Heat and Mass Transfer in HVAC Components

Many HVAC processes move heat and moisture at the same time: water evaporating from a cooling tower fill, condensate forming on a cooling coil, moisture sorbing into a desiccant. In each case a vapor crosses a boundary layer driven by a concentration difference, while heat crosses driven by a temperature difference, and the two are coupled because phase change absorbs or releases the latent heat. The mass transfer side has its own coefficient, analogous to the convective heat transfer coefficient, and its own rate equation:

The driving difference is a concentration difference, expressed here as mass concentration but equally writable as a partial pressure or humidity ratio difference. The surface concentration is the saturation value at the surface temperature, which is why surface temperature controls the mass transfer just as it controls the heat transfer. The coupled energy equation states that the latent heat carried by n_dot must come from (evaporation) or go to (condensation) the surface: q_latent = n_dot h_fg, where h_fg is the latent heat of vaporization at the surface temperature.

Measuring h_m directly is difficult, but the Chilton-Colburn analogy relates it to the far more familiar heat transfer coefficient. The analogy observes that heat, mass, and momentum transfer through boundary layers obey the same dimensionless form, so the j-factors for heat and mass transfer are equal:

Rearranging gives the working form engineers actually use:

For water vapor in air, the Lewis number is about 0.85, so Le^2/3 is about 0.90, close to unity. The practical result, often called the Lewis relation, is h = h_m rho c_p to a good approximation. This single relation is the hidden engine behind wet-coil analysis, cooling tower theory, and evaporative cooling calculations: it lets you get the mass transfer coefficient from the heat transfer coefficient, which means every correlation you know for h immediately gives you h_m. It is also why the psychrometric wet-bulb lines run nearly parallel to the constant-enthalpy lines: the near-unity Lewis number makes adiabatic saturation nearly isenthalpic.

The analogy has limits worth respecting. It assumes low mass transfer rates (no strong blowing or suction distorting the boundary layer), analogous boundary conditions, and constant properties. In cooling towers and coils these hold well enough for engineering work; in high-rate drying or combustion they do not. Within HVAC, the analogy is one of the most reliable shortcuts available.

Key takeaways

• Evaporation and condensation are driven by vapor concentration differences across the boundary layer, with h_m playing the role of h.
• The latent heat n_dot h_fg couples the mass transfer to the surface energy balance.
• The Chilton-Colburn analogy gives h_m from h; for air-water vapor the Lewis relation h = h_m rho c_p is accurate enough for engineering work.
• The near-unity Lewis number is why adiabatic saturation is nearly isenthalpic and why wet-bulb lines parallel enthalpy lines.

A cooling tower rejects heat by exposing warm condenser water to air, evaporating a small fraction of the water and carrying the heat away as latent heat in the exhaust air. Two temperature differences describe its operating point. The range is the cooling the water actually receives: T_w,in minus T_w,out. It is set by the heat load and the water flow rate, since q = m_dot_w c_pw x range. The approach is how close the leaving water gets to the entering air wet-bulb: T_w,out minus T_wb,in. It measures the tower's thermodynamic ambition: a small approach means the tower is pushing the water nearly to the theoretical limit.

That theoretical limit is the entering air wet-bulb temperature. No evaporative device can cool water below the wet-bulb of the air it uses, because at the wet-bulb the air is saturated and can accept no more vapor, so evaporation (and therefore cooling) stops. Tower effectiveness expresses how far the tower has moved from the entering water temperature toward that limit:

The energy balance ties the two sides together. To first order, the heat lost by the water equals the enthalpy gained by the air:

The rigorous theory behind tower sizing is Merkel's theory, which integrates the local driving enthalpy difference (the saturated-air enthalpy at the local water temperature minus the local air enthalpy) over the fill. The result is the tower characteristic, KaV/L, a dimensionless measure of the fill's transfer capability that manufacturers determine by test. Selecting a tower is then a matching exercise: the required KaV/L from the duty and the design wet-bulb must be within the fill's capability at the design air and water flows. You do not need to evaluate the Merkel integral by hand to operate this course's examples, but you should know it exists, because it is what tower selection software is computing.

