Heat Exchangers and Thermal Equipment

Introduction

A heat exchanger transfers thermal energy between two or more fluids at different temperatures, normally without allowing them to mix. Heat exchangers are central to power plants, refrigeration systems, engines, chemical processing, food production, HVAC systems, and renewable-energy equipment. Their design requires more than calculating heat duty: the engineer must also consider temperature driving force, flow arrangement, heat-transfer coefficients, fouling, pressure loss, materials, manufacturability, safety, maintenance, and applicable standards.

Two complementary design methods are used extensively. The logarithmic mean temperature difference (LMTD) method is convenient when inlet and outlet temperatures are known or specified. The effectiveness–NTU method is particularly useful during preliminary design, when outlet temperatures are unknown.

Learning Objectives

By the end of this chapter, the reader should be able to:

1. Explain the operation and classification of major heat exchangers.
2. Determine heat transfer using energy balances and the LMTD method.
3. Apply correction factors to multipass and crossflow exchangers.
4. Use the effectiveness–NTU method for parallel-flow, counterflow, and crossflow units.
5. Estimate overall heat-transfer coefficients, fouling effects, and pressure drop.
6. Compare shell-and-tube, compact, plate, regenerative, and direct-contact equipment.
7. Select and evaluate an exchanger using thermal, hydraulic, mechanical, economic, and standards-based criteria.

1. Classification and Operating Principles

Heat exchangers may be classified in several ways.

According to contact between fluids:

• Indirect-contact exchangers: fluids are separated by a wall. Shell-and-tube, plate, double-pipe, finned, and compact exchangers belong to this class.
• Direct-contact exchangers: fluids contact and exchange heat directly, as in cooling towers and spray condensers. They are unsuitable when mixing is unacceptable.

According to flow arrangement:

• Parallel flow: both fluids enter at the same end and move in the same direction.
• Counterflow: fluids enter at opposite ends and move in opposite directions.
• Crossflow: one fluid flows approximately perpendicular to the other.

According to operation:

• Recuperative: hot and cold fluids exchange heat continuously through a separating wall.
• Regenerative: a solid matrix is alternately heated by the hot stream and cooled by the cold stream.

The exchanger must satisfy an energy balance. Neglecting heat loss to the surroundings and changes in kinetic and potential energy,

Here, Q̇ is heat-transfer rate (W), ṁ is mass-flow rate (kg·s⁻¹), c_p is specific heat (J·kg⁻¹·K⁻¹), and subscripts h and c denote hot and cold streams. The symbols i and o denote inlet and outlet. This equation assumes negligible external heat loss and approximately constant specific heats. For phase change, the enthalpy form is more appropriate:

where h is specific enthalpy (J·kg⁻¹).

2. Temperature Profiles and the LMTD Method

For a differential area dA, the local heat-transfer rate is

where U is the overall heat-transfer coefficient (W·m⁻²·K⁻¹), and ΔT is the local temperature difference. If U and the fluid properties are sufficiently uniform, integration gives

The logarithmic mean temperature difference is

where ΔT₁ and ΔT₂ are the temperature differences at the two ends, defined consistently according to the flow arrangement.

For parallel flow,

For counterflow,

Temperatures must be expressed on one consistent scale. Temperature differences in kelvin and degrees Celsius have the same numerical value. The LMTD expression applies when the exchanger is steady, the flow arrangement is known, phase-change conditions are handled correctly, and U is reasonably represented by a mean value.

For multipass shell-and-tube and crossflow exchangers, the ideal counterflow LMTD is multiplied by a correction factor F:

The factor depends on temperature ratios and the number of shell and tube passes. Design charts or validated software are normally used. Values of F close to unity indicate effective counterflow behavior; very low values indicate inefficient temperature arrangement and may require a different configuration.

Worked Example 1: Counterflow LMTD Design

Water is heated from 20 °C to 60 °C at 2 kg·s⁻¹ by hot oil that cools from 120 °C to 80 °C. Take c_p for water as 4.18 kJ·kg⁻¹·K⁻¹ and U as 350 W·m⁻²·K⁻¹. Determine the heat duty and required area for counterflow operation.

The duty is

The terminal differences are

Thus, ΔT_lm = 60 K. The required area is

This result assumes negligible heat loss, constant properties, and a clean exchanger. A practical design would include a fouling allowance and verify pressure drop.

