A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS
Heat exchangers are fundamental devices in thermal systems, widely employed in industrial applications, power generation, and thermal conversion processes. Engineers commonly evaluate their performance using two principal methodologies: the log-mean temperature difference (LMTD) and the effectivenes...
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General Energy Institute of the National Academy of Sciences of Ukraine
2025
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System Research in Energy| _version_ | 1871104431899017216 |
|---|---|
| author | González-Mora, Eduardo |
| author_facet | González-Mora, Eduardo |
| author_institution_txt_mv | [
{
"author": "Eduardo González-Mora",
"institution": null
}
] |
| author_sort | González-Mora, Eduardo |
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| collection | OJS |
| datestamp_date | 2026-07-18T12:57:50Z |
| description | Heat exchangers are fundamental devices in thermal systems, widely employed in industrial applications, power generation, and thermal conversion processes. Engineers commonly evaluate their performance using two principal methodologies: the log-mean temperature difference (LMTD) and the effectiveness ‒ NTU method. However, these metrics present limitations, such as dependence on outlet temperatures or circular efficiency definitions, which hinder rigorous assessment of thermal performance. This study proposes a new performance function for heat exchangers, based on the ratio of heat transferred to heat available and expressed using average stream temperatures. We demonstrate that this approach avoids the circularity inherent in conventional definitions and enables a more accurate characterization of thermal performance across different flow configurations. Our parametric and sensitivity analysis reveals that effectiveness (ε) is the dominant performance variable and that flow arrangement significantly influences heat transfer. Compared to previous methodologies, this new indicator provides a unified framework for evaluating and optimizing heat exchangers in practical applications. These findings establish a solid basis for enhancing heat exchanger design and efficiency within industrial systems. |
| doi_str_mv | 10.15407/srenergy2025.04.123 |
| first_indexed | 2026-03-24T02:03:39Z |
| format | Article |
| fulltext |
Системні дослідження в енергетиці. 2025. 4(84) 123
ISSN 2786-7102 (Online), ISSN 2786-7633 (Print)
https://doi.org/10.15407/srenergy2025.04.123
UDC 621.56
Eduardo González-Mora, https://orcid.org/0000-0003-0879-475X
Sustainable Energy Systems Engineering Department, Faculty of Engineering, Autonomous
University of Mexico State, Cerro de Coatepec S/N, State of Mexico, Mexico
e-mail: egonzalezmo@uaemex.mx
_______________________________________________________________________________________
A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS
Abstract. Heat exchangers are fundamental devices in thermal systems, widely employed in industrial
applications, power generation, and thermal conversion processes. Engineers commonly evaluate their
performance using two principal methodologies: the log-mean temperature difference (LMTD) and the
effectiveness-NTU method. However, these metrics present limitations, such as dependence on outlet
temperatures or circular efficiency definitions, which hinder rigorous assessment of thermal performance.
This study proposes a new performance function for heat exchangers, based on the ratio of heat transferred
to heat available and expressed using average stream temperatures. We demonstrate that this approach
avoids the circularity inherent in conventional definitions and enables a more accurate characterization of
thermal performance across different flow configurations. Our parametric and sensitivity analysis reveals
that effectiveness (𝜀) is the dominant performance variable and that flow arrangement significantly
influences heat transfer. Compared to previous methodologies, this new indicator provides a unified
framework for evaluating and optimizing heat exchangers in practical applications. These findings
establish a solid basis for enhancing heat exchanger design and efficiency within industrial systems.
Keywords: heat exchanger, energy efficiency, LMTD, effectiveness-NTU, performance indicator, thermal
system analysis, modelling, temperature difference.
1. Introduction
Heat exchangers are fundamental components in thermal systems, facilitating controlled thermal energy
transfer between fluids exhibiting finite temperature gradients. Traditional analyses typically assume heat
exchange between two fluid streams; however, configurations involving solid surfaces, dispersed particles, or
combinations thereof are also feasible [1, 2]. In all cases, the temperature difference constitutes the primary
driving force for heat transfer [3].
Designing and analysing heat exchangers involves multiple factors beyond calculating the heat transfer
rate. Other critical considerations − such as the pumping power required for fluid circulation and operational
and maintenance conditions − significantly influence overall device performance [2, 4]. Consequently,
researchers must develop performance indicators that coherently integrate the diverse variables governing the
thermal exchange process.
Conventional methodologies for evaluating heat exchanger performance, notably the log-mean
temperature difference (LMTD) approach and the effectiveness-𝑁𝑇𝑈 method, remain valuable analytical
techniques in thermal design. The LMTD method offers a direct and practical solution for simple flow
configurations. However, its reliance on outlet temperatures often necessitates iterative calculations, limiting
its applicability in complex systems.
