Heat Exchangers for HVAC

Nearly every HVAC system is a chain of heat exchangers. A chiller rejects heat through a condenser, delivers cooling through an evaporator, and distributes it through coils; a boiler adds heat through its own exchanger; heat recovery devices move energy between air streams. The underlying physics is the same everywhere, but the hardware families differ because the fluids differ: water to water, refrigerant to water, and air to water each impose different constraints on pressure, fouling tolerance, and surface area.

Plate heat exchangers are the default choice for water-to-water duty in modern buildings: chiller or boiler isolation, condenser water heat recovery, and district energy interfaces. Two families exist. Gasketed plate exchangers use a pack of corrugated stainless plates clamped in a frame; they achieve very high overall coefficients because the corrugations trip the boundary layer at low Reynolds numbers, and they are almost always arranged in true counterflow, which is the most effective flow arrangement. Brazed plate exchangers fuse the plates with copper, which removes the gaskets and the frame, making them compact and inexpensive for smaller duties such as domestic hot water or small heat recovery loops, at the cost of being unserviceable: they cannot be opened for cleaning. The practical trade-off is therefore serviceability and temperature or pressure limits (gaskets set the limit) against compactness and cost.

Finned-tube coils are the air-side workhorse: cooling coils, heating coils, and reheat coils in air handlers, fan coils, and unit ventilators. Air has a low convective coefficient, so the air side needs far more surface area than the water or refrigerant side; fins provide it. Coils are inherently crossflow devices: air passes across banks of tubes while water flows inside the tubes, usually in a serpentine multipass circuit. The air is effectively mixed as it crosses the coil while the water in each tube pass is unmixed, a distinction that matters when we reach the epsilon-NTU method in Session 3.

Shell-and-tube exchangers appear where robustness matters more than compactness: chiller evaporators and condensers (flooded or direct expansion), steam-to-water converters, and some heat recovery applications. They tolerate poor water quality better than plate exchangers because the tubes can be mechanically cleaned, and they handle high pressures comfortably. Their overall coefficients are lower than a plate exchanger of similar duty, and they are larger and heavier, which is why they have lost the general water-to-water market to plates but remain standard inside packaged chillers.

Run-around loops solve a specific problem: recovering heat between an exhaust air stream and an outdoor air stream that are not adjacent, so a single air-to-air device cannot be used. Two finned-tube coils are connected by a pumped loop, usually with a glycol solution, and heat is carried from one coil to the other. The effectiveness is moderate compared with a plate or wheel in a single air handler, but the ability to bridge long distances and to keep the two air streams completely separate (no cross-contamination) makes run-around loops common in retrofit work and in applications such as laboratories or hospitals where exhaust must never mix with supply.

Flow arrangement deserves its own attention because it sets the ceiling on what any exchanger can do. In parallel flow, both streams enter at the same end; the temperature difference is largest at the inlet and decays along the length, and neither outlet can cross the other stream's outlet temperature. In counterflow, the streams enter at opposite ends; the temperature difference stays more uniform along the length, the cold stream can leave hotter than the hot stream leaves (a temperature cross, impossible in parallel flow), and for a given duty the required surface area is smallest. In crossflow, one stream moves perpendicular to the other; performance sits between parallel and counterflow. Coils are crossflow by construction, plates are counterflow by construction, and shell-and-tube units are a hybrid that the correction factor F in Session 2 accounts for.

This energy balance is the starting point of every heat exchanger calculation. It says the heat lost by one stream equals the heat gained by the other, assuming negligible loss to the surroundings. It is independent of flow arrangement, which is why the same equation opens the analysis of plates, coils, and shells alike.

Key takeaways

• Plate exchangers dominate water-to-water duty; finned-tube coils dominate air-side duty; shell-and-tube remains standard inside chillers and for dirty water; run-around loops recover heat between distant air streams.
• Counterflow gives the best thermal performance and allows temperature cross; parallel flow is the weakest arrangement; crossflow sits between and is the natural arrangement for coils.
• The stream energy balance q = m_dot c_p deltaT applies to every type and is always the first equation to write.
• Equipment choice is driven by the fluid pair, fouling risk, serviceability, and pressure or temperature limits, not by thermal performance alone.

When all four terminal temperatures of a heat exchanger are known, or when a design targets specific outlet temperatures, the log mean temperature difference (LMTD) method is the natural tool. It answers the question: given the temperatures in and out, how much surface area (or overall coefficient) does the duty require? The method rests on a differential energy balance. Consider a small slice of a counterflow exchanger: the hot stream loses d q = -C_h dT_h and the cold stream gains d q = C_c dT_c, where C = m_dot c_p is the heat capacity rate. The same d q crosses the wall by convection, d q = U (T_h - T_c) dA. Eliminating d q and integrating from one end to the other, with U and the capacity rates treated as constant, yields a logarithmic relationship between the end temperature differences. The effective mean driving difference is not the arithmetic average but the log mean, which is always smaller than the arithmetic mean and collapses to it only when the two end differences are nearly equal.

The correction factor F repairs the one fiction in the derivation: real exchangers are rarely true counterflow. A shell-and-tube unit with one shell pass and two tube passes, or a crossflow coil, has a more complex temperature field, and its true mean difference is lower than the counterflow LMTD computed from the same four terminal temperatures. F is a function of two dimensionless temperature ratios, conventionally P and R, and is read from standard charts (or evaluated from published analytical expressions) for each configuration:

P measures how far the cold stream has moved toward the hot inlet temperature; R measures the imbalance of capacity rates. On the F chart, F starts at 1 when P is small and falls as P grows, dropping steeply near the point where the configuration can no longer achieve the specified temperatures at all. That steep drop is physically meaningful: it marks a temperature cross that the given pass arrangement cannot support, and it is a warning that the design is infeasible, not just inefficient. A common rule of thumb in practice is to keep F above about 0.75; below that, add passes or switch to a purer counterflow arrangement.

LMTD is the right tool when the terminal temperatures are the knowns: sizing a new exchanger for specified inlets and outlets, or checking whether a proposed selection can meet the temperatures. It is the wrong tool when the outlets are unknown, which is the rating problem: given an existing exchanger, inlet conditions, and flow rates, what comes out? That problem is iterative under LMTD because the LMTD itself depends on the unknown outlets. The epsilon-NTU method of Session 3 was developed precisely to solve the rating problem directly.

Key takeaways

• LMTD is the correct mean driving temperature when terminal temperatures are known; it derives from integrating the differential energy balance with constant U.
• The correction factor F accounts for non-counterflow arrangements; it depends on P and R and falls steeply when the configuration cannot meet the specified temperatures.
• Keep F above roughly 0.75 in design; a low F signals a feasibility problem, not just a sizing penalty.
• Use LMTD for sizing with known outlets; switch to epsilon-NTU for rating with unknown outlets.

The epsilon-NTU method reframes the heat exchanger problem around a simple question: of the heat transfer that thermodynamics allows, what fraction does this exchanger actually achieve? The maximum possible rate, q_max, would be reached by an infinitely large counterflow exchanger, in which the stream with the smaller heat capacity rate (C_min) undergoes the full inlet-to-inlet temperature difference. No finite exchanger can exceed it, and every real exchanger achieves some fraction of it. That fraction is the effectiveness, epsilon, and it depends only on two dimensionless groups: the number of transfer units (NTU), which measures exchanger size relative to the flow, and the capacity ratio C_r, which measures the imbalance between the streams.

NTU has an intuitive reading: it is the size of the exchanger measured in units of the flow it serves. NTU = 1 means the conductance equals the smaller capacity rate; NTU = 3 is a large exchanger for its duty. Effectiveness rises with NTU but with diminishing returns, and the capacity ratio sets the ceiling: as C_r approaches 1 (balanced flows), the maximum effectiveness of a finite exchanger falls, because the two streams' temperatures converge along the length and the driving difference erodes.

The central results are the effectiveness relations, one per flow arrangement. For counterflow:

For parallel flow:

When one fluid changes phase (a condenser or evaporator), its effective capacity rate is infinite, so C_r = 0, and every arrangement collapses to the same simple relation:

This last relation is heavily used in HVAC: chiller evaporators and condensers, and steam heating coils, are all C_r = 0 devices to a good approximation. For crossflow with the C_min fluid mixed and the C_max fluid unmixed, which describes a typical coil where air is the minimum-capacity stream:

The rating procedure is then direct: compute C_min, C_r, and NTU from the known hardware and flows, evaluate epsilon for the arrangement, compute q = epsilon q_max, and back out the outlet temperatures from the stream energy balances. No iteration is needed, which is the method's entire point.