3. Effectiveness–NTU Method

The heat-capacity rate of a stream is

with units W·K⁻¹. Define

The exchanger effectiveness is

The number of transfer units is

Effectiveness is a function of flow arrangement, NTU, and C_r. For parallel flow,

For counterflow, when C_r ≠ 1,

When C_r = 1, the counterflow relation becomes

These relations assume steady operation, negligible heat loss, constant properties, and a known exchanger configuration. Crossflow relations depend on whether each fluid is mixed or unmixed; manufacturer data or standard correlations should be used rather than applying a counterflow formula indiscriminately.

Once effectiveness is known,

Outlet temperatures follow from the energy balance:

Worked Example 2: Counterflow Effectiveness

A counterflow exchanger has U A = 12,000 W·K⁻¹. The hot stream has C_h = 8,000 W·K⁻¹ and enters at 150 °C. The cold stream has C_c = 5,000 W·K⁻¹ and enters at 25 °C. Find the heat-transfer rate and outlet temperatures.

Here, C_min=5,000 W·K⁻¹, C_max=8,000 W·K⁻¹, C_r=0.625, and NTU=12,000/5,000=2.4. Therefore,

The heat-transfer rate is

The outlet temperatures are

The cold outlet remains below the hot inlet, as required for a physically feasible counterflow exchanger.

4. Overall Heat-Transfer Coefficient and Fouling

The overall coefficient combines convection, wall conduction, and fouling resistances. Based on outside area for a cylindrical tube, a useful resistance expression is

where h_i and h_o are inside and outside convection coefficients, R_f,i and R_f,o are fouling factors (m²·K·W⁻¹), and R_w is the wall conduction resistance (K·W⁻¹). For a cylindrical wall,

where r_i and r_o are tube radii, k_w is wall thermal conductivity, and L is tube length.

Fouling consists of deposits such as scale, corrosion products, biological films, or process solids. It reduces heat transfer and often increases pressure drop. A design coefficient may be obtained by adding specified fouling resistances to the clean resistance. Excessive fouling allowance, however, increases area, cost, and sometimes encourages low velocities that worsen deposition.

Performance monitoring should compare the current overall conductance UA with its clean or commissioning value. A falling UA may indicate fouling, noncondensable gas, maldistribution, loss of flow, or instrumentation error. Cleaning intervals should be based on measured performance and lifecycle cost rather than calendar time alone.

5. Pressure Drop and Hydraulic Design

A thermally satisfactory exchanger may be unacceptable if it requires excessive pumping or fan power. For a straight passage, a simplified pressure-drop estimate is

where f is the Darcy friction factor, L is flow length, D_h is hydraulic diameter, ρ is density, V is mean velocity, and ΣK represents entrance, exit, bend, contraction, and expansion losses. For noncircular passages,

where A_c is flow cross-sectional area and P_w is wetted perimeter.

The Darcy friction factor depends on Reynolds number and roughness. For internal flow,

where μ is dynamic viscosity. Laminar flow in a circular tube has f=64/Re. Turbulent flow requires an appropriate correlation or the Moody diagram. At the design stage, allowable pressure drop is allocated between heat-exchanger sides, piping, control valves, and pumps.

The pumping power associated with a stream is approximately

where V̇ is volumetric flow rate and η_p is pump efficiency. Thermal optimization must therefore consider both capital cost and operating energy.

6. Major Heat-Exchanger Types

Shell-and-Tube Exchangers

A shell-and-tube exchanger contains tubes enclosed within a shell. One fluid flows through the tubes and the other through the shell side. Baffles support tubes, direct shell-side flow, and increase turbulence. Tube passes can be arranged to increase velocity and heat transfer, although additional passes increase pressure drop.

Advantages include robustness, high pressure and temperature capability, ease of mechanical cleaning on suitable surfaces, and extensive industrial experience. Limitations include relatively large volume, possible shell-side maldistribution, vibration, leakage at tube sheets, and reduced performance when fouling is severe.

Selection follows the thermal design with checks on tube velocity, shell-side velocity, vibration, tube-sheet stresses, expansion, corrosion allowance, and maintainability. TEMA practices are widely used for mechanical construction and exchanger classification, while ASME Boiler and Pressure Vessel Code Section VIII is relevant to pressure-containing design. Applicable national pressure-equipment, materials, welding, and inspection regulations must also be followed.

Plate Heat Exchangers

Gasketed plate exchangers use corrugated plates clamped in a frame. Corrugations increase turbulence and create large heat-transfer area per volume. They are compact and can be opened for cleaning, but gasket temperature and chemical compatibility limit service. Brazed or welded plate exchangers eliminate some gasket limitations but may be harder to repair.