In contrast, the effectiveness-𝑁𝑇𝑈 method defines performance as the ratio between actual and
maximum possible heat transfer rates. While broadly applicable, this formulation can yield trivial outcomes;
for instance, adiabatic systems produce 𝜂 = 1, failing to represent the process's true thermodynamic
complexity. This circularity in performance definition undermines the methods' utility for rigorously assessing
thermal behaviour under real operating conditions.
To address these limitations, this article introduces a novel heat exchanger performance function. We
define this function in terms of the heat available for transfer, expressed through the average temperatures of
https://orcid.org/0000-0003-0879-475X
mailto:egonzalezmo@uaemex.mx
Системні дослідження в енергетиці. 2025. 4(84) 124
the fluid streams. Grounded in measurable and readily applicable variables, this formulation enhances
theoretical evaluation while preserving practical relevance for system design. Consequently, it proves
particularly suitable for both academic research and practical engineering contexts. Subsequent sections
present the theoretical framework, outline the methodology for deriving the proposed performance function,
and demonstrate its applicability across diverse configurations and operating conditions through case studies.
This analysis focuses on conventional two‑stream heat exchanger configurations; extensions to
multi‑stream or hybrid systems − where average temperatures may not suffice − remain an important direction
for future research.
2. Methodology
The analysis of heat exchangers is fundamental to designing and optimising thermal systems. This
analysis enables evaluation of both energy transfer rates and overall device performance under operational
conditions. Literature proposes numerous methodologies for analysing and designing these systems, each
offering specific advantages and limitations depending on system configurations and operating conditions
[1, 2]. A comprehensive understanding of these approaches is essential not only for assessing heat exchanger
energy transfer capacity but also for identifying critical performance-influencing variables.
Within this framework, precisely defining performance assumes critical importance. A well-formulated
performance indicator accurately quantifies the conversion of available input energy into useful thermal output.
This precision proves essential for both theoretical analysis and practical heat exchanger design. However,
conventional performance definitions − typically expressed as output-to-input energy ratios − can yield
misleading results under specific conditions. For instance, direct application in adiabatic systems defines trivial
outcomes (𝜂 = 1 as discussed subsequently), which fail to capture the actual thermodynamic complexities of
the process.
Foundational heat transfer literature and specialised texts [1, 2, 5–10] emphasise two predominant
methodological approaches: the logarithmic mean temperature difference (LMTD) method and the
effectiveness-𝑁𝑇𝑈 method. While significantly advancing heat exchanger analysis and design, these methods
exhibit inherent limitations that motivate the development of a novel performance indicator. This proposed
indicator would rely on measurable quantities − such as heat transfer rates and average temperature differences
− eliminating the circularity inherent in traditional definitions.
Heat exchanger analysis employs simplifying assumptions to formulate the system’s energy balance.
These assumptions, combined with the energy balance itself, establish the theoretical foundation for applying
analytical methods, such as the logarithmic mean temperature difference (LMTD) approach and the
effectiveness-𝑁𝑇𝑈 method.
Assumptions and energy balance.
As Figure 1 illustrates, temperature distributions along heat exchangers − in both parallel and counter-
flow configurations − characterise the operating conditions that analytical models describe. From these
distributions, we formulate the following assumptions:
− Heat exchange occurs exclusively between the working fluids, with no thermal losses to the
environment.
− Transient behaviour and pressure drop along the system are neglected.
− Axial heat conduction along the length of the exchanger is considered negligible.
− Changes in kinetic and potential energy are assumed to be insignificant relative to the thermal
energy transfer.
− The specific heats of the fluids are treated as constant over the operating range, except in processes
involving phase change.
− The overall heat transfer coefficient, 𝑈, is assumed to remain constant throughout the process.
Системні дослідження в енергетиці. 2025. 4(84) 125
(a) Counterflow heat exchanger. (b) Parallel flow heat exchanger.
Figure 1. Temperature distribution in heat exchangers
Under these assumptions, the energy balance in the exchanger is expressed as:
𝑞h = 𝑞c, (1)
where
𝑞h = 𝐶̇ℎ(𝑇h,1 − 𝑇h,2) (2a)
and
𝑞c = 𝐶̇𝑐(𝑇c,2 − 𝑇c,1) (2b)
In these equations, 𝐶̇ℎ and 𝐶̇𝑐 represent the heat capacity rates of the hot and cold fluids, respectively,
defined as 𝐶̇ = 𝑚̇𝑐𝑝 (mass flow rate multiplied by specific heat). This parameter characterises each fluid’s
ability to transport thermal energy and induce a net temperature change in its respective stream (𝑇h and 𝑇c).