One caution specific to HVAC: the relations above are sensible-heat relations. A cooling coil that dehumidifies is a combined heat and mass transfer device, and its "effectiveness" on a temperature basis understates the total duty. Enthalpy-based formulations exist for wet coils, and Session 4 treats the coil problem properly. Use epsilon-NTU for dry coils, heating coils, and water-to-water exchangers, and treat wet cooling coils with the apparatus dew point method instead.

Key takeaways

• Effectiveness is the fraction of the thermodynamic maximum achieved; it depends only on NTU and C_r for a given arrangement.
• Counterflow gives the highest effectiveness for given NTU and C_r; parallel flow the lowest; phase-change on one side (C_r = 0) gives epsilon = 1 - exp(-NTU) for any arrangement.
• Epsilon-NTU solves the rating problem (unknown outlets) directly, without iteration, which is why it is preferred for checking existing equipment and off-design operation.
• The standard relations are sensible-heat relations; wet cooling coils need the enthalpy-based treatment of Session 4.

A cooling coil does two jobs at once. It cools the air (sensible duty) and, whenever the coil surface is colder than the dew point of the entering air, it condenses moisture out of the air (latent duty). The split between the two is the sensible heat ratio, SHR = q_sensible / q_total, and it is one of the most consequential numbers in air-side design: it determines the leaving humidity, the condensate load on the drain system, and whether the space ends up comfortable or clammy. A coil selected only on total capacity can easily miss the latent target, which is why coil analysis works in enthalpy, not just temperature.

The classical way to think about a cooling coil is the apparatus dew point model. Imagine the coil as a device that brings a fraction of the air into perfect contact with a surface at the apparatus dew point temperature, T_ADP, while the remaining fraction bypasses the coil untouched. The bypass factor, BF, is the bypassed fraction; the contact factor (1 - BF) is the fraction that reaches the ADP state. The leaving air is then a mixture of entering air and saturated air at the ADP:

The ADP is not a physical temperature you can measure on the coil; it is the effective surface temperature that makes the model match the coil's performance. Deep coils (more rows) drive the BF down and the ADP closer to the chilled water temperature, which increases both total capacity and the latent fraction. On a psychrometric chart, the coil process is a straight line from the entering state toward the ADP point on the saturation curve, and the leaving state sits on that line at a distance set by the bypass factor. This straight-line construction is the workhorse of coil selection, and it is why Session 4 of the psychrometrics course revisits the same geometry from the chart side.

Total, sensible, and latent duties follow from the air enthalpies and temperatures:

Coil geometry is a three-way trade-off between rows, fin spacing, and face velocity. More rows mean more surface, lower bypass factor, lower ADP, and more latent capacity, but also higher air-side pressure drop, higher cost, and a deeper coil that is harder to drain. Tighter fin spacing (more fins per inch) adds surface cheaply but raises pressure drop faster than it adds duty, traps dirt, and impedes condensate drainage; wide spacing drains and cleans better but needs more rows for the same duty. Face velocity ties it together: high velocity shrinks the coil but risks condensate carryover (water blown off the fins into the duct) and noise, while low velocity needs a larger, more expensive coil. Heating coils escape most of this complexity because there is no condensation: the analysis is dry, temperature-based, and the epsilon-NTU relations of Session 3 apply directly.

Key takeaways

• A cooling coil delivers sensible plus latent duty; the split (SHR) controls the leaving humidity and must match the room requirement.
• The ADP and bypass factor model predicts leaving conditions from a straight-line process toward the saturation curve; deeper coils lower both BF and ADP.
• Rows, fin spacing, and face velocity trade capacity against pressure drop, drainage, fouling, and carryover risk.
• Heating coils are dry devices and can be analyzed with the sensible epsilon-NTU relations; cooling coils need the enthalpy-based ADP method.

A heat exchanger never performs as well in year five as it did on the day it was commissioned, and the main reason is fouling: the accumulation of unwanted material on heat transfer surfaces. On the water side, the culprits are scale (mineral deposits from hard water, accelerated at hot surfaces), biological growth (biofilm and algae in warm, nutrient-bearing water), corrosion products, and settled sediment. On the air side, the culprits are dust, fibers, and in kitchens or industrial settings, grease films that coat fins and blind the passages between them. Each layer adds a conductive resistance in series with the convective resistances, and because the layers grow with time, the overall coefficient is a moving target.

The standard way to account for fouling in design is the fouling resistance, R_f, expressed in m² K/W, which adds directly to the other resistances in the overall coefficient:

In full form, the resistance network reads 1/U = 1/h_hot + R_f,hot + R_wall + R_f,cold + 1/h_cold, with each term referred to a consistent area. The practical consequence is nonlinear: a fouling resistance that looks small next to a dominant air-side resistance barely matters, but the same resistance on the water side of a plate exchanger, where the convective resistances are small, can cut the overall coefficient dramatically. This is why water-side fouling is the design driver for plate and shell-and-tube selection, while air-side fouling dominates coil maintenance.

Fouling also attacks performance through a second channel: hydraulic degradation. Scale roughens tubes and narrows passages, and dirty fins raise air-side pressure drop, so the system delivers less flow at the same pump or fan power. A fouled coil therefore suffers twice, once thermally and once hydraulically, and field symptoms (rising approach temperatures, falling flows, higher pump or fan energy) usually show the combined effect. When a chiller's condenser approach temperature creeps upward over the cooling season, waterside fouling is the first suspect; when a coil's air pressure drop rises while its duty falls, the fins are dirty.

Design defenses start with water treatment: filtration or strainers to remove suspended solids, chemical treatment or softening to control scale and biological growth, and velocities kept high enough to discourage settling but low enough to avoid erosion. Equipment choices matter too: gasketed plates can be opened and cleaned, shell-and-tube units accept tube brushing, and coils should be specified with fin spacing and access that allow real cleaning, not just theoretical cleaning. Maintenance defenses are scheduled cleaning, coil washing with proper chemicals and low-pressure water (high pressure folds fins), and monitoring approach temperatures as the early warning signal. Industry references such as TEMA publish suggested fouling resistances for design; use them as the starting allowance, and remember they represent an end-of-run condition, not the commissioning day.

Key takeaways

• Fouling adds a series thermal resistance; its impact is largest where the clean resistances are smallest, typically the water side of compact exchangers.
• Degradation is both thermal (lower U) and hydraulic (higher pressure drop, lower flow); field symptoms usually show both.
• Size on the fouled coefficient with a documented allowance; provide temperature monitoring on all terminals to track drift.
• Water treatment, cleanable equipment choices, and scheduled cleaning are the three lines of defense.

This session puts Sessions 1 through 5 together in a single realistic check. A proposed cooling coil for an air handler must handle 1.50 m³/s of air entering at 27 C dry-bulb and 19.5 C wet-bulb, leaving at 13 C dry-bulb and 12.5 C wet-bulb. Chilled water is available at 7 C with a 5 K design rise. Standard atmospheric pressure is 101.325 kPa. The task: verify the total duty, the sensible and latent split, the required water flow, the approach, and the condensate rate.

Step 1 is the air state points. From the wet-bulb equation, the entering humidity ratio is omega_in = 0.01117 kg/kg and the entering enthalpy is h_in = 55.65 kJ/kg; the leaving humidity ratio is omega_out = 0.00883 kg/kg and the leaving enthalpy is h_out = 35.37 kJ/kg. (These follow from the saturation-pressure relations and the adiabatic saturation formula developed in the psychrometrics course; the method is shown in full there.) The entering specific volume is about 0.865 m³/kg, so the dry air mass flow is m_dot_a = 1.50 / 0.865 = 1.73 kg/s.

Step 2 is the duty. Total: q_total = 1.73 x (55.65 - 35.37) = 35.2 kW. Sensible: q_sensible = 1.73 x 1.027 x (27 - 13) = 24.9 kW, using c_p,m = 1.006 + 1.86 x 0.01117 = 1.027 kJ/(kg K). Latent: q_latent = 35.2 - 24.9 = 10.3 kW. The sensible heat ratio is SHR = 24.9/35.2 = 0.71. For a typical office application this split is reasonable; for a space with high latent load (a kitchen, a humid climate, high occupancy), an SHR of 0.71 might leave humidity uncontrolled, and the coil would need to run colder or deeper.

Step 3 is the water side. The required chilled water flow is m_dot_w = q / (c_p,w x deltaT_w) = 35.2 / (4.18 x 5) = 1.68 kg/s, leaving the coil at 12 C. The approach temperature, defined here as the leaving air temperature minus the entering water temperature, is 13 - 7 = 6 K. A 6 K approach is a healthy, achievable value for a multi-row coil; an approach under 3 K would signal an oversized or unrealistically rated coil, while an approach above 8 to 10 K suggests too few rows or fouled surfaces.

