [g(ρL-ρv)/σ]1/2 [(cp,LΔT) / (Csf hfg PrLn)]3 where σ = surface tension, Csf = surface-fluid constant
- Critical Heat Flux (CHF): qmax/A = 0.149 hfg ρv1/2 [σg(ρL-ρv)]1/4 (Zuber correlation)
4. Pressure Drop Analysis
4.1 Tube-Side Pressure Drop
| Component | Formula |
|---|---|
| Friction Loss | ΔPf = f (L/D) (ρV²/2) where f = Darcy friction factor, L = tube length, D = diameter, ρ = density, V = velocity |
| Return Loss | ΔPreturn = 4N (ρV²/2) where N = number of tube passes |
| Total Tube-Side | ΔPtotal = Np ΔPf + ΔPreturn where Np = number of passes |
4.1.1 Friction Factor Correlations
- Laminar (Re <> f = 64/Re
- Turbulent (Smooth Tubes): f = (0.79 ln Re - 1.64)-2 (Petukhov) or 1/√f = -2.0 log(ε/D/3.7 + 2.51/(Re√f)) (Colebrook)
- Turbulent (Rough Tubes): Use Moody chart or Colebrook equation with relative roughness ε/D
- Approximate: f ≈ 0.316 Re-0.25 for Re < 20,000="">
4.2 Shell-Side Pressure Drop
| Method | Description |
|---|---|
| Kern Method | ΔPs = f (Gs²/2ρ) (Ds/de) (L/lB) where Gs = mass velocity, Ds = shell diameter, de = equivalent diameter, lB = baffle spacing |
| Delaware Method | Accounts for bypass, leakage, and entrance/exit losses; ΔP = ΔPideal × Rb × Rl × Rs where R = correction factors |
4.2.1 Shell-Side Equivalent Diameter
- Square Pitch: de = (4 × flow area) / wetted perimeter = (4 × [PT² - πdo²/4]) / (πdo) where PT = tube pitch, do = outer diameter
- Triangular Pitch: de = (4 × [0.43PT² - πdo²/8]) / (πdo/2)
- Simplification (Square): de = 1.27(PT² - 0.785do²) / do
- Simplification (Triangular): de = 1.10(PT² - 0.917do²) / do
4.3 Design Pressure Drop Limits
- Liquids: 50-100 kPa (7-15 psi) for process fluids
- Gases: 10% of inlet pressure or 35 kPa (5 psi) maximum
- Steam: 10-20 kPa (1.5-3 psi)
- Boiling/Condensing: Minimize to avoid temperature change
5. Design Considerations and Selection
5.1 Tube Specifications
| Parameter | Standard Values |
|---|---|
| Tube OD | 3/4 in (19.05 mm) and 1 in (25.4 mm) most common; also 1/2 in, 5/8 in, 1-1/4 in, 1-1/2 in, 2 in |
| Tube Length | 8, 12, 16, 20 ft (2.4, 3.7, 4.9, 6.1 m); 20 ft common upper limit for standard design |
| Tube Pitch | 1.25 × OD (square pitch, cleaning lanes); 1.25-1.5 × OD (triangular pitch, maximum density) |
| Wall Thickness (BWG) | BWG 12, 14, 16, 18 common; BWG 14 (0.083 in, 2.11 mm) for 3/4 in tube standard |
5.2 Material Selection
| Material | Applications |
|---|---|
| Carbon Steel | Non-corrosive service; steam, water (treated), hydrocarbons; lowest cost |
| Stainless Steel (304, 316) | Corrosive fluids; food processing; high temperature; moderate cost |
| Copper/Brass/Admiralty | Seawater (admiralty with arsenic inhibitor); HVAC; good thermal conductivity |
| Titanium | Highly corrosive (chlorides, acids); seawater; long life; high cost |
| Nickel Alloys (Monel, Inconel) | Severe corrosion; high temperature; alkalis and acids |
| Aluminum | Cryogenic service; air separation; low density |
5.3 Fluid Allocation Guidelines
| Consideration | Tube Side |
|---|---|
| Corrosive Fluid | Tube side (less material needed) |
| Fouling Fluid | Tube side (easier to clean) |
| High Pressure | Tube side (tubes withstand pressure better than shell) |
| Low Flow Rate | Tube side (achieve turbulence easier) |
| Toxic/Hazardous | Tube side (reduced leak potential) |
| Viscous Fluid | Shell side (larger flow area) |
| Condensing Vapor | Shell side (easier vapor distribution) or horizontal tube bundle |
5.4 Performance Degradation Factors
- Fouling: Reduces U over time; clean periodically when U drops 20-30%
