DOI: 10.3303/CET25120080 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 02 May 2025; Revised: 20 August 2025; Accepted: 8 September 2025 
Please cite this article as: Kapustenko P., Kravanja Z., Plazl I., Varbanov P.S., Arsenyeva O., Nemet A., Tovazhnyanskyy L., 2025, Selection of 
Heat Transfer Enhancement Technique for Compact Mini and Micro Heat Exchangers Design, Chemical Engineering Transactions, 120, 475-
480  DOI:10.3303/CET25120080 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 120, 2025 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Bing Shen How, Viknesh Andiappan, Denny K.S. Ng, Hon Loong Lam, Petar S. Varbanov 

Copyright © 2025, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-21-2; ISSN 2283-9216 

Selection of Heat Transfer Enhancement Technique for 

Compact Mini and Micro Heat Exchangers Design  

Petro Kapustenkoa,*, Zdravko Kravanjab, Igor Plazlc, Petar Sabev Varbanovd, Olga 

Arsenyevae, Andrea Nemetb, Leonid Tovazhnyanskyyf  

aSustainable Process Integration Laboratory—SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of 

Technology—VUT Brno, Technická 2896/2, 616 69 Brno, Czech Republic   
bUniversity of Maribor, Faculty of Chemistry and Chemical Engineering, Smetanova ulica 17, 2000 Maribor, Slovenia 
cUniversity of Ljubljana, Faculty of Chemistry and Chemical Technology, Večna pot 113, 1000 Ljubljana, Slovenia  
dSzéchenyi István University: Győr, HU 
ePaderborn University, Chair of Fluid Process Engineering, Warburger Str. 100, 33098, Paderborn, Germany  
fNational Technical University "Kharkiv Polytechnic Institute", 2 Kyrpychova st., 61002 Kharkiv, Ukraine  

 kapustenko@fme.vutbr.cz  

The need to decrease the sizes and masses of heat exchangers while preserving their performance has 

stipulated the development of compact heat exchangers with mini and micro channels (MCHE). It is supported 

by the need for increased recuperation of heat energy, facilitating better energy efficiency with strict limitations 

for space, material and cost. The adequate substitution of conventional heat exchangers with MCHE requires 

maintaining the same heat load, not exceeding the allowable pressure losses. The different ways to increase 

the compactness are analysed, including the change of hydraulic diameter, and the use of various methods of 

heat transfer intensification by changing the channel geometry and flow structure. The Nusselt numbers and 

friction factors correlations for plane tubes and criss-cross flow channels of plate heat exchangers are compared. 

A newer form of the core velocity equation has been developed, which allows comparison of the performance 

of MCHE heating surfaces with different enhancement techniques in specific process conditions. The results of 

the calculations illustrate the influence of the channel's hydraulic diameter and length on the MCHE performance 

for channels with the considered methods of heat transfer intensification. The ways to decrease channel size to 

mini and micro scales are determined. The recommendations on choosing the best channel geometry and size, 

depending on specified process conditions and stream nature, are formulated.   

1. Introduction 

Increased heat recuperation is the main prerequisite for efficient energy use in thermal systems in chemical and 

many other industrial applications. The main components responsible for this and for the total size and weight 

of such a system are heat exchangers. With a further rise in demand for energy, limited space and material 

resources necessitate further developments in heat exchangers' construction and design principles. In that view, 

compact heat exchangers with mini and micro channels can be regarded as the next generation of heat transfer 

equipment, accounting for enhanced heat transfer and reduction of weight, volume and materials for their 

construction.  

According to Kandlikar and Grande (2003) minichannels can be classified by hydraulic diameters Dh from 3 mm 

to 0.2 mm, and microchannels as having Dh from 0.2 mm to 0.01 mm. The hydraulic diameters outside these 

ranges characterise conventional channels with Dh exceeding 3 mm and transitional microchannels and 

nanochannels with Dh smaller than 0.01 mm.  

Mini and microchannel heat exchangers have found a wide range of applications in microelectronics (Bhandari 

et al., 2024), micro process systems (Sharifian et al., 2024), waste heat utilisation involving supercritical CO2 

and Micro-Electromechanical Systems (MEMS) technology (Ejaz and Zubair, 2025), air conditioning systems 

(Han et al., 2012), communal sector and pasteurisation (Tuckerman et al., 2011), solar thermal energy and 

nuclear power (Ma et al., 2022), recuperators for micro gas turbines (Wang et al., 2024), refrigeration (Başaran 

475



and Benim, 2024), aerospace and defense aviation applications (Marseglia et al., 2024). It stipulated a large 

number of studies in this field. For 6 years only, from 2017 to 2023, the Scopus database contained 3877 papers 

on microchannel heat exchangers (Dwivedi et al., 2023). During that period, about 25 review papers were 

published only on microchannel heat sink studies (Bhandari et al., 2024), and approximately the same number 

for other applications. With such a large number of studies on heat transfer and friction in minichannels and 

microchannels, there are considerable differences in the results of experiments and the views on the applicability 

of conventional correlations. It was observed more than two decades ago by Sobhan and Garimella (2001), and 

not much changed later with the appearance of newer research results surveyed by Morini (2004) and later by 

Singh et al. (2019). It creates difficulties in designing real compact heat exchangers with mini and micro 

channels. The selection of the proper geometry of such channels requires an efficient method of estimating their 

thermal and hydraulic performance in specific conditions of operation in different applications. It becomes even 

more important with current trends of developing new methods of heat exchangers production with additive 

manufacturing, and heat transfer intensification using nanofluids. 

The objective of this paper is to present a method for comparing the efficiency of heat exchangers operating 

with different minichannels and microchannels, based on a developed equation for optimal fluid velocity inside 

the channels. This approach enables the full utilisation of the available pressure drop in the heat exchanger with 

minimal heat transfer surface area F. These values of heat transfer areas F, obtained for the different channels, 

can be compared by the proposed Specific Performance Index.   

2. Method 

To estimate heat transfer area for comparison of different heat exchangers, consider the heat exchanger strictly 

satisfying specific process conditions (with specified flow rates, temperature program and pressure losses), 

operating at pure counter current flow of heat exchanging streams. The heat transfer load Q calculated at the 

cold fluid side must be equal to the heat transferred through the heat transfer surface, following Eq(1). 

𝑄 = 𝑈 ⋅ 𝛥𝑇𝑙𝑛 ⋅ 𝐹 = 𝑊2 ⋅ 𝐹𝑐𝑠  ∙ 𝑐𝑝2 ⋅ 𝜌2 ∙ (𝑇22 − 𝑇21),                                                                         (1) 

where W2 is the cold stream flow velocity, m/s; F is the heat transfer area, m2; Fcs is the channel cross-section 

area, m2; T21 is the cold stream entrance and T22 is the cold stream exit temperature, K; cp2 is the cold fluid 

specific heat, J/(kg K); ρ2 is the fluid density, kg/m3; ΔTln is the Logarithmic Mean Temperature Difference. 

The number of heat transfer units NTU from Eq(1) can be written as Eq(2): 

𝑁𝑇𝑈 =
𝑈⋅𝐹

𝑊2⋅𝐹𝑐𝑠 ∙𝑐𝑝2⋅𝜌2
=

𝑇22−𝑇21

𝛥𝑇ln
                           (2) 

On the left-hand side, it is NTU satisfied by the heat exchanger, and on the right-hand side, it is NTU0 required 

by the specified process. The heat transfer area at the cold side can be expressed as the product of its length 

L multiplied by the wetted perimeter Π. Then the hydraulic diameter Dh of the channel is calculated by Eq(3): 

 𝐷ℎ = 4 ∙
𝐹𝑐𝑠

Π
         (3) 

The left part of Eq(2) can be expressed by Eq.(4), and for specific conditions must be equal to NTU0: 

 𝑁𝑇𝑈0 =
𝑈⋅4

𝑊2⋅𝑐𝑝2⋅𝜌2
∙
𝐿

𝐷ℎ
          (4) 

The heat exchanger must strictly satisfy the specified pressure drop ΔP2 for the cold fluid expressed by Eq.(5). 

 𝛥𝑃2 = 2 ⋅ 𝑓2 ⋅ 𝜌2 ⋅ 𝑊2
2 ∙

𝐿

𝐷ℎ
                                                                                                  (5) 

where f2 is the Fanning friction factor. Dividing Eq(5) on Eq(4) gives: 

 
𝛥𝑃2

𝑁𝑇𝑈0
=

𝑓2⋅𝑊2
3∙𝑐𝑝2⋅𝜌2

2

𝑈⋅2
                                                                                                             (6) 

For a known friction factor and overall heat transfer coefficient U, this Eq(6) determines the flow velocity in the 

channel that strictly satisfies the specified process conditions as equalities. It corresponds to a minimal heat 

transfer surface for these conditions, as all pressure drop is used and no margin on heat load. However, the 

values of U and f2 are not known, but can be determined by empirical correlations for the considered channel 

when thermal resistances for the hot side of the heat exchanger and its wall are known. For comparison of two 

different channels in the same conditions, it can be assumed that the thermal resistances on the hot side are 

the same for both channels, and the main resistance to heat transfer is concentrated on the cold side. In that 

case overall heat transfer coefficient U is equal to the heat transfer coefficient at the considered channel h2 and 

476



can be determined by the correlation for Nusselt number (Nu) in this channel, as well as the friction factor f2 by 

its correlation. For the same fluid and temperature program h2 and f2 depend only on fluid velocity in the channel 

under consideration and channel hydraulic diameter Dh, and Eq(6) can be transformed to Eq(7), as it is shown 

in more detail by Kapustenko et al. (2025). 