The approach cannot be zero because the driving difference vanishes as the water approaches the air wet-bulb. Near the cold end of the fill, the saturated-air enthalpy at the water temperature and the actual air enthalpy converge, the local transfer rate drops toward zero, and ever more fill depth buys ever less cooling. Zero approach would require infinite transfer area. In practice, economics sets the approach: tighter approaches need larger towers, more fill, and more fan energy, while looser approaches raise the condenser water temperature and penalize the chiller. Design approaches of a few kelvin are the economic compromise, and the chiller-versus-tower trade-off (colder condenser water helps the chiller, but costs tower size) is one of the classic system optimization problems in HVAC.

Key takeaways

• Range is the water cooling achieved; approach is the distance from the wet-bulb limit; effectiveness = range/(range + approach).
• The entering air wet-bulb is the absolute floor for the leaving water temperature.
• The water-side heat loss equals the air-side enthalpy gain; Merkel's theory (KaV/L) is the rigorous sizing basis behind selection software.
• Zero approach would need infinite area; the design approach balances tower cost and fan energy against chiller efficiency.

Evaporative cooling is refrigeration without a compressor: liquid water evaporates into an air stream, and the latent heat comes from the air's sensible heat, so the air cools as it humidifies. The process is the adiabatic saturation of the psychrometrics course, and its limit is the entering air wet-bulb temperature. The available cooling potential is the wet-bulb depression, T_db minus T_wb: the larger it is, the deeper the cooling. This one number decides whether evaporative cooling is a primary system, a precooling stage, or a nonstarter.

Direct evaporative cooling evaporates water into the supply air itself. Hardware ranges from wetted media pads (rigid cellulose or fiberglass) through spray chambers to high-pressure atomizing nozzles, but the thermodynamics is the same: the air follows the wet-bulb line toward saturation, leaving cooler and more humid. Performance is quoted as a saturation effectiveness:

Indirect evaporative cooling keeps the added moisture out of the supply air. A secondary air stream is evaporatively cooled, and a heat exchanger transfers that cooling to the primary (supply) stream without moisture exchange. The primary air cools at constant humidity ratio: a horizontal move left on the chart. Effectiveness is defined against the secondary stream's wet-bulb:

Two-stage systems chain the two: indirect precooling followed by direct cooling of the already-cooled air, reaching supply temperatures below either stage's wet-bulb limit alone. On the chart the path is a horizontal move left (indirect) followed by a diagonal down-left move (direct), a dogleg that ends cooler than a single direct stage could.

Climate suitability is read from the wet-bulb depression. Hot-dry climates with depressions of 12 to 20 K give deep, economical cooling and are the natural home of direct systems. Humid climates with depressions of 2 to 4 K give almost nothing: direct cooling there adds moisture without useful temperature drop, and even indirect stages struggle. The honest design response in marginal climates is hybrid operation: evaporative stages run when the depression is favorable and are bypassed when it is not, with conventional cooling carrying the humid hours. Plotting the site's design days on the chart and measuring the depressions makes the operating strategy visible before any equipment is priced.

Water consumption is the operating cost that balances the energy saving. Every kilogram of evaporated water removes about 2400 kJ of heat, so a system delivering 100 kW of evaporative cooling evaporates roughly 150 liters per hour. In water-scarce regions this trade needs explicit evaluation: the energy saving is real, but so is the water bill and the water treatment program from the psychrometrics course's design note.

Key takeaways

• The wet-bulb depression is the available cooling potential; it decides whether evaporative cooling is primary, supplementary, or unsuitable.
• Direct cooling adds moisture to the supply air; indirect cooling does not, at the cost of a heat exchanger and lower effectiveness.
• Effectiveness predicts the leaving temperature from the entering dry-bulb and the relevant wet-bulb.
• Water consumption is the real operating cost: roughly 150 L/h per 100 kW of evaporative cooling, plus treatment.