- Scaling: Hard water deposits; use water treatment or periodic acid cleaning
- Corrosion: Material loss; increases pressure drop; requires material selection and inhibitors
- Erosion: High velocity damage; limit tube-side velocity to 2-3 m/s for liquids, 15-20 m/s for gases
- Flow Maldistribution: Uneven flow across tubes; use proper baffling and inlet nozzles
5.5 Design Margins and Safety Factors
- Surface Area: Add 10-20% overdesign for fouling and uncertainty
- Pressure Rating: Design pressure = 1.1 × maximum operating pressure or operating + 25 psi minimum
- Temperature Rating: Design temperature = maximum operating + 15-25°C
- U Value Estimation: Use conservative values from literature for preliminary sizing
6. Operating Parameters and Limits
6.1 Velocity Limits
| Fluid Type | Recommended Velocity |
|---|---|
| Water (Tube Side) | 1-3 m/s (3-10 ft/s); 2 m/s optimal |
| Water (Shell Side) | 0.3-1 m/s (1-3 ft/s) |
| Steam | 20-50 m/s (65-165 ft/s) |
| Light Hydrocarbons | 1-2 m/s (3-7 ft/s) |
| Heavy Oils | 0.3-1 m/s (1-3 ft/s) |
| Gases (Atmospheric) | 10-30 m/s (30-100 ft/s) |
6.2 Temperature Approach and Cross
- Minimum Approach (Counterflow): 3-5°C (5-10°F) for economic design; smaller requires excessive area
- Temperature Cross: Occurs when Tc,out > Th,out; impossible in single-pass parallel flow
- LMTD Validity: ΔT1 and ΔT2 must be same sign; if not, use multiple zones
- Pinch Point: Location of minimum ΔT; often at phase change transitions
6.3 Typical Overall Heat Transfer Coefficients
| Service | U (W/m²·K) |
|---|---|
| Water-Water | 800-1500 |
| Water-Oil | 100-350 |
| Water-Gasoline | 300-600 |
| Steam-Water | 1500-4000 |
| Steam-Oil | 200-500 |
| Steam-Condensate | 1000-1500 |
| Gas-Gas | 10-50 |
| Gas-Liquid | 10-300 |
| Condensing Vapor-Water | 800-1500 |
| Boiling Water (Steam) | 2500-8500 |
6.4 Maintenance and Inspection
- Cleaning Methods: Chemical cleaning (acid/alkali), mechanical (brushes, water jets), online (backflushing)
- Inspection Frequency: Annually or when performance drops 20%; more frequent for fouling service
- Tube Plugging: Maximum 10% of tubes can be plugged before replacement required
- Leak Testing: Hydrostatic test at 1.5 × design pressure; pneumatic test for tube-to-tubesheet joints
- NDT Methods: Eddy current testing for tube wall thickness; ultrasonic for shell thickness
7. Design Procedure Summary
7.1 LMTD Method Design Steps
- Determine heat duty: Q = ṁcpΔT for each stream; verify energy balance
- Calculate outlet temperatures from energy balance if unknown
- Select flow arrangement (counterflow preferred for efficiency)
- Calculate LMTD for counterflow: ΔTlm,cf
- Determine correction factor F from charts using P and R parameters
- Calculate corrected LMTD: ΔTm = F × ΔTlm,cf
- Estimate overall heat transfer coefficient U from tables
- Calculate required area: A = Q / (U × ΔTm)
- Select tube size, length, pitch, and number; calculate actual area
- Verify pressure drops are acceptable; iterate if needed
- Refine U calculation using correlations; recalculate area
- Apply design margins (10-20% overdesign)
7.2 Effectiveness-NTU Method Design Steps
- Calculate heat capacity rates: Ch = (ṁcp)h and Cc = (ṁcp)c
- Identify Cmin and Cmax; calculate Cr = Cmin / Cmax
- Calculate Qmax = Cmin (Th,in - Tc,in)
- Determine actual heat transfer Q from known temperatures
- Calculate effectiveness: ε = Q / Qmax
- Use appropriate ε-NTU relation (or chart) to find NTU for given Cr and configuration
- Estimate overall heat transfer coefficient U
