Heat Exchangers — Fundamentals and Types

Heat exchangers transfer thermal energy between fluids separated by a solid wall or by direct contact. They are essential in power plants, chemical processes, HVAC, refrigeration, automotive, and electronics cooling. This page covers classifications, common designs, governing equations, sizing methods, and practical selection tips.

Classification

• By contact: Indirect (wall separating fluids), Direct-contact (fluids mix; e.g., cooling towers, spray condensers).
• By phase: Single-phase (both remain liquid or gas), Two-phase (condensers, evaporators, boilers, reboilers).
• By construction: Shell-and-tube, Double-pipe, Plate (gasketed, brazed, welded), Plate-fin/compact, Finned-tube (air-cooled), Spiral, Printed/3D compact cores.
• By flow arrangement: Parallel, Counterflow, Crossflow (mixed/unmixed), Multi-pass (tube/shell passes), Multi-stream.
• By duty: Heater, Cooler, Condenser, Evaporator, Economizer, Recuperator, Regenerator, Intercooler/Aftercooler.
• By mobility: Fixed, Removable bundle, Plate packs; Cleanability and maintenance access vary accordingly.

Flow Arrangements

Parallel Flow

Both fluids enter at the same end and move in the same direction. Hot–cold temperature difference is large at the inlet and diminishes toward the outlet; outlet cold temperature cannot exceed the outlet hot temperature.

Counterflow

Fluids move in opposite directions, maximizing the average driving temperature difference. Counterflow provides higher effectiveness for given area and can achieve cold outlet temperatures approaching hot inlet temperature.

Crossflow

Fluids move perpendicular to each other. Behavior depends on mixing: one or both streams may be unmixed (confined by fins or plates) or mixed (plenum/headers allow lateral mixing). Crossflow needs a correction factor when using LMTD.

Multi-pass and Shell Arrangements

Shell-and-tube units often use multiple tube passes and/or multiple shell passes to enhance heat transfer and control pressure drop. Baffles direct shell-side flow across tube bundles (increasing turbulence and area utilization).

Common Heat Exchanger Types

Double-Pipe Heat Exchanger

• Construction: One pipe inside another; counterflow or parallel flow.
• Use: Small duties, high pressures/temperatures, fouling services with simple cleaning.
• Pros: Simple, robust; Cons: Lower area density; modular but bulky for large duties.

Shell-and-Tube Heat Exchanger

• Construction: Tube bundle within a shell; baffles support tubes and direct shell-side crossflow.
• Variations: Single- or multi-pass tubes; different shell types and baffle cuts; removable bundles for cleaning.
• Use: High-pressure, high-temperature, dirty or corrosive services, two-phase (condensers/reboilers).
• Pros: Versatile, scalable, well-standardized; Cons: Larger footprint, baffle leakage/bypass losses.

Plate Heat Exchanger (PHE)

• Construction: Corrugated plates with gaskets (or brazed/welded), forming alternating channels.
• Use: Food processing, HVAC, clean liquids, moderate pressures; brazed PHEs for refrigerants.
• Pros: Very high area density and heat transfer coefficients; Cons: Gasket limits, narrower channels can foul.

Finned-Tube (Air-Cooled) Exchanger

• Construction: Extended surfaces (fins) on tubes to enhance air-side area.
• Use: When cooling water is scarce; air coolers in refineries, radiators, electronics heat sinks.
• Pros: No cooling water; Cons: Low air-side coefficients require large fin area and fans.

Plate-Fin and Compact Exchangers

• Construction: Thin plates with offset strip/louvered fins brazed into compact cores.
• Use: Cryogenics, aerospace, recuperators; high effectiveness, low mass.
• Cons: Sensitive to fouling; cleaning/repair can be difficult.

Spiral Heat Exchanger

• Construction: Two spiral channels wound around a center; high shear and self-cleaning tendencies.
• Use: Viscous or fouling fluids, slurries, limited footprint.

Two-Phase Devices

• Condensers: Vapor → liquid; high heat flux, need condensate drainage and non-condensable management.
• Evaporators/Boilers: Nucleate/film boiling; critical heat flux and dry-out constraints; distribution matters in PHEs.
• Reboilers: Kettle, thermosiphon, once-through; ensure proper circulation and level control.

