Heat Exchangers in HVAC Applications: Design, Selection & Performance Analysis

Heat Exchangers in HVAC Applications: Design, Selection & Performance Analysis

Heat exchangers transfer thermal energy between fluid streams without mixing, forming the core of HVAC equipment including cooling coils, condensers, evaporators, boilers, and energy recovery systems. This guide provides the mathematical framework, design procedures, and performance analysis methods for specifying, sizing, and evaluating heat exchangers in commercial and industrial HVAC applications.

Heat Transfer Fundamentals

Three Modes of Heat Transfer

Heat transfer through exchanger surfaces involves three distinct mechanisms operating simultaneously.

Conduction through solid walls (Fourier’s Law):

$$q = -k A \frac{dT}{dx}$$

Where:

• $q$ = heat transfer rate (Btu/h or W)
• $k$ = thermal conductivity (Btu/(h·ft·°F) or W/(m·K))
• $A$ = cross-sectional area (ft² or m²)
• $dT/dx$ = temperature gradient (°F/ft or K/m)

For thin-walled tubes (typical heat exchanger construction):

$$q = \frac{2\pi k L (T_1 - T_2)}{\ln(r_o/r_i)}$$

Where:

• $L$ = tube length (ft or m)
• $r_o$ = outer radius (ft or m)
• $r_i$ = inner radius (ft or m)

Convection at fluid-solid interfaces (Newton’s Law of Cooling):

$$q = h A (T_s - T_f)$$

Where:

• $h$ = convection coefficient (Btu/(h·ft²·°F) or W/(m²·K))
• $T_s$ = surface temperature (°F or K)
• $T_f$ = bulk fluid temperature (°F or K)

Radiation between surfaces (minor contributor in most HVAC exchangers):

$$q = \sigma \epsilon A (T_1^4 - T_2^4)$$

Where:

• $\sigma$ = Stefan-Boltzmann constant = 0.1714×10⁻⁸ Btu/(h·ft²·R⁴)
• $\epsilon$ = emissivity (dimensionless, 0-1)

Overall Heat Transfer Coefficient

Heat transfer through exchanger walls combines convection on both sides and conduction through the wall in series thermal resistance:

$$\frac{1}{UA} = \frac{1}{h_i A_i} + \frac{r_o \ln(r_o/r_i)}{2\pi k L} + \frac{1}{h_o A_o}$$

For thin-walled tubes where $A_i \approx A_o \approx A$:

$$U = \frac{1}{\frac{1}{h_i} + \frac{t}{k} + \frac{1}{h_o}}$$

Where:

• $U$ = overall heat transfer coefficient (Btu/(h·ft²·°F) or W/(m²·K))
• $t$ = wall thickness (ft or m)
• $h_i$ = inside convection coefficient
• $h_o$ = outside convection coefficient

Typical U-values for HVAC heat exchangers:

Convection Correlations

Accurate convection coefficient calculation requires empirical correlations based on dimensionless numbers.

Reynolds Number (flow regime):

$$Re = \frac{\rho V D}{\mu} = \frac{V D}{\nu}$$

Where:

• $\rho$ = density (lb/ft³ or kg/m³)
• $V$ = velocity (ft/s or m/s)
• $D$ = characteristic dimension (ft or m)
• $\mu$ = dynamic viscosity (lb/(ft·s) or Pa·s)
• $\nu$ = kinematic viscosity (ft²/s or m²/s)

Prandtl Number (thermal vs momentum diffusivity):

$$Pr = \frac{c_p \mu}{k} = \frac{\nu}{\alpha}$$

Where:

• $c_p$ = specific heat (Btu/(lb·°F) or J/(kg·K))
• $\alpha$ = thermal diffusivity (ft²/s or m²/s)

Nusselt Number (dimensionless heat transfer):

$$Nu = \frac{h D}{k}$$

Dittus-Boelter equation (turbulent flow in tubes, Re > 10,000):

$$Nu = 0.023 Re^{0.8} Pr^n$$

Where:

• $n = 0.4$ for heating (fluid being heated)
• $n = 0.3$ for cooling (fluid being cooled)

Sieder-Tate correlation (improved accuracy with viscosity correction):

$$Nu = 0.027 Re^{0.8} Pr^{1/3} \left(\frac{\mu_b}{\mu_w}\right)^{0.14}$$

Where:

• $\mu_b$ = viscosity at bulk fluid temperature
• $\mu_w$ = viscosity at wall temperature

Laminar flow in tubes (Re < 2,300):

$$Nu = 3.66 \quad \text{(constant wall temperature)}$$ $$Nu = 4.36 \quad \text{(constant heat flux)}$$

Log Mean Temperature Difference (LMTD) Method

The LMTD method calculates heat exchanger performance when inlet and outlet temperatures are known. This direct approach suits rating problems (verifying performance of existing equipment).