- Calculate required area: A = (NTU × Cmin) / U
- Select geometry and verify pressure drops
- Refine U and iterate if necessary
7.3 Rating vs. Sizing Problems
| Problem Type | Known Parameters |
|---|---|
| Sizing (Design) | Inlet/outlet temperatures, flow rates; find required area and geometry |
| Rating (Performance) | Geometry, inlet temperatures, flow rates; find outlet temperatures and heat transfer |
- Sizing: Use LMTD method (straightforward calculation)
- Rating: Use ε-NTU method (no iteration needed) or iterative LMTD
7.4 Key Design Checks
- F Factor: Must be ≥ 0.75; if lower, change configuration or add shell passes
- Velocity Range: Verify within recommended limits for erosion and heat transfer
- Reynolds Number: Check flow regime; Re > 10,000 for high heat transfer
- Pressure Drop: Verify within allowable limits; adjust passes or diameter if excessive
- Temperature Limits: Ensure materials rated for operating temperatures
- Thermal Stress: For large ΔT between shell and tubes (>75°C), use expansion joint or floating head
- Tube Bundle Removal: Ensure removable for cleaning (U-tube, floating head, or pull-through designs)
8. Special Considerations
8.1 Phase Change Heat Exchangers
| Type | Key Considerations |
|---|---|
| Condensers | Horizontal tubes preferred; condensate drainage critical; non-condensables venting required; Cr = 0 (infinite heat capacity); high hcondensation |
| Reboilers | Kettle type (pool boiling) or thermosyphon; heat flux limits to avoid CHF; circulation rate critical; horizontal or vertical orientation |
| Evaporators | Falling film, rising film, or forced circulation; prevent dry-out; maintain liquid coverage |
| Steam Heaters | Cr ≈ 0; steam side fouling minimal; condensate subcooling affects performance; steam trap selection important |
8.2 High-Temperature Applications
- Thermal Expansion: Differential expansion between shell and tubes; use floating head, U-tubes, or expansion joints
- Material Creep: Consider creep strength above 400°C for steels
- Gasket Selection: Limited to ~260°C for PTFE; use metal gaskets or welded construction above
- Insulation: Required for temperatures >50°C to reduce heat loss and protect personnel
8.3 Cryogenic Service
- Materials: Aluminum, stainless steel, or nickel alloys; avoid carbon steel (brittle)
- Thermal Contraction: Design for contraction during cooldown
- Vacuum Jacketing: Minimize heat leak from environment
- Plate-Fin Type: Common for air separation and LNG service
8.4 Compact Heat Exchangers
- Definition: Surface area density >700 m²/m³ (compact) or >300 m²/m³ (moderately compact)
- Types: Plate, plate-fin, spiral, printed circuit heat exchangers (PCHE)
- Advantages: Small footprint, high effectiveness, lower inventory
- Applications: Aerospace, automotive, cryogenics, process intensification
8.5 Thermal Design Margin
- Overdesign: Provide 10-20% excess area to account for fouling and uncertainties
- Performance Monitoring: Track U value degradation; clean when drops 20-30%
- Turndown Ratio: Ability to operate at reduced capacity; control via flow rate or bypass
8.6 Code and Standards
- ASME Section VIII: Pressure vessel design code for shell-and-tube exchangers
- TEMA: Standards of Tubular Exchanger Manufacturers Association; classification (R, C, B classes)
- API 660/661: Shell-and-tube and air-cooled heat exchangers for petroleum industry
- ASME B31.3: Process piping code for connections
- HEI Standards: Heat Exchange Institute standards for power plant condensers
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