Condensation occurs whenever a surface is colder than the dew point of the air touching it. That is the entire criterion, and every condensation problem in buildings is an instance of it: sweating ducts in an unconditioned attic, dripping chilled water pipes, mold behind furniture on a cold wall, moisture on a window frame. The analysis therefore has two halves: the dew point of the adjacent air (from the psychrometrics course) and the surface temperature (from heat transfer). Control the two so the surface stays above the dew point with margin, and condensation does not occur.

Surface temperature follows from the thermal resistance network. For an interior building surface exposed to room air on one side and outdoor conditions on the other:

The ratio R_si/R_total is the fraction of the total temperature drop that occurs at the interior surface film. Well-insulated constructions keep this fraction small and the surface warm; thermal bridges (a steel beam penetrating insulation, a concrete balcony slab, a poorly insulated window frame) create local paths with small R_total, so the surface runs cold exactly where the bridge is. Condensation therefore appears in spots and stripes that map the thermal bridges, a diagnostic pattern every building investigator recognizes.

Ducts and pipes in unconditioned spaces follow the same logic with cylindrical resistances. A supply duct carrying 13 C air through a 32 C attic with humid air will sweat on its outer surface unless insulation keeps that surface above the attic air's dew point. The check is: compute the outer surface temperature from the insulation resistance and the air-side film coefficients, compute the dew point of the surrounding air, and require T_surface greater than T_dp with a margin of a few kelvin for safety. Vapor retarders on the warm side of the insulation prevent a second failure mode: vapor diffusing into the insulation and condensing inside it, which wets the insulation from within and destroys its resistance.

Cooling coils are the intentional exception: their surfaces are designed to run below the dew point, and the condensate is collected and drained by design. The distinction between a coil and a sweating duct is not the physics but the management: the coil has a drain pan, a trap, and a drain line; the duct does not. Design measures for unwanted condensation are therefore: insulate to keep surfaces warm, place vapor retarders correctly (warm side in heating climates), break thermal bridges, control indoor humidity at its source, and where cold surfaces are unavoidable, give the condensate a managed path.

Key takeaways

• Condensation occurs when surface temperature falls below the adjacent air's dew point; check both halves of the criterion.
• Surface temperature follows from the resistance network; thermal bridges create local cold spots where condensation strikes first.
• Ducts and pipes in unconditioned spaces need insulation plus a warm-side vapor retarder, with sealed joints.
• Coils are intentional condensing surfaces with managed drainage; every other cold surface needs prevention, not drainage.

Vapor-compression dehumidification cools air below its dew point and drains the condensate. It is simple and efficient for ordinary comfort duty, but it struggles where the required dew point is very low, where the latent load dominates the sensible load, or where overcooling plus reheat wastes too much energy. Desiccant dehumidification takes a different route: it removes moisture by sorption onto or into a desiccant material, without cooling the air to saturation. The trade is heat: the desiccant must be regenerated with thermal energy, so desiccants win where heat is cheap and deep dehumidification is valuable.

The cycle has two halves. In the process (sorption) step, humid air passes through the desiccant, water vapor is sorbed, and the air leaves drier. Sorption releases the heat of sorption (slightly larger than the latent heat of condensation), so the process air leaves warmer as well as drier: on the chart it moves down and to the right. In the regeneration step, a separate heated air stream passes through the moisture-laden desiccant, driving the water back off into the regeneration air, which leaves hot and humid and is exhausted. The desiccant then returns to the process stream, and the cycle repeats. Energy enters as regeneration heat; moisture leaves in the exhaust.

Solid desiccant systems use a rotary wheel: a honeycomb matrix coated with silica gel, molecular sieve, or another sorbent, rotating slowly between the process and regeneration air streams. The wheel is compact, has no liquid to manage, and is the dominant form in commercial and industrial air handlers. Liquid desiccant systems circulate an absorbent salt solution, typically lithium chloride or lithium bromide, over a contactor: process air gives up moisture to the strong solution, and a regenerator reconcentrates the diluted solution with heat. Liquid systems handle very large moisture loads, allow the absorption and regeneration to happen in separate locations, and store the solution as a form of latent energy storage, at the cost of managing a corrosive liquid and preventing carryover droplets into the supply air.

Desiccants beat vapor compression in specific territory. Low dew point requirements (below about 0 to 5 C, where refrigeration coils frost and lose capacity) belong to desiccants: ice rinks, cold storage, dry rooms for battery or pharmaceutical manufacturing. Latent-heavy loads with little sensible load (supermarkets with open refrigerated cases, humid-climate ventilation air) favor desiccants because vapor compression would overcool severely. And wherever waste heat, solar thermal, or combined heat and power provides cheap regeneration heat, the operating economics tilt strongly toward desiccants. The moisture removal in every case follows the same accounting as any dehumidifier: m_dot_w = m_dot_a (omega_in - omega_out), with the energy cost appearing as regeneration heat rather than compressor power.

Key takeaways

• Desiccants remove moisture by sorption and release it in a heated regeneration stream; the process air leaves drier and warmer.
• Solid desiccant wheels dominate commercial duty; liquid desiccants (lithium chloride or bromide) suit very large loads and allow separate regeneration.
• Desiccants win at low dew points, latent-dominated loads, and where cheap regeneration heat is available.
• Always account for the downstream cooling of the warmed process air; the wheel plus cooling stage is the real system.

This session checks a complete tower operating point the way a field engineer would: from a few measured temperatures and flows, derive everything else and test for consistency. The data: a mechanical-draft tower serves a chiller plant with 10.0 kg/s of condenser water entering at 35 C and leaving at 30 C. The entering air is at 30 C dry-bulb and 26 C wet-bulb. Atmospheric pressure is 101.325 kPa. The task: confirm the effectiveness, estimate the air flow, and estimate the evaporation (makeup) rate.

Step 1 is the operating point. Range = 35 - 30 = 5 K. Approach = 30 - 26 = 4 K. Effectiveness = 5/(5 + 4) = 0.556. Heat rejected: q = 10.0 x 4.18 x 5 = 209 kW. These three numbers already tell the story: the tower is doing a moderate 5 K of cooling, sitting 4 K above the wet-bulb limit, at 55.6 percent of the thermodynamic maximum.

Step 2 is the air side. Entering air at 30 C dry-bulb and 26 C wet-bulb has omega_in = 0.01970 kg/kg and h_in = 80.56 kJ/kg (from the psychrometric relations of the earlier course). For the leaving air, assume it exits near saturation at 31 C, a reasonable field assumption since tower exhaust typically leaves close to saturation a few degrees below the entering water temperature. Saturated air at 31 C: omega_out = 0.02888 kg/kg, h_out = 105.09 kJ/kg. From the energy balance, the air flow is m_dot_a = q/(h_out - h_in) = 209/(105.09 - 80.56) = 209/24.53 = 8.52 kg/s. The water-to-air ratio is L/G = 10.0/8.52 = 1.17, a plausible operating point for a mechanical-draft tower.

Step 3 is the water loss. The air picks up moisture equal to the humidity ratio rise: m_dot_evap = m_dot_a (omega_out - omega_in) = 8.52 x (0.02888 - 0.01970) = 8.52 x 0.00918 = 0.0782 kg/s, which is 282 liters per hour. Step 4 is the cross-check: nearly all the rejected heat leaves as latent heat of the evaporated water, so m_dot_evap should be close to q/h_fg. With h_fg about 2430 kJ/kg near 28 C: 209/2430 = 0.0860 kg/s, or 310 L/h. The two estimates agree within 10 percent, which is the expected accuracy given the leaving-air assumption; the small difference is the sensible portion of the transfer. The makeup water system must therefore supply roughly 280 to 310 L/h at full load, plus blowdown and drift.