LMTD Definition

Temperature difference varies along heat exchanger length as fluids exchange heat. The log mean temperature difference accounts for this variation:

$$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$$

Where:

• $\Delta T_1$ = temperature difference at one end
• $\Delta T_2$ = temperature difference at other end

For counterflow arrangement:

$$\Delta T_1 = T_{h,in} - T_{c,out}$$ $$\Delta T_2 = T_{h,out} - T_{c,in}$$

For parallel flow arrangement:

$$\Delta T_1 = T_{h,in} - T_{c,in}$$ $$\Delta T_2 = T_{h,out} - T_{c,out}$$

graph LR
    subgraph Counterflow
    A1[Hot In<br/>T_h_in] -->|Direction| B1[Hot Out<br/>T_h_out]
    C1[Cold Out<br/>T_c_out] -->|Direction| D1[Cold In<br/>T_c_in]
    end

    subgraph Parallel Flow
    A2[Hot In<br/>T_h_in] -->|Direction| B2[Hot Out<br/>T_h_out]
    D2[Cold In<br/>T_c_in] -->|Direction| C2[Cold Out<br/>T_c_out]
    end

    style A1 fill:#ff9999
    style B1 fill:#ffcccc
    style C1 fill:#9999ff
    style D1 fill:#ccccff
    style A2 fill:#ff9999
    style B2 fill:#ffcccc
    style C2 fill:#9999ff
    style D2 fill:#ccccff

Heat Transfer Rate Equation

$$q = U A \Delta T_{lm}$$

Where:

• $q$ = heat transfer rate (Btu/h or W)
• $U$ = overall heat transfer coefficient (Btu/(h·ft²·°F) or W/(m²·K))
• $A$ = heat transfer surface area (ft² or m²)
• $\Delta T_{lm}$ = log mean temperature difference (°F or K)

Energy Balance

Heat lost by hot fluid equals heat gained by cold fluid (neglecting losses):

$$q = \dot{m}h c{p,h} (T_{h,in} - T_{h,out}) = \dot{m}c c{p,c} (T_{c,out} - T_{c,in})$$

Where:

• $\dot{m}$ = mass flow rate (lb/h or kg/s)
• $c_p$ = specific heat (Btu/(lb·°F) or J/(kg·K))

Heat capacity rate:

$$C = \dot{m} c_p$$

Units: Btu/(h·°F) or W/K

LMTD Correction Factor for Crossflow and Multi-Pass

Real heat exchangers rarely achieve pure counterflow. Correction factors account for flow configuration:

$$q = U A F \Delta T_{lm,cf}$$

Where:

• $F$ = LMTD correction factor (dimensionless, 0 < F ≤ 1.0)
• $\Delta T_{lm,cf}$ = LMTD for counterflow configuration

Correction factor parameters:

$$P = \frac{T_{c,out} - T_{c,in}}{T_{h,in} - T_{c,in}} = \frac{\text{cold fluid temperature rise}}{\text{max possible temperature rise}}$$

$$R = \frac{T_{h,in} - T_{h,out}}{T_{c,out} - T_{c,in}} = \frac{C_c}{C_h} = \frac{\dot{m}c c{p,c}}{\dot{m}h c{p,h}}$$

Typical F-values:

• Counterflow: $F = 1.00$ (by definition)
• Parallel flow: $F = 0.90$ to 0.98
• 1-shell pass, 2-tube pass: $F = 0.80$ to 0.95
• Crossflow (both unmixed): $F = 0.95$ to 0.99

Design guideline: Select configurations with $F \geq 0.80$ to maintain reasonable heat exchanger size.

Effectiveness-NTU (ε-NTU) Method

The ε-NTU method solves sizing problems when inlet temperatures and flow rates are known but outlet temperatures are unknown. This approach suits design problems (selecting heat exchanger size).