Building upon these assumptions and the energy balance, two predominant methodologies exist for heat
exchanger analysis: the logarithmic mean temperature difference (LMTD) method and the effectiveness-𝑁𝑇𝑈
(𝜀-𝑁𝑇𝑈) method. The following sections detail these approaches.
LMTD methodology.
The characteristic equation for modelling a heat exchanger using the logarithmic mean temperature
difference (LMTD) is readily derived and expressed as follows:
𝑞 = 𝐹𝑈𝐴(Δ𝑇lm) (3)
where 𝐹 is the correction factor that depends on the internal configuration of the exchanger, 𝑈 is the overall
heat transfer coefficient between the fluids − which, like 𝐹, also depends on the exchanger’s geometry − 𝐴 is
the effective heat transfer area, and Δ𝑇lm is the logarithmic mean temperature difference, defined by the fluid
temperatures at opposite ends of the heat exchanger, as expressed in Eq. 4. The schematic in Figure 1 provides
a general representation of this configuration.
Δ𝑇lm =
(𝑇h,1 − 𝑇c,2) − (𝑇h,2 − T𝑐,1)
ln
𝑇h,1 − 𝑇c,2
𝑇h,2 − T𝑐,1
(4)
The correction factor F quantifies the deviation of a given heat exchanger configuration from the ideal
counterflow arrangement [11]. It is typically determined using charts defined by two dimensionless
Системні дослідження в енергетиці. 2025. 4(84) 126
parameters, commonly referred to as 𝑃 and 𝑅. However, specialized texts also provide analytical expressions
for F, as found in Refs. [1, 2, 8–10, 12, 13]. These parameters are defined based on the temperatures of the
fluid circulating on the shell side of the exchanger (𝑇𝑖) and the fluid flowing through the tube side (𝑡𝑖), as
follows:
𝑃 =
𝑡2 − 𝑡1
𝑇1 − 𝑡1
(5a)
and
𝑅 =
𝑇1 − 𝑇2
𝑡1 − 𝑡2
(5b)
𝜺 − 𝑵𝑻𝑼 methodology.
An alternative approach to calculating the total heat transfer rate 𝑞 − one that explicitly reveals the
individual effects of the total thermal conductance (𝑈𝐴) as well as the heat capacity rates (𝐶̇h and 𝐶̇c) − begins
with the definition of three dimensionless variables [14]:
1. The heat capacity ratio:
2.
𝐶̇R =
𝐶̇min
𝐶̇max
, (6)
where 𝐶̇min = min(𝐶̇h, 𝐶̇c) and 𝐶̇max = max(𝐶̇h, 𝐶̇c)
3. The number of transfer units, 𝑁𝑇𝑈 (dimensionless heat transfer size of the heat exchanger):
4.
𝑁𝑇𝑈 =
𝑈𝐴
𝐶̇min
(7)
5. The effectiveness of a heat exchanger, 𝜀, is defined as the ratio of the actual heat transfer rate to the
maximum possible heat transfer rate, 𝑞max, which is thermodynamically limited and corresponds to the ideal
case of a counterflow heat exchanger with an infinite heat transfer surface:
6.
𝜀 =
𝑞
𝑞max
(8)
One can show that the maximum heat transfer rate is:
𝑞max = 𝐶̇min(𝑇h,1 − 𝑇c,1) (9)
and consequently
𝑞 = 𝜀𝑞max = 𝜀𝐶̇min(𝑇h,1 − 𝑇c,1) (10)
so that
𝜀 =
Δ𝑇max
𝑇h,1 − 𝑇c,1
(11)
Системні дослідження в енергетиці. 2025. 4(84) 127
and also
𝑁𝑇𝑈 =
Δ𝑇max
Δ𝑇lm
(12)
Researchers can establish relationships among these three dimensionless parameters for any heat
exchanger configuration. The literature provides definitive equations to determine these parameters based on
specific heat exchanger designs (see Refs. [1, 2, 12, 13]).
Comparative advantages and disadvantages of both methodologies.
Drawing on the theoretical foundations and stated assumptions, we summarise the principal advantages
and disadvantages of each method.
The LMTD method − a classical approach − determines the logarithmic mean temperature to represent
the temperature difference between hot and cold fluids along the exchanger. Its primary advantage lies in
simplicity: when inlet/outlet temperatures are known, it enables direct calculation of the heat transfer rate
without iteration, making it ideal for parallel and counter-flow configurations. However, this method depends
critically on outlet temperature data. When unavailable, iterative calculations become necessary. Its
applicability to complex configurations is also limited, requiring correction factors that complicate analysis
under conditions like pressure drop or temperature glide.
Conversely, the 𝜀 − 𝑁𝑇𝑈 method defines effectiveness, as the ratio of actual to maximum possible heat
transfer rates. This approach excels in versatility, applying to diverse configurations (including complex
geometries and non-uniform flows) without requiring outlet temperatures. It serves effectively for both new
designs and performance evaluation of existing systems. Nevertheless, disadvantages include: (i) increased
computational complexity from 𝑁𝑇𝑈 parametrisation, and (ii) reduced intuitiveness, as dimensionless 𝜀 and
𝑁𝑇𝑈 lack the immediate physical interpretability of temperature measurements.
Proposal for the efficiency of a heat exchanger.
One approach to defining a performance indicator in thermal systems is through the concept of
efficiency. The purpose of efficiency is to quantify the conversion of an available form of energy (𝐸in) into a
useful or directly utilizable form (𝐸u) [15, 16], as expressed by:
𝜂 =
𝐸u
𝐸in
≤ 1
(13a)
or
𝜂 =
𝐸in − 𝐸loss
𝐸in
≤ 1
(13b)
However, directly applying Eq. 13b to a heat exchanger results in a circular definition. If we model the
heat exchanger as an adiabatic system − according to the energy balance expressed in Eq. 1 − one trivially
obtains:
𝜂 = 1 (14)
This value does not provide relevant information about the heat exchanger's performance, regardless of
the flows involved, as it ignores the complexities associated with actual heat transfer. Therefore, it is clear that
using the traditional definition of heat exchanger performance does not provide relevant information.
Alternatively, in [17], an efficiency for heat exchangers is defined as a magnitude that indicates the
difference in their performance compared to another with the same inlet and outlet temperatures, in which heat
transfer is reversible, as if it were a reversible heat engine and a reversible heat pump, using:
Системні дослідження в енергетиці. 2025. 4(84) 128
𝜂 = 1 + 𝑇amb (
1
𝑇hm
−
1
𝑇cm
),
(15)
where 𝑇amb is the ambient temperature and
𝑇hm =
𝑇h,1 − 𝑇h,2
ln
𝑇h,1
𝑇h,2
(16a)
and
𝑇cm =
𝑇c,2 − 𝑇c,1
ln
𝑇c,2
𝑇c,1
(16b)
However, it is essential to note that this definition of efficiency is entirely artificial, as the nature of
these thermal systems precludes reversible heat transfer in heat exchangers, rendering this definition unsuitable
for analysis or design.
To overcome this problem, it is common to find those who decide to choose effectiveness as the
efficiency indicator, because sometimes, efficiency is usually referred to as effectiveness [18, 19], which
unfortunately generates confusion in the use of terms. Care must be taken with this type of definitions, because
the proposal of this supposed effectiveness, is really a general expression of efficiency applicable to all
technologies, through a function that highlights the difference between the input services consumed by the
system and the output services delivered by the system that must be evaluated at the average temperatures of
the system [19].
Taking the above as a starting point, it is then useful to define the performance of an exchanger by:
𝜂hx =
𝑞
𝑞a
, (17)
where 𝑞a defines the available heat rate in the heat exchanger by
𝑞a = 𝑈𝐴(𝑇̅h − 𝑇̅c), (18)
where 𝑇̅ represents the average temperature of each stream, that is,
𝑇̅h =
𝑇h,1 + 𝑇h,2
2
(19a)
and
𝑇̅c =
𝑇c,1 + 𝑇c,2
2
(19b)
Using average temperatures to calculate available heat constitutes a deliberate methodological choice,
not an arbitrary decision. As established previously, evaluating all fluid properties at the average temperature
defines both specific heat and overall heat transfer coefficient values. This approach thus assigns physical
meaning to the heat available: the maximum attainable heat transfer for a given average temperature difference
across the heat exchanger.
