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Effectiveness-NTU Method

1955
  • W. M. Kays
  • A. L. London
Heat exchanger used in thermodynamics for effectiveness-NTU method analysis.

(generated image for illustration only)

The Effectiveness-NTU method is used in heat exchanger analysis when fluid inlet temperatures are known, but outlet temperatures are not. Effectiveness (\(\epsilon\)) is the ratio of actual heat transfer to the maximum possible heat transfer. The Number of Transfer Units (NTU) is a dimensionless measure of the heat exchanger’s size, defined as \(NTU = \frac{UA}{C_{min}}\).

The Effectiveness-NTU method provides a powerful alternative to the LMTD method, especially in situations where iterating to find outlet temperatures would be cumbersome. The core of the method lies in three dimensionless parameters: effectiveness (\(\epsilon\)), the number of transfer units (NTU), and the heat capacity rate ratio (\(C_r = C_{min}/C_{max}\)). The maximum possible heat transfer rate, \(Q_{max}\), occurs in a hypothetical infinitely long counter-flow heat exchanger, where the fluid with the smaller heat capacity rate (\(C_{min}\)) undergoes the maximum possible temperature change, \(\Delta T_{max} = T_{h,in} – T_{c,in}\). Thus, \(Q_{max} = C_{min}(T_{h,in} – T_{c,in})\). The actual heat transfer is then simply \(Q = \epsilon Q_{max}\). The key is that effectiveness (\(\epsilon\)) can be expressed as a function of only NTU and \(C_r\) for a given flow arrangement. For example, for a parallel-flow exchanger, the relationship is \(\epsilon = \frac{1 – \exp[-NTU(1+C_r)]}{1+C_r}\). These relationships have been derived and charted for numerous common heat exchanger configurations, allowing engineers to quickly determine the performance of a given exchanger or to size a new one without knowing the outlet temperatures beforehand. This method is particularly useful in design and optimization studies where the impact of changing the exchanger’s size (and thus NTU) on its performance (effectiveness) is being investigated.

UNESCO Nomenclature: 3328
– Thermodynamics

Type

Abstract System

Disruption

Incremental

Usage

Widespread Use

Precursors

  • LMTD method for heat exchanger analysis
  • concept of dimensionless numbers in fluid mechanics and heat transfer (e.g., reynolds, prandtl numbers)
  • advances in thermodynamics and fluid dynamics during the early 20th century

Applications

  • analysis of gas turbine regenerators
  • design of compact heat exchangers where outlet temperatures are difficult to predict
  • performance evaluation of electronics cooling systems
  • automotive radiator design
  • aerospace thermal management systems

Patents:

NA

Potential Innovations Ideas

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Related to: effectiveness, NTU, heat exchanger, heat transfer, Kays and London, thermodynamics, dimensionless number, thermal design, compact heat exchanger, capacity rate ratio.

Historical Context

Effectiveness-NTU Method

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1960

(if date is unknown or not relevant, e.g. "fluid mechanics", a rounded estimation of its notable emergence is provided)

Related Invention, Innovation & Technical Principles

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