Compact and Finned Exchangers

Compact exchangers have a high surface-area-to-volume ratio, often exceeding 700 m²·m⁻³. Fins increase air-side area where the air-side coefficient is small. Applications include automotive radiators, air-conditioning coils, gas turbines, and aircraft systems. Their small passages are sensitive to dust, blockage, frost, and maldistribution; air-side pressure loss and cleaning access are important design constraints.

Double-Pipe Exchangers

A double-pipe exchanger has one fluid in an inner tube and the other in the annulus. It is simple and suitable for small duties, high pressures, or modular arrangements. Its area-to-volume ratio is low for large duties, making shell-and-tube equipment more economical in many industrial applications.

Regenerative Exchangers

A regenerator stores heat temporarily in a matrix. Rotary regenerators use a rotating wheel, while fixed-bed regenerators alternate flow direction. Regenerators can achieve high effectiveness and compactness, especially in gas turbines and cryogenic systems. Leakage, carryover, matrix contamination, sealing, and cyclic thermal stress require careful control.

Condensers, Boilers, and Evaporators

When a fluid changes phase, latent heat dominates and the temperature may remain nearly constant. Condensers must manage condensate drainage and removal of noncondensable gases. Boilers and evaporators must account for nucleate boiling, dryout, flow instability, and pressure drop. Phase-change correlations should be selected for the fluid, orientation, regime, and pressure range rather than treating the process as single-phase convection.

7. Thermal and Hydraulic Degradation

Actual performance differs from design because of fouling, aging, corrosion, erosion, leakage, vibration, fouling-induced blockage, control-valve changes, and sensor drift. Common diagnostic indicators include:

• decreasing heat duty at unchanged flow rates;
• increasing pressure drop;
• reduced temperature approach;
• unequal temperature distribution among parallel channels;
• unexplained material balance or cross-contamination.

A useful operational workflow is to verify instruments, calculate current duty from both streams, estimate current UA, compare it with the clean baseline, and then inspect hydraulic and mechanical evidence. Cleaning should be selected according to deposit chemistry: mechanical cleaning, chemical cleaning, backflushing, hydroblasting, or replacement may be appropriate. Chemical cleaning requires compatibility and environmental controls.

8. A Standards-Based Design and Selection Procedure

A professional selection procedure is iterative:

1. Define the duty: fluid identities, flow rates, inlet temperatures, desired outlet temperatures, phase changes, operating and design pressures, and turndown.
2. Establish constraints: allowable pressure drops, materials, corrosion risks, hazardous-area classification, access, footprint, noise, and cleaning method.
3. Choose a configuration: compare counterflow, crossflow, shell-and-tube, plate, compact, or regenerative arrangements.
4. Perform the thermal calculation: use LMTD when terminal temperatures are known; use effectiveness–NTU when outlet temperatures are unknown.
5. Estimate U: include convection, wall resistance, fouling, and fin efficiency where applicable.
6. Size the area: calculate A = Q̇/(U F ΔT_lm) or A = NTU C_min/U.
7. Check hydraulics: calculate velocities, Reynolds numbers, pressure drops, and pumping or fan power.
8. Check mechanical integrity: pressure containment, thermal expansion, vibration, tube supports, seals, welding, inspection, and relief protection.
9. Evaluate lifecycle economics: capital cost, energy cost, cleaning, downtime, spares, and replacement.
10. Specify verification: factory inspection, pressure testing, performance testing, materials certification, and commissioning measurements.

Standards do not replace engineering judgment. The designer must identify the governing jurisdiction and applicable editions of pressure-vessel, piping, materials, welding, inspection, and environmental standards. Vendor guarantees should state test conditions, uncertainty, fouling assumptions, pressure-drop limits, and permitted deviations.

9. Illustrative Industrial Case: Cooling a Process Oil

Background. A process plant must cool oil from 140 °C to 90 °C using cooling water entering at 25 °C. The oil flow is 4 kg·s⁻¹ with c_p,o=2.2 kJ·kg⁻¹·K⁻¹. Water flows at 5 kg·s⁻¹ with c_p,w=4.18 kJ·kg⁻¹·K⁻¹. A shell-and-tube exchanger is being considered.

Problem. The exchanger must achieve the duty without exceeding 60 kPa pressure drop on either side. Oil is moderately fouling and must be chemically compatible with the tube material.