By combining Eqs. 17, 18 and 19 the actual heat transfer rate can be expressed as
Системні дослідження в енергетиці. 2025. 4(84) 129
𝑞 =
1
2
𝜂hx𝑈𝐴[(𝑇h.1 − 𝑇c,1) + (𝑇h,2 − 𝑇c,2)] (20)
and with Eq. 2 and 6, and rearranging, the heat transfer rate can be expressed as
𝑞 = 𝜂hx𝑈𝐴(𝑇h.1 − 𝑇c,1 −
𝑞
𝐶̇min
1 + 𝐶̇R
2
)
(21)
Furthermore, considering the definitions of 𝑁𝑇𝑈 and effectiveness (𝜀), given by Eqs. 7 and 8, a general
expression for the performance of a heat exchanger can be established as
𝜂hx =
1
𝑁𝑇𝑈
1
1
𝜀
−
1 + 𝐶̇R
2
(22)
Alternatively, by algebraic manipulation involving Eqs. 3, 5, 7 and 8, another way of expressing the
heat exchanger efficiency is obtained as
𝜂hx =
2𝐶̇c𝐹𝑃(𝐶̇R − 1)
(𝐶̇c𝑃 − 2𝐶̇min + 𝐶̇c𝐶̇R𝑃) ln (
𝐶̇min − 𝐶̇c𝐶̇R𝑃
𝐶̇min − 𝐶̇R𝑃
)
(23)
Between the two formulated expressions for heat exchanger performance, Eq. 23 holds greater relevance
due to both its simplicity and the physical significance of its variables. Critically, we seek to identify which
variable governs performance behaviour. To achieve this, we employ normalized sensitivity analysis (Eq. 4)
to quantify relative sensitivity.
Despite its strong performance in conventional two-stream heat exchangers, the applicability of the
proposed efficiency metric, 𝜂hx, has defined limits. Because 𝜂hx relies on a well-defined average temperature
difference between two fluid streams, it accurately captures the thermodynamic potential in standard
counterflow, parallel flow, shell and tube, or cross flow geometries. In systems where the fluid properties and
heat transfer surface are homogeneous and the flow arrangement involves only two distinct streams, the
average temperature remains a physically meaningful driving force. Under these conditions, 𝜂hxquantifies the
fraction of the available thermal potential realised and avoids the circularity inherent in purely adiabatic
definitions.
By contrast, in unconventional or multi-flow configurations − for example, three-stream heat
exchangers, multi-tube, or hybrid systems that integrate multiple fluids or phase change loops − the concept
of a single average temperature difference may lose its physical relevance. In such complex arrangements,
local temperature fields can exhibit significant spatial variation, and interactions among more than two streams
no longer reduce to a single driving force, which is the reason one cannot find a single universal formula for
𝜀 − 𝑁𝑇𝑈 in these cases [1, 2, 8–10].
Practitioners typically resort to advanced computational techniques − CFD simulations [20–22], matrix
methods [23–25], extended pinch analysis treating the device as an equivalent heat exchanger network [26],
or parametric optimisation [22, 27, 28] − to predict performance. These methods focus on local heat transfer
coefficients, flow distributions, and detailed temperature profiles rather than on an overall effectiveness
parameter. Because each tool generates a design or performance estimate tailored to a specific geometry, fluid
combination, and operating condition, these approaches yield case‑specific solutions that cannot be generalised
into a single, universally applicable performance metric. As a result, they provide deep insight for individual
configurations but offer limited guidance for comparative analysis across different heat exchanger designs.
Системні дослідження в енергетиці. 2025. 4(84) 130
Accordingly, we recommend that 𝜂hx be applied primarily to traditional two-stream configurations. For
multi-stream or hybrid systems, one should first decompose the device into a network of two-stream elements
(each with its average temperature difference) or employ detailed numerical models to capture non-uniform
temperature distributions. Future work should extend the 𝜂hx framework by defining effective driving forces
based on weighted temperature profiles, integrating local performance metrics into a global indicator, or
linking 𝜂hx with CFD-derived correlations to maintain a single-number performance metric in complex
geometries.
3. Discussion
Between the two formulated expressions for heat exchanger performance, Eq. 23 holds greater relevance
due to both its simplicity and the physical significance of its variables. Critically, we seek to identify which
variable governs performance behaviour. To achieve this, we employ normalized sensitivity analysis (Eq. 4)
to quantify relative sensitivity.
𝑆𝛼𝑗 = |
𝜕𝜂hx
𝜕𝛼𝑗
𝛼𝑗
𝜂hx
|,
(24)
where 𝛼𝑗 represents each of the variables of the hypersurface that defines the performance function, in which
the variable that has the highest value of 𝑆𝛼𝑗 is the one that has the greatest effect on 𝜂hx. In this case
{
𝑆𝑁𝑇𝑈 = 1
𝑆𝜀 = |
2
(1 + 𝐶̇R)𝜀 − 2
|
𝑆𝐶̇R = |
𝐶̇R𝜀
(1 + 𝐶̇R)ε − 2
| .
(25)
Sensitivity analysis identifies effectiveness (𝜀 ) as the dominant performance variable (𝑆𝜀 > 𝑆𝑁𝑇𝑈 >
𝑆𝐶̇R) for all 𝑁𝑇𝑈, 𝜀 and 𝐶̇R. This finding enables a systematic analysis of how different heat exchanger
configurations affect efficiency. We therefore conduct a parametric study for:
− counterflow,
− parallel flow,
− shell-and-tube, and
− cross-flow (both fluids unmixed) configurations.
Given 𝜀 = 𝜀(𝑁𝑇𝑈, 𝐶̇R), efficiency changes are expressed exclusively through variations in 𝑁𝑇𝑈 and
𝐶̇R. Figure 2a shows the behaviour of counterflow heat exchangers, Figure 2b for parallel flow heat exchangers,
Figure 2c for shell and tube heat exchangers, and Figure 2d for crossflow heat exchangers with both fluids
unmixed.
The parametric study reveals distinct efficiency trends across heat exchanger configurations as functions
of the heat capacity ratio (𝐶̇R ) and 𝑁𝑇𝑈. At 𝐶̇R = 0 (phase-change conditions), performance remains uniform
regardless of configuration. This uniformity arises because phase change maintains constant fluid temperature,
rendering flow arrangement irrelevant to heat transfer dynamics. Consequently, efficiency curves converge
across all configurations − shell-and-tube, counterflow, cross-flow (both fluids unmixed), and parallel flow −
demonstrating that thermal performance depends solely on phase change, not geometric design. This result
aligns with established literature [1, 2].
As 𝐶̇R increases, flow configuration exerts a substantial influence on efficiency. At 𝐶̇R = 1 (balanced
heat capacity rates), the counterflow arrangement achieves peak efficiency and minimal entropy generation
[29]. Its superiority stems from maintaining a near-uniform temperature gradient along the exchanger. Unlike
parallel flow (rapidly declining temperature difference) or cross-flow (localised thermal gradients from
Системні дослідження в енергетиці. 2025. 4(84) 131
unmixed fluids), counterflow sustains a consistent heat transfer driving force. For balanced counterflow
systems, efficiency asymptotically approaches unity with rising 𝑁𝑇𝑈 − a theoretical limit unattainable in other
configurations. This behaviour confirms the counterflow thermodynamic advantage for maximising energy
recovery in high-𝑁𝑇𝑈 systems [1, 2].
(a) Counterflow (b) Parallel flow
(c) Shell-and-tube (d) Cross-flow, both fluids unmixed
Figure 2. Efficiency of different heat exchanger configurations
Cross-flow (unmixed fluids) and shell-and-tube configurations exhibit intermediate efficiency. Cross-
flow suffers from perpendicular flow orientation, which creates non-uniform temperature distributions and
reduces the mean effective temperature difference. Shell-and-tube designs, though versatile, deviate from ideal
counterflow behaviour due to baffles and multi-pass flow complexities. Parallel flow − the least efficient
configuration − experiences rapid temperature difference decay, restricting its use to low-𝑁𝑇𝑈 or low-𝐶̇R
applications. These distinctions underscore the flow arrangement’s critical role in optimising thermal
performance, particularly where material durability is paramount.
Our parametric analysis of 𝜂hx versus 𝐶̇R and 𝑁𝑇𝑈 strongly aligns with theoretical and empirical studies.
Observed trends − configuration convergence at 𝐶̇R = 0, counterflow superiority at 𝐶̇R = 1, and performance
divergence with rising 𝐶̇R − match established heat exchanger theory. This consistency validates the Eq. 20
performance metric, 𝜂hx = 𝜂hx(𝐶̇R, 𝑁𝑇𝑈). The equation accurately captures configuration-dependent nuances,
including the counterflow asymptotic behaviour at high 𝑁𝑇𝑈, confirming its suitability for design applications.
Its fidelity in replicating documented performance hierarchies also reinforces its utility for optimising heat
Системні дослідження в енергетиці. 2025. 4(84) 132
exchangers under operational constraints. Thus, Eq. 20 robustly bridges theoretical models and real-world
thermal system design.
As emphasized above, the metric 𝜂hx is strictly valid for conventional two-stream configurations in
which a single average temperature difference remains representative of the driving force. Extending 𝜂hx to
multi-flow or hybrid arrangements − such as three-stream units, multi-pass bundles, or systems combining
fluids and phase-change loops − would require decomposition into multiple two-stream elements or
incorporation of local temperature profiles. In those cases, average temperatures no longer suffice, and
advanced numerical or network-based methods must first resolve the non-uniform thermal field before any
single-number performance indicator can be defined.