Heat Exchanger Effectiveness

Effectiveness represents actual heat transfer as a fraction of maximum thermodynamically possible transfer:

$$\epsilon = \frac{q_{actual}}{q_{max}}$$

Maximum heat transfer occurs when the fluid with minimum heat capacity undergoes maximum temperature change:

$$q_{max} = C_{min}(T_{h,in} - T_{c,in})$$

Where:

$$C_{min} = \min(C_h, C_c) = \min(\dot{m}h c{p,h}, \dot{m}c c{p,c})$$

Actual heat transfer:

$$q_{actual} = C_h(T_{h,in} - T_{h,out}) = C_c(T_{c,out} - T_{c,in})$$

Number of Transfer Units (NTU)

NTU represents heat exchanger thermal size relative to fluid heat capacity:

$$NTU = \frac{UA}{C_{min}}$$

Physical interpretation: NTU measures the heat exchanger’s ability to drive the cold fluid temperature toward the hot fluid inlet temperature. Larger NTU means:

• Larger surface area
• Higher overall U-value
• Lower minimum heat capacity rate

Heat Capacity Ratio

$$C_r = \frac{C_{min}}{C_{max}}$$

Where $0 \leq C_r \leq 1$

Special cases:

• $C_r = 0$: Phase change fluid (boiling or condensing)
• $C_r = 1$: Balanced heat capacities
• $C_r \to 0$: One fluid has much larger heat capacity

Effectiveness Relations for Flow Configurations

Counterflow:

$$\epsilon = \frac{1 - e^{-NTU(1-C_r)}}{1 - C_r e^{-NTU(1-C_r)}} \quad \text{for } C_r < 1$$

$$\epsilon = \frac{NTU}{1 + NTU} \quad \text{for } C_r = 1$$

Parallel flow:

$$\epsilon = \frac{1 - e^{-NTU(1+C_r)}}{1 + C_r}$$

Crossflow (both fluids unmixed):

$$\epsilon = 1 - \exp\left[\frac{NTU^{0.22}}{C_r}(e^{-C_r \cdot NTU^{0.78}} - 1)\right]$$

Phase change (condensing or evaporating, $C_r = 0$):

$$\epsilon = 1 - e^{-NTU}$$

All configurations achieve same effectiveness limit as NTU → ∞:

$$\epsilon_{max} = \begin{cases} 1.0 & C_r = 0 \ \frac{C_r}{1+C_r} & C_r > 0, \text{ parallel flow} \ 1.0 & \text{counterflow} \end{cases}$$

Counterflow superiority: Counterflow achieves ε → 1.0 for any $C_r$, while parallel flow maximum effectiveness decreases with increasing $C_r$.

graph TB
    A[Known:<br/>T_h_in, T_c_in<br/>m_h, m_c<br/>c_p_h, c_p_c] --> B[Calculate:<br/>C_h, C_c<br/>C_min, C_max<br/>C_r]
    B --> C[Assume:<br/>UA or NTU]
    C --> D[Calculate:<br/>NTU = UA/C_min]
    D --> E[Find ε from<br/>ε-NTU relation<br/>for flow type]
    E --> F[Calculate:<br/>q = ε × C_min × ΔT_max]
    F --> G[Find outlet temps:<br/>T_h_out, T_c_out]
    G --> H{Check:<br/>q matches<br/>requirement?}
    H -->|No| C
    H -->|Yes| I[Final Design:<br/>A, U, Temperatures]

    style A fill:#e1f5ff
    style I fill:#c3ffc3

Heat Exchanger Types for HVAC Applications

Shell-and-Tube Heat Exchangers

Shell-and-tube configurations handle high pressures, large capacities, and phase-change processes. Applications include chillers, condensers, steam-to-water, and hot-water generators.

Construction:

• Tubes: Straight copper or steel tubes, typically 3/4" to 1" diameter
• Shell: Steel or copper shell housing tube bundle
• Tube sheets: Tube ends fixed to thick metal plates
• Baffles: Direct shell-side flow across tubes, increase turbulence
• Passes: Multiple tube passes increase velocity and heat transfer

Flow arrangements:

• 1-shell pass, 2-tube pass (most common)
• 1-shell pass, 4-tube pass (high tube-side velocity)
• 2-shell pass, 4-tube pass (closer to counterflow)

Design parameters:

Tube-side velocity: 3-10 ft/s (water), prevents fouling and maintains turbulent flow

Shell-side velocity: 1-3 ft/s, limited by pressure drop

Tube pitch: 1.25 × tube OD (triangular) or 1.25 × tube OD (square), affects cleaning access

Advantages:

• High pressure capability (>300 psig)
• Large capacity (>1,000 tons cooling)
• Proven reliability
• Field-serviceable
• Handles fouling fluids

Disadvantages:

• Large physical size
• Heavy weight
• Expensive
• Low effectiveness (typically 0.6-0.8)

Pressure drop (tube side, turbulent flow):

$$\Delta P = \left(f \frac{L}{D} + K\right) \frac{\rho V^2}{2g_c}$$

Where:

• $f$ = Darcy friction factor (dimensionless)
• $L$ = tube length (ft)
• $D$ = tube inside diameter (ft)
• $K$ = loss coefficient for fittings and passes (dimensionless)
• $g_c$ = 32.2 ft/s² (gravitational constant)

Friction factor (turbulent, smooth tubes):

$$f = \frac{0.316}{Re^{0.25}} \quad \text{for } Re < 20,000$$

$$f = 0.184 Re^{-0.2} \quad \text{for } Re > 20,000$$

Plate Heat Exchangers

Plate heat exchangers use thin corrugated metal plates in a frame, creating alternating hot and cold flow channels. Applications include hydronic heating/cooling, domestic hot water, and heat recovery.

Construction:

• Plates: Thin stainless steel, titanium, or copper-brazed, 0.4-0.8 mm thick
• Gaskets: Elastomer seals between plates (gasketed type) or brazed joints (brazed type)
• Frame: Steel frame compresses plate stack
• Ports: Corner ports direct flow through channels

Flow pattern: Plates create complex turbulent flow with high heat transfer coefficients

Design parameters:

Plate spacing: 3-5 mm between plates

Channel velocity: 0.3-1.0 m/s (water)

Port velocity: <3 m/s (erosion limit)

Advantages:

• Very compact (1/5 size of shell-and-tube)
• High effectiveness (0.85-0.95)
• Very high U-values (200-500 Btu/(h·ft²·°F) for water-water)
• Easy to expand (add plates)
• True counterflow
• Low fouling (high turbulence)

Disadvantages:

• Pressure limit (150-300 psig depending on type)
• Temperature limit (gaskets: <350°F, brazed: <450°F)
• Gasket replacement required
• Susceptible to debris fouling between plates
• Higher pressure drop than shell-and-tube

Pressure drop estimation:

$$\Delta P = \frac{4fLG^2}{2\rho D_h} + 1.3 \times \frac{N_{channels}G^2}{2\rho}$$

Where:

• $G$ = mass flux (lb/(h·ft²))
• $D_h$ = hydraulic diameter (ft)
• $N_{channels}$ = number of channels
• Second term accounts for port and distribution losses

Finned-Tube Coils

Finned-tube coils transfer heat between air and liquid, dominating HVAC air-side applications. Applications include cooling coils, heating coils, condensers, and evaporators.

Construction:

• Tubes: Copper tubes, 3/8" to 5/8" OD
• Fins: Aluminum fins mechanically bonded to tubes, 8-18 fins per inch
• Circuiting: Tubes connected in series-parallel for desired velocity
• Face area: Coil frontal area exposed to airflow

Fin types:

• Plate fins: Flat aluminum plates, most common
• Corrugated fins: Enhanced turbulence
• Louvered fins: Cut and bent louvers improve heat transfer
• Spine fins: Individual fins on each tube

Design parameters:

Face velocity: 300-600 fpm (cooling), 400-800 fpm (heating)

Rows deep: 3-8 rows for cooling, 1-4 rows for heating

Fin spacing: 8-14 fins/inch (cooling), 10-18 fins/inch (heating)

Tube velocity: 2-8 ft/s (water), 20-60 ft/s (refrigerant evaporation)

Air-side heat transfer:

Finned surfaces provide 10-20× more air-side area than bare tubes, compensating for low air-side convection coefficients.