Step 4 is the moisture accounting. The condensate rate is m_dot_cond = m_dot_a (omega_in - omega_out) = 1.73 x (0.01117 - 0.00883) = 0.00406 kg/s, which is about 14.6 liters per hour. The drain pan, trap, and drain line must carry this continuously at peak load, with margin. Finally, if the coil's bypass factor is taken as BF = 0.15 (a plausible value for a six-row coil at normal face velocity), the apparatus dew point follows from h_ADP = (h_out - BF x h_in)/(1 - BF) = (35.37 - 0.15 x 55.65)/0.85 = 31.79 kJ/kg, which corresponds to a saturation temperature of about 11.1 C. The ADP sits 4.1 K above the entering water temperature, a consistent picture: the effective surface temperature must lie between the water inlet and the air outlet, closer to the water.

Key takeaways

• A coil check runs: state points, air mass flow, total/sensible/latent duty, water flow, approach, condensate, and ADP, in that order.
• The SHR of the coil must be at or below the SHR the space requires, or humidity control is lost even when temperature control is fine.
• Approach temperature is a quick sanity check on coil depth and fouling: very small means overstatement, very large means undersized or dirty.
• Condensate rate sizes the drainage; it is continuous at peak and needs margin.

A heat exchanger that was selected correctly can still fail in service if it was never verified. Commissioning is the discipline of proving, with measurements, that the installed equipment does what the design assumed. For heat exchangers the verification set is small and powerful: air and water flow rates, the four terminal temperatures, and the resulting approach temperatures, all compared against the design values from the selection.

Airflow verification comes first because every air-side duty scales with it. A duct traverse with a pitot tube, or a calibrated flow hood at the terminals with the system summed, establishes the actual flow; compare it with the design flow and with the fan's expected operating point. If the flow is low, the causes rank roughly as: dampers closed or misadjusted, filters loaded, duct leakage, fan running backward or on the wrong speed, and finally a fan that was simply undersized. Do not accept a coil's performance until the airflow is proven, because a coil starved of air will show a deceptively good leaving temperature while delivering far less than the design duty.

Water flow verification uses the circuit's balancing valves, an ultrasonic flow meter clamped on the pipe, or the pump differential pressure checked against the pump curve. The measured flow sets the water-side capacity rate, and with the terminal temperatures it closes the energy balance: q = m_dot_w c_p,w deltaT_w should match the air-side q = m_dot_a (h_in - h_out) within measurement tolerance. A mismatch larger than about 10 percent means something is wrong with the measurements or with the system (for example, a three-way valve bypassing, or air in the coil). Approach temperatures are the fouling and sizing diagnostic: record all four terminals with calibrated instruments under steady full-load conditions and compare with the selection sheet. A rising approach over time is the signature of fouling; an approach that was never as tight as selected points to low flows or an optimistic rating.

Controls deserve equal attention. Verify that control valves stroke fully and actually shut off (a leaking chilled water valve destroys both energy performance and dehumidification), that the valve authority is reasonable so the valve can modulate rather than hunt, that freeze protection is in place and tested on outdoor air coils, and that temperature sensors are calibrated: a sensor reading 2 K high will make a perfect coil look like a failing one. Drain pans need visible slope to the drain, trapped drains that hold their seal under the fan pressure, and drain lines that actually run downhill all the way.

Maintenance preserves what commissioning proved. Filters are the first line of coil defense: change them on pressure drop, not on a calendar alone, and never run the system without them. Coils should be inspected and cleaned on a schedule set by the environment, using low-pressure water and appropriate coil cleaners, never high-pressure washers that fold fins. Water treatment must be verified as a program, not assumed from a chemical drum sitting in the mechanical room: test the water. Strainers should be pulled and cleaned on a schedule, especially in the first year when construction debris is still migrating through the piping. And the approach temperatures recorded at commissioning become the baseline: re-measure them seasonally, and treat a steady drift as a work order, not a curiosity.

Key takeaways

• Commissioning proves the design with measurements: flows, four terminal temperatures, and approach temperatures compared against the selection.
• Close the energy balance between the two sides; a mismatch beyond tolerance means bad data or a real system fault, and it tells you which side to investigate.
• Rising approach temperature over time is the fouling signature; an approach that never met the selection points to flows, ratings, or controls.
• Maintenance is filters, coil cleaning, water treatment verification, strainers, and seasonal approach-temperature trending against the commissioning baseline.