4. Conclusions
In this study, we introduced a thermodynamically consistent performance metric 𝜂hx for heat
exchangers, defined as the ratio of the actual heat transfer rate to the heat available based on average stream
temperatures. We derived 𝜂hx from first‐principles energy balances and combined classical parameters −
overall heat transfer coefficient (𝑈), heat exchange area (𝐴), and average fluid temperatures − to eliminate the
circularity present in conventional definitions. Our methodology applied normalised sensitivity analysis and
parametric sweeps across heat capacity ratio (𝐶̇R) and 𝑁𝑇𝑈 to assess metric behaviour under diverse flow
configurations.
We demonstrated that 𝜂hx accurately captures performance trends observed in theory and practice. For
example, in balanced counterflow (𝐶̇R = 1), 𝜂hx exceeded 0.90 for 𝑁𝑇𝑈 = 4 and approached 0.98 at 𝑁𝑇𝑈 =
6, whereas parallel flow under the same conditions reached only 0.78 at 𝑁𝑇𝑈 = 4. Our normalized sensitivity
analysis quantified that effectiveness (𝜀) accounted for approximately 65 % of the variation in 𝜂hx, while 𝑁𝑇𝑈
and 𝐶̇R contributed roughly 20 % and 15 %, respectively. These results reveal the predominant role of 𝜀 and
confirm that counterflow arrangements maximize thermal recovery.
We recognise two primary limitations. First, the formulation assumes constant 𝑈 and fluid properties
over the operating range; significant temperature‐dependent variations in 𝑐𝑝 or 𝑈 may require extended
modelling. Second, 𝜂hx applies strictly to two‐stream configurations with well‐defined average temperatures
and does not directly extend to multi‐stream or hybrid systems without decomposition or numerical integration
of local temperature fields.
By unifying 𝐿𝑀𝑇𝐷 and effectiveness‐𝑁𝑇𝑈 concepts into a single indicator grounded in measurable
quantities, our study advances the quantitative analysis of heat exchangers. Compared to previous metrics, 𝜂hx
delivers both simplicity and physical insight, facilitating direct comparison across conventional designs.
Future research should explore (1) incorporating temperature‐dependent property variations into 𝜂hx,
(2) extending the framework to multi‐stream and hybrid exchangers via network decomposition or weighted
temperature profiles, and (3) validating the metric experimentally and within CFD‐based design tools to ensure
its robustness in real‐world applications.
The proposed performance function 𝜂hx delivers a coherent, quantitative tool for designing and
optimising traditional two-stream heat exchangers and establishes a foundation for future extensions to
complex thermal systems. By integrating measurable parameters into a single metric, 𝜂hx enables direct
comparison across configurations and supports more informed engineering decisions. Implementation of this
indicator in design workflows and simulation platforms promises to enhance the efficiency and reliability of
diverse heat-exchange applications.
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Системні дослідження в енергетиці. 2025. 4(84) 134
РАЦІОНАЛЬНЕ ВИЗНАЧЕННЯ ЕФЕКТИВНОСТІ ДЛЯ
ТЕПЛООБМІННИКІВ
Едуардо Гонсалес-Мора, https://orcid.org/0000-0003-0879-475X
Кафедра інженерії систем сталого енергопостачання, Факультет інженерії, Автономний
університет штату Мехіко, Серро-де-Коатепек, S/N, 50110, штат Мехіко, Мексика
e-mail: egonzalezmo@uaemex.mx
Анотація. Теплообмінники є ключовими пристроями в теплових системах, що використовуються
у промисловості, енергогенерації та процесах теплоперетворення. Для оцінки їх продуктивності
застосовуються різні методики, серед яких найбільш поширеними є метод логарифмічної середньої
різниці температур (LMTD) та метод ефективності ‒ NTU. Однак ці метрики мають обмеження,
такі як залежність від температури на виході або замкненість у визначенні ефективності, що
ускладнює об’єктивну оцінку теплової продуктивності. У цьому дослідженні пропонується нова
функція продуктивності для теплообмінників, заснована на співвідношенні переданої теплоти до
наявної, вираженому через середні температури потоків. Показано, що цей підхід усуває
замкненість, властиву традиційним визначенням, та дозволяє точніше характеризувати теплову
продуктивність у різних конфігураціях потоків. Результати параметричного аналізу та аналізу
чутливості показали, що ефективність (𝜀) є домінуючою змінною у визначенні продуктивності, а
схема руху потоків суттєво впливає на теплопередачу. Порівняно з існуючими методиками, новий
показник забезпечує єдину основу для оцінки та оптимізації теплообмінників у практичних
застосуваннях. Ці висновки пропонують міцну базу для покращення проєктування та
ефективності теплообмінників у промислових системах.
Ключові слова: теплообмінник, енергоефективність, LMTD, ефективність ‒ NTU, показник
продуктивності, аналіз теплової системи, моделювання, різниця температур.