Total surface ratio:

$$\frac{A_{total}}{A_{tube,bare}} = 1 + \frac{A_{fin}}{A_{tube,bare}} \times \eta_{fin}$$

Fin efficiency:

Fins conduct heat from base to tip. Temperature decreases along fin length, reducing effectiveness.

$$\eta_{fin} = \frac{\tanh(mL)}{mL}$$

Where:

$$m = \sqrt{\frac{2h}{k t}}$$

• $h$ = air-side convection coefficient (Btu/(h·ft²·°F))
• $k$ = fin thermal conductivity (Btu/(h·ft·°F))
• $t$ = fin thickness (ft)
• $L$ = fin height from tube surface to tip (ft)

Typical aluminum fin efficiency: 0.70-0.85

Overall surface efficiency:

$$\eta_o = 1 - \frac{A_{fin}}{A_{total}}(1 - \eta_{fin})$$

Advantages:

• Standard HVAC equipment
• Low cost
• Wide range of capacities
• Handles wet-coil operation (dehumidification)

Disadvantages:

• Susceptible to dirt accumulation on fins
• Air-side pressure drop increases with dirt
• Condensate carryover at high face velocities
• Freezing risk in cold climates

Air-side pressure drop:

$$\Delta P_{air} = \frac{12.5 \times (FPM/1000)^{1.9} \times rows}{1000} \text{ in. w.g.}$$

Approximation for clean coils with 10-12 fins/inch.

Plate-Fin Heat Exchangers

Plate-fin heat exchangers bond fins between parallel plates, creating compact high-performance exchangers for gas-gas applications. Applications include air-to-air energy recovery and cryogenic systems.

Construction:

• Plates: Aluminum or stainless steel plates form flow passages
• Fins: Corrugated, louvered, or offset-strip fins brazed to plates
• Headers: Manifolds distribute flow to passages
• Core: Brazed assembly creates monolithic structure

Flow arrangement: True counterflow or crossflow

Design parameters:

Hydraulic diameter: 1-4 mm (very compact)

Fin density: 400-1000 fins/m² of frontal area

Surface area density: 700-4000 m²/m³ (extremely compact)

Advantages:

• Highest surface area density of any heat exchanger
• Excellent for gas-gas applications
• Lightweight
• High effectiveness (>0.90)

Disadvantages:

• Cannot be disassembled for cleaning
• Susceptible to fouling
• Expensive manufacturing
• Limited to compatible materials (brazable)

Effectiveness and Performance Calculations

Maximum Effectiveness Limits

Flow configuration and heat capacity ratio limit achievable effectiveness:

(All values at NTU → ∞)

Design implications:

• Counterflow always superior for non-phase-change applications
• Balanced heat capacities ($C_r$ near 1.0) penalize non-counterflow arrangements
• Phase change ($C_r = 0$) eliminates flow pattern effects

Temperature Effectiveness

Alternative effectiveness definition based on either fluid:

Hot fluid effectiveness:

$$\epsilon_h = \frac{T_{h,in} - T_{h,out}}{T_{h,in} - T_{c,in}}$$

Cold fluid effectiveness:

$$\epsilon_c = \frac{T_{c,out} - T_{c,in}}{T_{h,in} - T_{c,in}}$$

Relationship to overall effectiveness:

$$\epsilon = \epsilon_h \times C_r \quad \text{if cold stream is } C_{min}$$

$$\epsilon = \epsilon_c \times C_r \quad \text{if hot stream is } C_{min}$$

Performance Rating

Heat exchanger performance depends on cleanliness, fluid properties, and flow rates. Rating calculations predict performance at off-design conditions.

Fouling resistance: Deposits on heat transfer surfaces reduce U-value over time

$$\frac{1}{U_{fouled}} = \frac{1}{U_{clean}} + R_{f,i} + R_{f,o}$$

Where:

• $R_f$ = fouling resistance (h·ft²·°F/Btu)
• Subscripts $i$ and $o$ denote inside and outside surfaces

Typical fouling resistances (TEMA standards):

Design fouling factor: Add 15-30% to calculated surface area to accommodate fouling:

$$A_{design} = A_{clean} \times (1 + fouling : margin)$$

Typical fouling margins:

• Clean fluids (treated water, refrigerants): 15-20%
• Moderate fouling (cooling tower water): 20-30%
• Heavy fouling (river water, air): 30-50%

Fouling Factors and Maintenance

Fouling Mechanisms

Crystallization fouling: Dissolved minerals precipitate on heat transfer surfaces

• Causes: Hard water, calcium carbonate, calcium sulfate
• Locations: Hot surfaces (>140°F), evaporators
• Prevention: Water treatment, maintain velocity >3 ft/s

Particulate fouling: Suspended particles settle and accumulate

• Causes: Dirt, sand, corrosion products
• Locations: Low-velocity regions, shell side
• Prevention: Filtration, maintain turbulent flow

Chemical reaction fouling: Chemical reactions produce deposits

• Causes: Polymerization, oxidation, corrosion
• Locations: High-temperature surfaces
• Prevention: Corrosion inhibitors, pH control

Biological fouling: Microorganism growth forms biofilm

• Causes: Bacteria, algae, fungi
• Locations: Cooling tower water systems, <140°F
• Prevention: Biocides, UV treatment, maintain velocity

Corrosion fouling: Corrosion products accumulate as deposits

• Causes: Oxygen, pH imbalance, galvanic corrosion
• Locations: Dissimilar metals, stagnant regions
• Prevention: Material selection, corrosion inhibitors

Cleaning Methods

Mechanical cleaning:

• Tube brushing: Manual or pneumatic brushes through tubes
• High-pressure water jetting: 3,000-10,000 psig removes hard deposits
• Bullet cleaning: Plastic projectiles shot through tubes
• Frequency: Annually for cooling tower water systems

Chemical cleaning:

• Acid cleaning: Dissolves mineral deposits (hydrochloric, sulfamic acid)
• Alkaline cleaning: Removes organic deposits
• Descaling: Removes hard water scale
• Frequency: Every 3-5 years or as-needed

Design for cleanability:

• Removable tube bundles
• Straight tubes (no U-tubes for mechanical cleaning)
• Square tube pitch (cleaning lane access)
• Cleanout ports and access doors
• Isolation valves for system removal

Monitoring and Performance Degradation

Performance indicators:

$$U_{actual} = \frac{q}{A \Delta T_{lm}}$$

Compare to design U-value. Degradation >20% indicates fouling.

Temperature approach:

$$Approach = T_{cold,out} - T_{hot,out}$$

Increasing approach indicates fouling.

Pressure drop increase: Fouling increases flow resistance

$$\frac{\Delta P_{fouled}}{\Delta P_{clean}} > 1.2 \text{ indicates fouling}$$

Pressure Drop Analysis

General Pressure Drop Equation

$$\Delta P = \Delta P_{friction} + \Delta P_{acceleration} + \Delta P_{elevation}$$

For horizontal single-phase flow, elevation term = 0.

Friction pressure drop (internal flow):

$$\Delta P_f = f \frac{L}{D} \frac{\rho V^2}{2g_c}$$

Darcy friction factor:

Laminar flow (Re < 2,300):

$$f = \frac{64}{Re}$$

Turbulent flow, smooth pipes (Blasius equation, Re < 100,000):

$$f = \frac{0.316}{Re^{0.25}}$$

Turbulent flow, rough pipes (Colebrook equation):

$$\frac{1}{\sqrt{f}} = -2.0 \log\left(\frac{\epsilon/D}{3.7} + \frac{2.51}{Re\sqrt{f}}\right)$$

Where $\epsilon$ = absolute roughness (ft)

Minor losses (fittings, entrance, exit):

$$\Delta P_{minor} = K \frac{\rho V^2}{2g_c}$$

Typical K-values:

• 90° elbow: K = 0.9
• 45° elbow: K = 0.4
• Tee (through flow): K = 0.6
• Tee (branch flow): K = 1.8
• Gate valve (open): K = 0.2
• Entrance (sharp): K = 0.5
• Exit: K = 1.0

Air-Side Pressure Drop

Coil pressure drop:

$$\Delta P_{coil} = K_{coil} \left(\frac{V_{face}}{1000}\right)^{1.9} \times rows$$

Units: inches water gauge (in. w.g.)

Where $V_{face}$ = face velocity (fpm)

Typical $K_{coil}$ values:

• 8 fins/inch: $K_{coil}$ = 0.08
• 10 fins/inch: $K_{coil}$ = 0.10
• 12 fins/inch: $K_{coil}$ = 0.12
• 14 fins/inch: $K_{coil}$ = 0.15

Duct system pressure drop:

Total system pressure drop includes coils, filters, dampers, ductwork:

$$\Delta P_{total} = \Delta P_{coil} + \Delta P_{filter} + \Delta P_{duct} + \Delta P_{fittings}$$

Design for total system pressure drop: 1.5-3.0 in. w.g. for typical HVAC systems

Water-Side Pressure Drop

Tube-side pressure drop:

$$\Delta P_{tube} = \left(f \frac{L}{D} + 4N_{passes}\right) \frac{\rho V^2}{2g_c}$$

Where:

• $4N_{passes}$ accounts for entrance/exit losses at each pass
• Convert to psi: divide by 144 in²/ft²

Design pressure drop limits:

• Chilled water: 10-20 ft head (4.3-8.7 psi)
• Condenser water: 15-30 ft head (6.5-13 psi)
• Hot water heating: 10-25 ft head (4.3-10.8 psi)

Higher pressure drops increase pumping energy:

$$P_{pump} = \frac{GPM \times \Delta P_{ft}}{3956 \times \eta_{pump}}$$

Units: horsepower (HP)

Where $\eta_{pump}$ = pump efficiency (typically 0.60-0.80)

Selection Criteria and Sizing

Selection Flowchart

graph TD
    A[Define Requirements:<br/>Fluids, Flow Rates,<br/>Temperatures, Capacity] --> B{Fluids?}
    B -->|Liquid-Liquid| C{Pressure?}
    B -->|Gas-Gas| D[Plate-Fin or<br/>Finned-Tube]
    B -->|Liquid-Gas| E[Finned-Tube Coil]
    B -->|Phase Change| F{Condensing or<br/>Evaporating?}

    C -->|<150 psi| G{Fouling?}
    C -->|>150 psi| H[Shell-and-Tube]

    G -->|Low| I[Plate HX]
    G -->|High| H

    F -->|Condensing| J[Shell-and-Tube<br/>or Plate]
    F -->|Evaporating| K[Shell-and-Tube<br/>or Plate]

    I --> L[Calculate:<br/>ε, NTU, UA, Area]
    H --> L
    D --> L
    E --> L
    J --> L
    K --> L

    L --> M{Performance<br/>OK?}
    M -->|No| N[Increase Area<br/>or Change Type]
    M -->|Yes| O[Check:<br/>Pressure Drop]

    N --> L

    O --> P{ΔP<br/>Acceptable?}
    P -->|No| Q[Increase Flow Area<br/>or Change Type]
    P -->|Yes| R[Final Design]

    Q --> L

    style A fill:#e1f5ff
    style R fill:#c3ffc3

Design Procedure

Step 1: Define requirements

• Heat transfer rate (Btu/h or tons)
• Fluid types and properties
• Inlet temperatures
• Flow rates or outlet temperatures
• Pressure limits
• Fouling factors
• Space constraints

Step 2: Calculate heat capacity rates

$$C_h = \dot{m}h c{p,h}$$ $$C_c = \dot{m}c c{p,c}$$ $$C_{min} = \min(C_h, C_c)$$ $$C_r = C_{min}/C_{max}$$

Step 3: Calculate required effectiveness

$$\epsilon_{required} = \frac{q}{C_{min}(T_{h,in} - T_{c,in})}$$

Step 4: Select flow configuration

• Counterflow for highest effectiveness
• Crossflow for air-side applications
• Multi-pass shell-and-tube for space constraints

Step 5: Calculate required NTU

Use ε-NTU relation for selected configuration.

Step 6: Estimate overall heat transfer coefficient

Based on fluids and heat exchanger type (use tables in this guide).

Step 7: Calculate required surface area

$$A = \frac{NTU \times C_{min}}{U_{clean}}$$

Step 8: Add fouling margin

$$A_{design} = A_{clean} \times (1.0 + fouling : margin)$$

Step 9: Calculate pressure drop

Check both fluid streams against pressure limits.

Step 10: Iterate if necessary

Adjust U-value, flow configuration, or heat exchanger type.

Optimization Criteria

Economic optimization:

Minimize total lifetime cost = capital cost + operating cost

$$Cost_{total} = Cost_{HX} + PV(Cost_{energy})$$

Where:

• $Cost_{HX}$ = heat exchanger purchase and installation cost
• $PV(Cost_{energy})$ = present value of pumping/fan energy over equipment life

Larger heat exchangers (higher effectiveness, lower ΔT) reduce energy consumption but increase first cost. Optimum balances these factors.

Performance optimization:

Maximize effectiveness subject to:

• Pressure drop constraints
• Size constraints
• Cost constraints

Generally achieved by:

• Counterflow configuration
• Maximizing NTU (surface area)
• Minimizing $C_r$ (unbalanced flow)

Counterflow vs Parallel Flow vs Crossflow

Temperature Profiles

Counterflow: Hot and cold fluids flow in opposite directions

Temperature profile:

• Maximum heat transfer for given size
• Closest approach between outlet temperatures
• Cold outlet can exceed hot outlet (if $C_c < C_h$)

Parallel flow: Hot and cold fluids flow in same direction

Temperature profile:

• Lower effectiveness than counterflow
• Hot and cold outlets approach same temperature
• Cold outlet cannot exceed hot outlet