Direct-Contact Heat Exchangers

• Cooling towers: Water–air contact; evaporation drives heat and mass transfer.
• Spray/jet condensers: Vapor directly contacts cooling liquid; no separating wall, simple and compact.

Thermal Design Fundamentals

Energy Balance

For single-phase on both sides:

\[ Q = \dot{m}_h c_{p,h}\,(T_{h,in} - T_{h,out}) = \dot{m}_c c_{p,c}\,(T_{c,out} - T_{c,in}) \]

Define capacity rates and ratios:

\[ C_h = \dot{m}_h c_{p,h},\quad C_c = \dot{m}_c c_{p,c},\quad C_{\min} = \min(C_h, C_c),\quad C_{\max} = \max(C_h, C_c),\quad C_r = \frac{C_{\min}}{C_{\max}} \]

Overall Heat Transfer Coefficient

The overall conductance combines film, wall, and fouling resistances. For a cylindrical wall (tube side “i”, shell side “o”):

\[ \frac{1}{U_o A_o} = \frac{1}{h_o A_o} + R_{f,o} + \frac{\ln(r_o/r_i)}{2\pi k L} + \frac{R_{f,i}}{A_i} + \frac{1}{h_i A_i} \]

Use a consistent reference area (inner, outer, or mean) when relating \( U \), \( A \), and \( Q \).

LMTD Method

The log-mean temperature difference (LMTD) for a single shell/tube pass counterflow or parallel-flow exchanger:

\[ \Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln\!\left(\dfrac{\Delta T_1}{\Delta T_2}\right)}, \quad Q = U\,A\,F\,\Delta T_{lm} \]

\(\Delta T_1\) and \(\Delta T_2\) are end temperature differences. The correction factor \( F \le 1 \) accounts for crossflow or multipass arrangements.

Effectiveness–NTU Method

Define effectiveness \( \varepsilon \) and NTU:

\[ \varepsilon = \frac{Q}{C_{\min}(T_{h,in} - T_{c,in})},\qquad \mathrm{NTU} = \frac{U A}{C_{\min}} \]

Common formulas:

• Parallel flow: \[ \varepsilon = \frac{1 - e^{-\mathrm{NTU}(1 + C_r)}}{1 + C_r} \]
• Counterflow: \[ \varepsilon = \frac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r\,e^{-\mathrm{NTU}(1 - C_r)}} \]
• Crossflow (both unmixed): Use standard charts/correlations; typically \[ \varepsilon = 1 - \exp\!\left\{-\frac{1}{C_r}\left[1 - \exp\!\left(-C_r\,\mathrm{NTU}\right)\right]\right\} \] as an approximation for guidance (check specific geometry correlations).

Worked Example — Sizing by LMTD

Design a counterflow exchanger. Water is cooled by water.

• Hot side: \(\dot{m}_h = 2.0\,\text{kg/s},\; c_{p,h}=4180\,\text{J/(kg·K)},\; T_{h,in}=90^\circ\text{C}\)
• Cold side: \(\dot{m}_c = 1.5\,\text{kg/s},\; c_{p,c}=4180\,\text{J/(kg·K)},\; T_{c,in}=20^\circ\text{C}\)
• Target: \(T_{c,out}=60^\circ\text{C}\) (find area with \(U=800\,\text{W/(m}^2\!\cdot\!\text{K)}\))

Heat duty:

\[ Q = \dot{m}_c c_{p,c}(T_{c,out}-T_{c,in}) = 1.5\times 4180\times (60-20) = 2.508\times 10^5\,\text{W} \]

Hot outlet:

\[ T_{h,out} = T_{h,in} - \frac{Q}{\dot{m}_h c_{p,h}} = 90 - \frac{2.508\times 10^5}{2\times 4180} \approx 60^\circ\text{C} \]

End temperature differences (counterflow):

\[ \Delta T_1 = T_{h,in} - T_{c,out} = 90 - 60 = 30\,\text{K},\quad \Delta T_2 = T_{h,out} - T_{c,in} = 60 - 20 = 40\,\text{K} \]

LMTD and required area (\(F=1\) for ideal counterflow):

\[ \Delta T_{lm} = \frac{40-30}{\ln(40/30)} \approx 34.75\,\text{K},\qquad A = \frac{Q}{U\,\Delta T_{lm}} \approx \frac{2.508\times 10^5}{800\times 34.75} \approx 9.0\,\text{m}^2 \]

Check with \( \varepsilon\text{–NTU} \):

\[ C_h=8360,\; C_c=6270\,\text{W/K}\Rightarrow C_{\min}=6270,\; C_r=0.75,\quad \mathrm{NTU}=\frac{UA}{C_{\min}}\approx \frac{800\times 9.0}{6270}\approx 1.15 \]

Counterflow effectiveness:

\[ \varepsilon=\frac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r e^{-\mathrm{NTU}(1 - C_r)}} = \frac{1 - e^{-1.15\times 0.25}}{1 - 0.75\,e^{-1.15\times 0.25}} \approx 0.571 \]

Then \(Q=\varepsilon\,C_{\min}(T_{h,in}-T_{c,in})\approx 0.571\times 6270\times 70\approx 2.51\times 10^5\,\text{W}\) (consistent).

Selection Guidelines

• Thermal duty and approach: Required \(Q\), allowable terminal temperature differences, and approach to pinch influence area and type.
• Fluids and fouling: Dirty/viscous fluids favor shell-and-tube or spiral; clean liquids favor plate units.
• Pressure and temperature: High pressure/temperature services often use shell-and-tube or double-pipe; gasketed plate units have limits.
• Pressure drop budget: Air side is typically limiting; finned surfaces and flow distribution become critical.
• Maintenance and cleaning: Removable bundles (S&T) and openable plate packs aid cleaning; brazed cores are compact but not serviceable.
• Materials and corrosion: Match metallurgy to fluid chemistry; consider galvanic pairs, stress corrosion, and erosion.
• Footprint and weight: Compact exchangers maximize area density where space is constrained.
• Phase change needs: For condensers/boilers, ensure proper distribution, drainage, venting of non-condensables, and control of critical heat flux.

Fouling and Maintenance

• Fouling factors: Account for \(R_f\) on both sides in \(1/U\); plan for performance degradation and cleaning intervals.
• Mitigation: Filtration/strainers, chemical treatment, higher shear designs (corrugations/fins), periodic backflushing or CIP.
• Inspection: Monitor approach temperatures, pressure drops, and heat duty to detect fouling or maldistribution.

Pressure Drop and Mechanical Constraints

• Allowables: Allocate \(\Delta p\) per side early; thermal performance must meet both \(Q\) and \(\Delta p\).
• Distribution: Ensure even flow across channels (PHE headers, shell baffle design) to avoid bypassing and hotspots.
• Vibration and supports: Shell-side crossflow can induce tube vibration; check span, baffle cut, and fluid velocity.
• Thermal expansion: Large temperature differences may require expansion joints or floating heads in S&T.

Quick Reference

• Energy balance: \[ Q = \dot{m}_h c_{p,h}(T_{h,in}-T_{h,out}) = \dot{m}_c c_{p,c}(T_{c,out}-T_{c,in}) \]
• LMTD: \[ \Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1/\Delta T_2)},\quad Q = UAF\Delta T_{lm} \]
• Effectiveness–NTU: \[ \varepsilon = \frac{Q}{C_{\min}(T_{h,in}-T_{c,in})},\quad \mathrm{NTU} = \frac{UA}{C_{\min}} \]
• Counterflow effectiveness: \[ \varepsilon = \frac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r e^{-\mathrm{NTU}(1 - C_r)}} \]
• Overall resistance (tube outside area basis): \[ \frac{1}{U_o} = \frac{1}{h_o} + R_{f,o} + \frac{A_o}{2\pi k L}\ln\!\frac{r_o}{r_i} + R_{f,i}\frac{A_o}{A_i} + \frac{A_o}{h_i A_i} \]