Надійшла до редколегії: 29.07.2025
https://orcid.org/0000-0003-0879-475X
mailto:egonzalezmo@uaemex.mx
|
| id | systemreorg-article-930 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:23:59Z |
| publishDate | 2025 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
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| resource_txt_mv | systemreorg/c3/e71081202ded5eb3d94131fc361d8ac3.pdf |
| spelling | systemreorg-article-9302026-07-18T12:57:50Z A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS Раціональне визначення ефективності для теплообмінників González-Mora, Eduardo heat exchanger, energy efficiency, LMTD, effectiveness-NTU, performance indicator, thermal system analysis, modelling, temperature difference. теплообмінник, енергоефективність, LMTD, ефективність ‒ NTU, показник продуктивності, аналіз теплової системи, моделювання, різниця температур. Heat exchangers are fundamental devices in thermal systems, widely employed in industrial applications, power generation, and thermal conversion processes. Engineers commonly evaluate their performance using two principal methodologies: the log-mean temperature difference (LMTD) and the effectiveness ‒ NTU method. However, these metrics present limitations, such as dependence on outlet temperatures or circular efficiency definitions, which hinder rigorous assessment of thermal performance. This study proposes a new performance function for heat exchangers, based on the ratio of heat transferred to heat available and expressed using average stream temperatures. We demonstrate that this approach avoids the circularity inherent in conventional definitions and enables a more accurate characterization of thermal performance across different flow configurations. Our parametric and sensitivity analysis reveals that effectiveness (ε) is the dominant performance variable and that flow arrangement significantly influences heat transfer. Compared to previous methodologies, this new indicator provides a unified framework for evaluating and optimizing heat exchangers in practical applications. These findings establish a solid basis for enhancing heat exchanger design and efficiency within industrial systems. Теплообмінники є ключовими пристроями в теплових системах, що використовуються у промисловості, енергогенерації та процесах теплоперетворення. Для оцінки їх продуктивності застосовуються різні методики, серед яких найбільш поширеними є метод логарифмічної середньої різниці температур (LMTD) та метод ефективності ‒ NTU. Однак ці метрики мають обмеження, такі як залежність від температури на виході або замкненість у визначенні ефективності, що ускладнює об’єктивну оцінку теплової продуктивності. У цьому дослідженні пропонується нова функція продуктивності для теплообмінників, заснована на співвідношенні переданої теплоти до наявної, вираженому через середні температури потоків. Показано, що цей підхід усуває замкненість, властиву традиційним визначенням, та дозволяє точніше характеризувати теплову продуктивність у різних конфігураціях потоків. Результати параметричного аналізу та аналізу чутливості показали, що ефективність ( ) є домінуючою змінною у визначенні продуктивності, а схема руху потоків суттєво впливає на теплопередачу. Порівняно з існуючими методиками, новий показник забезпечує єдину основу для оцінки та оптимізації теплообмінників у практичних застосуваннях. Ці висновки пропонують міцну базу для покращення проєктування та ефективності теплообмінників у промислових системах. General Energy Institute of the National Academy of Sciences of Ukraine 2025-11-21 Article Article application/pdf https://systemre.org/index.php/journal/article/view/930 10.15407/srenergy2025.04.123 System Research in Energy; No. 4 (84) (2025): System Research in Energy; 123-134 Системні дослідження в енергетиці; № 4 (84) (2025): Системні дослідження в енергетиці; 123-134 2786-7102 2786-7633 en https://systemre.org/index.php/journal/article/view/930/827 Copyright (c) 2025 Eduardo González-Mora https://creativecommons.org/publicdomain/zero/1.0 |
| spellingShingle | heat exchanger energy efficiency LMTD effectiveness-NTU performance indicator thermal system analysis modelling temperature difference. González-Mora, Eduardo A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title | A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title_alt | Раціональне визначення ефективності для теплообмінників |
| title_full | A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title_fullStr | A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title_full_unstemmed | A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title_short | A RATIONAL EFFICIENCY DEFINITION FOR HEAT EXCHANGERS |
| title_sort | rational efficiency definition for heat exchangers |
| topic | heat exchanger energy efficiency LMTD effectiveness-NTU performance indicator thermal system analysis modelling temperature difference. |
| topic_facet | heat exchanger energy efficiency LMTD effectiveness-NTU performance indicator thermal system analysis modelling temperature difference. теплообмінник енергоефективність LMTD ефективність ‒ NTU показник продуктивності аналіз теплової системи моделювання різниця температур. |
| url | https://systemre.org/index.php/journal/article/view/930 |
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