Crossflow: Fluids flow perpendicular

Temperature profile:

• Effectiveness between counterflow and parallel
• Depends on whether fluids are mixed or unmixed

graph LR
    subgraph Counterflow Temperature Profile
    A1[" "] ---|Hot Fluid| B1[" "]
    C1[" "] ---|Cold Fluid| D1[" "]
    E1["T_h_in (high)"] -.-> A1
    F1["T_h_out (medium-low)"] -.-> B1
    G1["T_c_in (low)"] -.-> D1
    H1["T_c_out (medium-high)"] -.-> C1
    end

    subgraph Parallel Flow Temperature Profile
    A2[" "] ---|Hot Fluid| B2[" "]
    D2[" "] ---|Cold Fluid| C2[" "]
    E2["T_h_in (high)"] -.-> A2
    F2["T_h_out (medium)"] -.-> B2
    G2["T_c_in (low)"] -.-> D2
    H2["T_c_out (medium)"] -.-> C2
    end

    style A1 fill:#ff6666
    style B1 fill:#ffcccc
    style C1 fill:#9999ff
    style D1 fill:#ccccff
    style A2 fill:#ff6666
    style B2 fill:#ffcccc
    style C2 fill:#9999ff
    style D2 fill:#ccccff

Effectiveness Comparison

For same NTU and $C_r$:

$$\epsilon_{counterflow} > \epsilon_{crossflow} > \epsilon_{parallel}$$

Example: NTU = 2.0, $C_r$ = 0.75

Application Guidelines

Use counterflow when:

• Maximum effectiveness required
• Tight temperature approach needed
• Heat recovery applications
• Liquid-liquid exchangers

Use parallel flow when:

• Temperature-sensitive materials (limits hot outlet)
• Emergency cooling (rapid initial cooling)
• Rarely specified in modern HVAC

Use crossflow when:

• Air-liquid heat transfer (coils)
• Compact packaging required
• One fluid distributed over large area

Practical Design Examples

Summary

Heat exchanger design for HVAC applications requires integration of heat transfer fundamentals, flow configuration analysis, and practical constraints:

Key Principles:

• Overall heat transfer coefficient $U$ combines convection resistances and wall conduction in series
• LMTD method suits rating problems (known temperatures)
• ε-NTU method suits sizing problems (unknown outlet temperatures)
• Counterflow maximizes effectiveness for any heat capacity ratio
• Fouling degrades performance over time, requiring oversizing

Heat Exchanger Selection:

• Shell-and-tube: High pressure, large capacity, proven reliability
• Plate: Compact, high effectiveness, liquid-liquid
• Finned-tube: Air-liquid, standard HVAC equipment
• Plate-fin: Gas-gas, ultra-compact aerospace applications

Design Procedure:

1. Define thermal requirements and fluid properties
2. Calculate heat capacity rates and required effectiveness
3. Select flow configuration and heat exchanger type
4. Determine NTU and surface area using ε-NTU relations
5. Add fouling margin (15-50%)
6. Verify pressure drop constraints
7. Iterate until performance and cost optimized

Maintenance Considerations:

• Monitor U-value degradation through temperature measurements
• Clean when performance drops >20% or pressure drop increases >20%
• Mechanical cleaning for tube-side, chemical cleaning for hard deposits
• Design for accessibility (removable bundles, cleanout ports)

Proper heat exchanger selection and sizing ensures energy-efficient HVAC system performance with acceptable first cost, operating cost, and maintenance requirements.

Related Technical Guides:

• Heat Transfer Fundamentals
• Building Envelope Heat Transfer
• Fluid Mechanics for HVAC
• Energy Recovery Systems
• Cooling Tower Performance
• Chiller Performance Analysis

References:

• ASHRAE Handbook of Fundamentals, Chapter 4: Heat Transfer
• Incropera, F.P., DeWitt, D.P., Fundamentals of Heat and Mass Transfer, 7th Edition
• Kays, W.M., London, A.L., Compact Heat Exchangers, 3rd Edition
• Shah, R.K., Sekulic, D.P., Fundamentals of Heat Exchanger Design
• TEMA Standards, Standards of the Tubular Exchanger Manufacturers Association, 10th Edition
• ARI Standard 410: Forced-Circulation Air-Cooling and Air-Heating Coils
• Wang, S.K., Handbook of Air Conditioning and Refrigeration, 2nd Edition