Heat Transfer in Cooling Coils

Chilled-water cooling coils are finned-tube heat exchangers consisting of rows of tubes (usually copper) that pass through sheets of formed fins (usually aluminium). As air passes through the coil and contacts the cold fin surfaces, heat transfers from the air to the water flowing through the tubes.

The following equation quantifies the heat-transfer process:

Q = U × A × LMTD

Where,
Q = amount of heat transferred, Btu/hr (W)
U = heat-transfer coefficient, Btu/hr • ft² • °F (W/m² • °K)
A = effective surface area for heat transfer, ft² (m²)
LMTD = log-mean temperature difference across the coil surface, °F (°C)

Increasing any one of these variables (heat-transfer coefficient, surface area, or log-mean temperature difference) results in more heat transfer.

Arguably the most effective way to improve heat-transfer performance is to increase the log-mean temperature difference (LMTD). In the context of a chilled-water cooling coil, LMTD describes the difference between the temperatures of the air passing across the coil fins and the water flowing through the coil tubes:

LMTD = (TD2TD1) / ln (TD2 / TD1)

Where;
TD1 = leaving-air and entering-water temperature difference at the coil (°C)
TD2 = entering-air and leaving-water temperature difference at the coil (°C)

One way to increase LMTD is to supply the coil with colder water.

Heat-transfer coefficient, Q = U × A × LMTD
Also called U-value or thermal transmittance value, the heat-transfer coefficient describes the overall rate of heat flow through the coil. Three factors determine this rate:

• Airside film coefficient describes the “barrier” (resistance to heat transfer) between the passing air stream and the fin surfaces
• Waterside film coefficient describes a similar “barrier” between the inside surfaces of the copper tubes and the circulating fluid
• Thermal conductance describes the rate at which heat flows through the aluminium fins and copper tubes of the coil

System designers can do little to affect thermal conductance, but they can alter the film coefficients. Increasing the rate of airflow reduces heat-transfer resistance on the air side of the cooling coil. Likewise, increasing the water velocity reduces the waterside resistance to heat transfer.

Fin geometry can improve the overall heat-transfer coefficient, too, by lessening the airside film coefficient. Like velocity, fin geometry can be specified as part of the design of the HVAC system. For comfort-cooling applications, coil fins are usually stamped into waveforms resembling corrugated cardboard. These waveforms create turbulence in the passing air stream, which lessens the resistance to heat transfer. More exaggerated waveforms produce more turbulence.

Turbulent water flow, like turbulent airflow, also reduces resistance to heat transfer. And, like fin geometry, it can become an important criterion for coil selection. Waterside turbulence can be created by metal ribbons or inside the tubes. Called turbulators, these devices create eddies as the water flows across them.

Both methods of improving the heat-transfer coefficient (increased velocity and turbulence) create higher pressure drops, which can mean additional fan or pump power.

Coil surface area, Q = U × A × LMTD

The third determinant of heat transfer is the coil’s surface area. Typically, fin spacing for comfort heating or cooling ranges from 24 to 50 fins per metre. Spacing the fins closer together multiplies the surface area by permitting more fins per linear unit. Although the airside pressure drop may increase, adding fins extends the available surface area without affecting the overall size of the coil.

Adding rows of tubes also increases the heat-transfer surface area. Most coils are constructed with same-end connections, so rows are usually added in pairs. The weight and cost of the coil increase accordingly, but the airside pressure drop may not. (Wider fin spacing often accompanies the decision to add rows.)

The best way to extend the surface area for heat transfer is to decrease the face velocity of the coil, that is, face area relative to airflow:

face velocity = airflow / face area

Face velocity can be reduced in one of two ways: by increasing the size of the coil or (paradoxically) by reducing the required airflow. Selecting a physically larger coil increases the initial investment in the coil and the air handler, and may also enlarge the air-handler footprint ... seldom desirable outcomes. So, how can we reduce the required airflow without sacrificing coil capacity?

Improving Coil Performance

Lowering the supply air temperature reduces the amount of air required for sensible cooling and saves fan energy. From our review of the heat-transfer equation, we know that: less airflow increases airside film resistance, which reduces heat-transfer coefficient U; and requires colder air, which decreases LMTD.

To compensate for the negative effects on coil performance that accompany less airflow, we must find a way to increase U (heat-transfer coefficient) and/or A (surface area). In other words, we must select a cooling coil with better-than-average heat-transfer characteristics.

Increase U
Recall that turbulent flow reduces the film resistance to heat transfer. Choosing a fin configuration with a more pronounced waveform and/or adding turbulators inside the coil tubes will improve the heat-transfer coefficient.

Increase A
Any additional increase in heat-transfer capacity must be achieved by physically increasing the available surface area; that is, by: