LMTD Formula for Heat Exchangers and HVAC Coils

LMTD formula applied to a microchannel HVAC heat exchanger coil

Temperature difference drives heat transfer, but that difference changes as fluids move through a heat exchanger. The LMTD formula accounts for this shifting gradient by calculating an effective average temperature difference. Engineers use LMTD to estimate heat transfer capacity, evaluate flow arrangements, and support the selection of HVAC and refrigeration coils.

What is the LMTD Formula?

LMTD stands for logarithmic mean temperature difference. The standard heat exchanger LMTD formula is:

\text{LMTD} = \frac{\Delta T_1 – \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)}

Where:

Symbol	Meaning
LMTD	Logarithmic mean temperature difference
ΔT₁	Temperature difference between the fluids at one end
ΔT₂	Temperature difference between the fluids at the other end
ln	Natural logarithm

LMTD can be expressed in degrees Fahrenheit or degrees Celsius. Use the same temperature scale for every reading in the calculation.

The formula remains the same for counterflow and parallel-flow heat exchangers. The difference is how the inlet and outlet temperatures are paired.

LMTD Formula for Counterflow and Parallel Flow

In a counterflow heat exchanger, the hot and cold fluids move in opposite directions. The LMTD formula for counter flow uses the following temperature differences:

\begin{aligned} \Delta T_1 &= T_{h,in} – T_{c,out} \\ \Delta T_2 &= T_{h,out} – T_{c,in} \end{aligned}

In a parallel-flow heat exchanger, both fluids enter at the same end and move in the same direction:

\begin{aligned} \Delta T_1 &= T_{h,in} – T_{c,in} \\ \Delta T_2 &= T_{h,out} – T_{c,out} \end{aligned}

Counterflow generally maintains a more even temperature difference across the heat exchanger. For the same inlet and outlet conditions, this usually produces a higher LMTD than parallel flow.

Counterflow LMTD Calculation Example

Consider a counterflow heat exchanger with these temperatures:

Temperature	Reading
Hot fluid entering	200°F
Hot fluid leaving	150°F
Cold fluid entering	70°F
Cold fluid leaving	110°F

First, calculate the temperature difference at each end:

\begin{aligned} \Delta T_1 &= 200 – 110 = 90^\circ\text{F} \\ \Delta T_2 &= 150 – 70 = 80^\circ\text{F} \end{aligned}

Enter these values into the LMTD counter flow formula:

\begin{aligned} \text{LMTD} &= \frac{90 – 80}{\ln\left(\frac{90}{80}\right)} \\ \text{LMTD} &\approx 84.9^\circ\text{F} \end{aligned}

The effective average temperature difference across the heat exchanger is approximately 84.9°F.

If ΔT₁ and ΔT₂ are equal, the equation produces zero divided by zero. In this special case, the LMTD equals the common temperature difference.

How LMTD Applies to HVAC Coils

The LMTD heat exchanger formula is commonly used with the basic heat transfer equation:

Q=U×A×LMTD

Where:

Symbol	Meaning
Q	Rate of heat transfer, typically Btu/h or watts
U	Overall heat transfer coefficient
A	Effective heat transfer surface area
LMTD	Average temperature difference driving heat transfer

This equation shows that heat transfer depends on more than temperature difference. Coil construction, surface area, airflow, fluid flow, refrigerant properties, fin spacing, circuiting, and surface condition can all affect capacity.

In a microchannel coil, flat multi-port tubes provide multiple small refrigerant passages and broad contact with the fins. This geometry supports heat transfer on both the air and refrigerant sides, influencing the overall U-value along with airflow, fin design, circuiting, refrigerant conditions, and coil cleanliness.

Real HVAC coils also do not always operate as ideal counterflow or parallel-flow heat exchangers. In many coils, air moves across the coil face while water, glycol, or refrigerant moves through the tubes. This creates a crossflow arrangement.

For crossflow or multipass equipment, engineers may use an LMTD correction factor:

Q=U×A×F×LMTD

In this equation, F adjusts for the actual flow arrangement. Its value depends on the heat exchanger configuration and operating temperatures.

Refrigerant coils require further consideration because the refrigerant may change phase as it moves through an evaporator or condenser. Much of the refrigerant can remain near its saturation temperature during this process. Manufacturer data and coil-selection software are normally used to account for phase change, circuiting, airflow, pressure drop, and other application conditions.

LMTD vs. Delta T

Delta T is the difference between two temperature readings. In an HVAC system, it may describe the difference between entering and leaving air or between supply and return water.

LMTD is different. It uses the temperature differences between the hot and cold sides at both ends of the heat exchanger. This produces an effective average across the heat-transfer surface.

A single airside or waterside delta T cannot replace the four terminal temperatures used in a complete LMTD calculation.

Common LMTD Calculation Mistakes

Pairing the wrong inlet and outlet temperatures
Using a base-10 logarithm instead of the natural logarithm
Mixing Fahrenheit and Celsius readings
Ignoring the correction factor for a crossflow or multipass design
Using readings taken while the system is starting, stopping, or cycling
Treating LMTD as a complete coil-sizing calculation

Temperature readings should be taken under steady operating conditions. Fluctuating readings may not represent the coil’s normal performance.

Need Help Selecting or Replacing a Coil?

LMTD is one part of selecting a heat exchanger. CS Coil’s engineering team also reviews operating conditions, capacity requirements, airflow, pressure drop, dimensions, and circuiting before recommending a custom or replacement coil. We manufacture custom microchannel condenser coils, evaporator coils, and fluid coolers for HVAC, refrigeration, commercial, and industrial applications.

Contact CS Coil today to get started!

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