Key takeaways

• A tower check runs: range, approach, effectiveness, heat rejected, air flow from the air-side balance, evaporation from the moisture balance.
• Cross-check evaporation against q/h_fg; agreement within about 10 percent confirms the assumptions.
• Makeup must cover evaporation plus blowdown and drift; evaporation alone is roughly the heat rejected divided by the latent heat.
• Tower performance is always relative to the entering wet-bulb at the inlet; quote the design wet-bulb with every performance claim.

Cooling towers, evaporative condensers, and evaporative coolers all share one feature that sets them apart from closed HVAC equipment: warm water in contact with air, recirculated for long periods. That environment concentrates dissolved minerals through evaporation, accumulates airborne dust and nutrients, and sits in the temperature band where biological growth thrives. Left unmanaged, the consequences are fouled fill and reduced heat transfer (Session 5 of the heat exchanger course), corroded basins and piping, and the growth of Legionella bacteria, which cause Legionnaires' disease when inhaled in water aerosols. None of this is mysterious, and all of it is manageable with a disciplined program. This session is deliberately practical and brief: the goal is awareness and correct practice, not alarm.

Legionella pneumophila is a naturally occurring water bacterium. It becomes a health concern when three conditions coincide: water temperatures in the growth range (roughly 20 to 45 C, the exact band every cooling tower operates in), the presence of nutrients and biofilm that shelter it, and aerosol generation that can carry contaminated droplets to people. Cooling towers generate aerosols by design (drift), which is why they receive the most attention, but any warm stagnant water with a spray or mist pathway deserves the same discipline. The engineering response is to break at least one leg of that triangle everywhere: keep water treated so biofilm cannot establish, avoid stagnation and dead legs where treatment cannot reach, and control drift with well-maintained drift eliminators.

A sound water management program has a written plan, assigned responsibility, and verification, not just chemical drums. Its elements: a treatment regime matched to the water chemistry (scale and corrosion inhibitors, plus biocides or other disinfection, dosed by a qualified water treatment provider); bleed or blowdown control to limit mineral concentration, since evaporation concentrates everything left behind; scheduled physical cleaning of basins, fill, and sumps, because treatment suppresses growth but does not remove sediment and debris; drift eliminator inspection and maintenance; elimination of dead legs and stagnant branches in the piping; and routine monitoring (dip slides or laboratory testing for bacteria, plus treatment parameter logs) with defined response thresholds. When a system is shut down seasonally, the startup procedure matters as much as the operating program: stagnant warm water sitting for months is the highest-risk condition, and recommissioning should include cleaning, disinfection, and verification before the tower returns to service.

The governing references are public and specific. ASHRAE Guideline 12, "Managing the Risk of Legionellosis Associated with Building Water Systems," is the industry's central document for water management programs in buildings, and it covers cooling towers alongside domestic water systems. Local regulations may add registration, testing, or reporting requirements for cooling towers, so the program should be checked against the jurisdiction's current rules. Designers contribute by specifying equipment that can be cleaned (access to basins and fill, cleanable surfaces), providing water treatment connections and monitoring points, eliminating dead legs in the layout, and documenting the water management requirements in the handover package so the operating team inherits a program, not a surprise.

Key takeaways

• Open evaporative equipment needs active water management: treatment, blowdown, cleaning, and monitoring, with assigned responsibility.
• Legionella risk is controlled by breaking the growth triangle: treated water without biofilm, no stagnation, and controlled drift.
• Seasonal shutdown and startup are the highest-risk transitions; recommission with cleaning, disinfection, and verification.
• ASHRAE Guideline 12 is the central industry reference; check local regulations for additional tower requirements.