 ## Analyzing Heat Exchanges: LMTD vs. Effectiveness-NTU

When sizing and selecting a heat exchanger or analyzing its thermal performance, there are various ways to approach a solution. If the selected heat exchanger is undersized, the design heat transfer conditions will not be achieved. Resulting in less heat transfer and higher outlet fluid temperatures, which leads to off-quality production, exceeding environmental limits, or creating safety hazards that require mitigation. Corrective action would require the purchase and installation of a properly sized heat exchanger, causing additional downtime for installation.

The Log Mean Temperature Difference (LMTD) and Effectiveness-NTU are two solution methods that approach heat exchanger analysis from different angles. Both methods share common parameters and concepts and will arrive at the same solution to heat exchanger thermal capacity. To understand the difference between these two methods, we need to understand the key terminology and the equations used in each solution method.

In PIPE-FLO® all parameters in both methods are calculated to help system design engineers, heat exchanger manufacturers, and plant engineers size, select, and evaluate the performance of heat exchangers in their piping systems.

## The LMTD Method

The Log Mean Temperature Difference or LMTD method is perhaps the most commonly known method used to analyze heat transfer in heat exchangers and is described in the Tubular Exchanger Manufacturers Association (TEMA) Standards and other well-known industry references.  The equation to calculate the heat transfer rate is given by: Where:

• = Heat Transfer Rate (BTU/hr or W)
• UA = Heat Exchanger Thermal Capacity (BTU/hr·°F or W/°C)
• U = Heat Transfer Coefficient (BTU/hr·ft2·°F or W/ m2·°C)
• A = Heat Transfer Area (ft2 or m2)
• CMTD = Corrected (or True) Mean Temperature Difference (°F or °C)
• LMTD = Logarithmic Mean Temperature Difference (°F or °C)
• CF = Configuration Correction Factor (dimensionless)

The Log Mean Temperature Difference (LMTD) is calculated using the equation for the counter-current flow pattern (unless it is a completely single path parallel flow pattern):
Where:

• dTA = (T hot in – T cold out)
• dTB = (T hot out – T cold in) ## Effectiveness-NTU Method

The Effectiveness-NTU method takes a different approach to solving heat exchange analysis by using three dimensionless parameters: Heat Capacity Rate Ratio (HCRR), Effectiveness (ε), and Number of Transfer Units (NTU). The relationship between these three parameters depends on the type of heat exchanger and the internal flow pattern.

## Heat Capacity Rate Rate (HCR) and Heat Capacity Ratio (HCRR)

The first dimensionless parameter is the Heat Capacity Rate Ratio (HCRR), the ratio of the minimum to the maximum value of Heat Capacity Rate (HCR) for the hot and cold fluids. The HCR of a fluid is a measure of its ability to release or absorb heat. The HCR is calculated for both fluids as the product of the mass flow rate times the specific heat capacity of the fluid. Where:

• HCR = Heat Capacity Rate of the hot or cold fluid (BTU/hr·°F or W/°C)
• w = mass flow rate of the fluid (lb/hr or kg/sec)
• cp = specific heat

The equation for Heat Capacity Rate Ratio (HCRR) is: Where:

• HCRmin = minimum value of Heat Capacity Rate of the hot or cold fluid
• HCRmax = maximum value of Heat Capacity Rate of the hot or cold fluid

The HCRR is limited to values between 0 and 1.0 and is similar to the R ratio in the LMTD method. When R ≤ 1.0 HCRR = R. For values of R > 1.0, HCRR = 1/R.

## Effectiveness (ε)

The second parameter, Effectiveness (ε), is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate for the given flow and temperature conditions. Where: This definition of Effectiveness (ε) is similar to the definition of Temperature Effectiveness (P) in the LMTD method but uses the side with the minimum value of the Heat Capacity Rate as the reference instead of the tube side. When R ≤ 1.0, ε = P. For values of R > 1.0, ε = PR.

## Number of Transfer Units (NTU)

The last dimensionless parameter, the Number of Transfer Units (NTU), is the ratio of the heat exchanger’s ability to transfer heat (UA) to the fluid’s minimum ability to absorb heat (HCR min). The NTU is a function of the Effectiveness and HCRR established by the process temperatures and flow rates and is indicative of the size of the heat exchanger needed. The greater the value of NTU, the larger the heat transfer surface area (A) required to meet the process conditions.

NTU is normally not calculated from the equation above, but instead solved graphically or using equations for NTU as a function of the Effectiveness and HCRR.

### Conclusion

Piping systems are built to transport fluid to do work, transfer heat, and make a product. When designing piping systems to support heat transfer between fluids, both the hydraulic and thermal conditions must be evaluated to ensure the proper equipment is selected and installed. Evaluating both the hydraulic and thermal conditions of a system can be a daunting task for any engineer and is often divided into different groups who specialize in a specific field. The division often results in misunderstanding, miscommunication, and mistakes when integrating the work of the various groups.

Improperly sized equipment, whether the equipment is a pump, control valve or heat exchanger, results in additional capital and maintenance costs, off-quality production, environmental excursions, and potentially increase safety risks. Using comprehensive software tools like PIPE-FLO® Professional helps the design engineer, process engineer, and owner/operator have a clear view of the system operation.

### PIPE-FLO: All You Need To KNO

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