Analysis. The required duty from the oil is

The water temperature rise is

so the water outlet is approximately 46.1 °C. For counterflow, the terminal differences are

Thus,

Suppose a preliminary fouled coefficient of 300 W·m⁻²·K⁻¹ and correction factor F=0.95 are selected. The estimated area is

Approach and solution. A vendor evaluates a two-pass shell-and-tube arrangement with approximately 20 m² of area. The vendor checks tube-side velocity, shell-side baffle spacing, tube vibration, allowable pressure drops, fouling factors, thermal expansion, and cleaning access. If pressure drop is too high, additional parallel tubes or a larger shell may be preferable to simply reducing velocity, because very low velocity can increase fouling.

Outcome. The preliminary design is acceptable only after hydraulic and mechanical checks. Commissioning data should establish the clean UA, and operating limits should trigger cleaning when duty or pressure drop deviates beyond an agreed tolerance.

Learning points. Thermal sizing alone is insufficient. The exchanger must meet duty, approach temperature, pressure-drop, materials, inspection, maintenance, and lifecycle requirements simultaneously.

10. Contemporary Developments and Professional Practice

Additive manufacturing is enabling complex compact passages and enhanced surfaces, although certification, inspection, fatigue, and fouling remain concerns. Digital twins can combine measured temperatures, flows, and pressures with exchanger models to estimate fouling resistance and predict cleaning needs. Machine-learning systems may identify abnormal performance, but they require reliable sensors, representative historical data, and physical validation. They should support—not replace—engineering review, safety interlocks, and documented decision authority.

Sustainable design increasingly evaluates total energy, refrigerant or process-fluid leakage, material recyclability, water consumption, cleaning chemicals, and end-of-life recovery. Heat integration methods such as pinch analysis can identify opportunities to recover heat before adding new utility equipment. Designers should also consider worker exposure during cleaning, safe isolation, pressure relief, confined-space hazards, and environmental discharge requirements.

Challenges and Limitations

The principal limitations of simplified exchanger calculations are variable properties, nonuniform flow, uncertain fouling, phase-change regime transitions, imperfect correction factors, manufacturing tolerances, and uncertain operating conditions. LMTD requires known terminal temperatures and can become numerically sensitive when temperature differences are close. Effectiveness–NTU requires a reliable UA and configuration-specific relation. Neither method alone predicts local hot spots, vibration, maldistribution, erosion, or structural failure. Detailed rating software, validated correlations, computational fluid dynamics, and specialist mechanical analysis may therefore be necessary for critical equipment.

Chapter Summary

Heat exchangers transfer energy between streams through direct contact or a separating wall. Energy balances determine duty, while the LMTD method sizes an exchanger when terminal temperatures are known. The effectiveness–NTU method is valuable when outlet temperatures are unknown and expresses performance through ε, NTU, and the heat-capacity-rate ratio. Counterflow generally provides a larger temperature driving force than parallel flow, whereas crossflow and multipass arrangements require configuration-specific relations or correction factors.

The overall coefficient includes convection, wall conduction, and fouling resistances. Fouling reduces thermal performance and may increase pressure drop. A sound design therefore combines thermal sizing with hydraulic, mechanical, materials, maintenance, safety, standards, and lifecycle-economic evaluation. Shell-and-tube, plate, compact, finned, double-pipe, and regenerative exchangers each have distinct advantages and limitations. Monitoring UA, duty, temperature approach, and pressure drop supports condition-based maintenance and reliable operation.

Key Terms

Heat exchanger: Device that transfers heat between fluids at different temperatures.

Recuperator: Continuous indirect-contact heat exchanger.

Regenerator: Exchanger that temporarily stores heat in a solid matrix.

Parallel flow: Arrangement in which both fluids move in the same direction.

Counterflow: Arrangement in which fluids move in opposite directions.

Crossflow: Arrangement in which fluid streams move approximately perpendicular to each other.

LMTD: Logarithmic mean temperature difference used as an average thermal driving force.

Effectiveness: Actual heat transfer divided by the maximum possible heat transfer.

NTU: Number of transfer units, defined as UA/C_min.

Heat-capacity rate: Product of mass-flow rate and specific heat, ṁc_p.

Overall heat-transfer coefficient: Coefficient combining convection, conduction, and fouling resistances.

Fouling factor: Thermal resistance caused by deposits on heat-transfer surfaces.

Hydraulic diameter: Equivalent diameter used for noncircular passages.

Pressure drop: Reduction in fluid pressure caused by friction and fittings.

Shell-and-tube exchanger: Exchanger with tubes enclosed within a shell.

Compact exchanger: Exchanger with a high surface-area-to-volume ratio.

Correction factor: Factor adjusting ideal counterflow LMTD for multipass or crossflow arrangements.

Thermal approach: Temperature difference between a hot and cold stream at a selected terminal location.

Pinch analysis: Method for identifying heat-recovery and utility opportunities.

Review Questions

Short Answer Questions

1. Define exchanger effectiveness and explain its physical meaning.
2. Why is counterflow commonly more thermally effective than parallel flow?
3. State the main resistances included in an overall heat-transfer coefficient.
4. What is the purpose of an LMTD correction factor?
5. Name two operational indicators of exchanger fouling.

Long Answer Questions

1. Derive the energy balance for a two-stream exchanger and state its assumptions.
2. Explain the LMTD method for parallel-flow and counterflow exchangers.
3. Describe the effectiveness–NTU method and explain the roles of C_min, C_r, and NTU.
4. Compare shell-and-tube, plate, compact, and regenerative exchangers for industrial service.
5. Develop a standards-based procedure for selecting and specifying a shell-and-tube exchanger.

Analytical / Application Questions

1. A counterflow exchanger heats water from 15 °C to 55 °C at 1.5 kg·s⁻¹. The hot stream enters at 110 °C and leaves at 70 °C. If U=450 W·m⁻²·K⁻¹, calculate the duty and required clean area.
2. An exchanger shows a 15% fall in duty and a 30% rise in pressure drop at unchanged inlet conditions. Propose a diagnostic sequence and distinguish likely fouling from instrumentation or flow-control faults.
3. Select between a plate exchanger and a shell-and-tube exchanger for a high-pressure, fouling liquid service. Justify the choice using thermal, hydraulic, mechanical, maintenance, safety, and lifecycle considerations.

Multiple Choice Questions with Answers

Question 1

Which flow arrangement generally provides the greatest temperature driving force for a given pair of inlet temperatures?

A. Parallel flow

B. Counterflow

C. Single-pass crossflow only

D. Direct-contact flow only

Correct Answer: B. Counterflow

Question 2

The heat-capacity rate of a fluid stream is defined as:

A. ṁ/c_p

B. ṁc_p

C. UA/C_min

D. ρVD_h/μ

Correct Answer: B. ṁc_p

Question 3

For a heat exchanger with Q̇=200 kW, U=400 W·m⁻²·K⁻¹, and ΔT_lm=50 K, the required area, neglecting correction factors, is:

A. 5 m²

B. 10 m²

C. 20 m²

D. 40 m²

Correct Answer: C. 20 m²

Question 4

The effectiveness of a heat exchanger is the ratio of:

A. Actual heat transfer to maximum possible heat transfer

B. Pressure drop to pumping power

C. Hot-stream capacity rate to cold-stream capacity rate

D. Fouled coefficient to clean coefficient

Correct Answer: A. Actual heat transfer to maximum possible heat transfer

Question 5

Which method is especially useful when outlet temperatures are unknown during preliminary design?

A. LMTD method only

B. Effectiveness–NTU method

C. Darcy friction-factor method

D. Pinch analysis only

Correct Answer: B. Effectiveness–NTU method

Question 6

For laminar flow in a circular tube, the Darcy friction factor is:

A. Re/64

B. 64/Re

C. 4/Re

D. Re²/64

Correct Answer: B. 64/Re

Question 7

Which change normally increases the thermal resistance of an exchanger?

A. Removing deposits

B. Increasing clean surface area

C. Adding a fouling layer

D. Increasing wall conductivity

Correct Answer: C. Adding a fouling layer

Question 8

A multipass shell-and-tube exchanger uses an LMTD correction factor because:

A. The fluids have zero heat capacity

B. Its temperature pattern is not ideal counterflow

C. Pressure drop is always zero

D. The wall has no conduction resistance

Correct Answer: B. Its temperature pattern is not ideal counterflow

Question 9

If C_h=8000 W·K⁻¹ and C_c=5000 W·K⁻¹, then C_min is:

A. 3,000 W·K⁻¹

B. 5,000 W·K⁻¹

C. 8,000 W·K⁻¹

D. 13,000 W·K⁻¹

Correct Answer: B. 5,000 W·K⁻¹

Question 10

Which consideration is primarily hydraulic rather than thermal?

A. Logarithmic mean temperature difference

B. Overall heat-transfer coefficient

C. Allowable pressure drop

D. Heat-capacity-rate ratio

Correct Answer: C. Allowable pressure drop