𝑊2 = √
2⋅𝛥𝑃2⋅ℎ2(𝐷ℎ,𝑊2)

𝑐𝑝2⋅𝜌2
2⋅𝑁𝑇𝑈⋅𝑓2(𝐷ℎ,𝑊2)

3
                                                                                                     (7) 

For the fixed value of hydraulic diameter Dh, Eq(7) can be solved by iterations, with the initial value of W2 equal 

to 0.5 m/s. The calculations are repeated until the difference between two consecutive values of W2 becomes 

smaller than 0.001 m/s.  After that, heat transfer area F is determined by Eq(1). This value corresponds to the 

channel of the considered geometry, with the length of the heat transfer area strictly satisfying the specified 

process conditions. It is valid for the ranges of Reynolds (Re) and Prandtl (Pr) numbers at which there are 

accurate correlations for Nu and f. With maintained geometrical similarity of the channel, the change of Dh does 

not affect these correlations until the continuum approach with no wall slip is valid for the flow of the considered 

fluid (Kandlikar and Grande, 2003). With diminishing hydraulic diameter of microchannels, such a conventional 

approach will not be satisfied starting with some lower value of Dh. By the estimates of different scholars, this 

value can lie somewhere between 0.01 and 1 mm. It will be checked later by comparing experimental results 

published by the different authors. As the basis of conventional correlations for smooth tubes, the following 

applies. 

An Equation Eq(8) developed by Churchill (1977) correlates the Fanning friction factor for all flow regimes 

(laminar, transitional and turbulent). 

𝑓 = 2 ⋅

{
  
 

  
 

(
8

𝑅𝑒
)
12
+

1

([2.457⋅ln(
1

(
7
𝑅𝑒)

0.9
+0.27⋅

0
𝐷

)]

16

+(
37,530

𝑅𝑒
)
16
)

3
2

}
  
 

  
 

1

12

                (8) 

For the Nusselt number Nu in turbulent flow inside tubes is used the Eq(9) of Gnielinski (1975):  

𝑁𝑢 = 𝑁𝑢𝑇 =
𝑓⋅𝑃𝑟⋅(Re−1000)

2⋅[1+12.7⋅√𝑓 2⁄ ⋅(𝑃𝑟
2
3⁄ −1)]

 for Re > 4,000 
(9) 

At lower Reynolds numbers the Eq(10) and Eq(11) of Gnielinski (2013) are used. 

For Re≤2300 (laminar flow) 

𝑁𝑢𝐿 = [3.66
3 + 0.73 + (1.615√𝑅𝑒 ⋅ 𝑃𝑟 ⋅

𝐷

𝐿

3
− 0.7)

3

+ (
2

1+22⋅𝑃𝑟
)

1

6
⋅ (𝑅𝑒 ⋅ 𝑃𝑟 ⋅

𝐷

𝐿
)

1

2
]

1

3

  (10) 

For 4000≥Re>2,300 (transitional flow regime) 

𝑁𝑢 = 𝑁𝑢𝐿.2300 +
(𝑁𝑢𝑇.4000−𝑁𝑢𝐿.2300)⋅(𝑅𝑒−2,300)

4,000−2,300
  (11) 

Here, Re is the Reynolds number; Pr is the Prandtl number; D is the tube diameter, m; L is the tube length, m. 

The effect on heat transfer of a temperature change from the mainstream to the wall is neglected. 

3. Results and discussion 

The method is illustrated by the example of heating an incompressible liquid. For microchannels, this process 

usually occurs at Re numbers below 4,000. The flow of gases is not considered in this paper. It is necessary to 

heat water at a flow rate of 2.9 kg/s from 5 °C to 55 °C at the exit of a heat exchanger, using vapour at 

temperature 60 °C exhausted with the temperature 60 °C. The available pressure difference on the cold water 

side is ΔP2 = 20,000 Pa. The results of calculations by Eq(7), using Eqs(8-11) for smooth tubes, are presented 

in Figure 1. The character of the heat transfer area changes with the decrease in hydraulic diameter is 

complicated in the region corresponding to the transition between laminar and turbulent flow regimes. In the 

considered example, when Dh becomes smaller than 3 mm, F grows up to four times. This peak in F at Dh ≈ 1–

3 mm arises from deterioration of convective heat transfer in transition from turbulent flow regime at 

4,000>Re>2,300, with flow becoming laminar at Re<2,300. With further decrease of Dh, the heat transfer surface 

area F decreases with a smaller hydraulic diameter. It diminishes again to the values at turbulent flow regime 

477



(Dh>3 mm) only at Dh about 0.3 mm. However, even such a reduction of F becomes doubtful, accounting for the 

possible change of correlations in microchannels with a hydraulic diameter less than 1 mm. According to Wu 

and Cheng (2003), in straight channels of hydraulic diameters from 25.9 to 209.8 μm, the Nu number can be 

from 10 % to 90 % smaller than the value calculated by the equation for a smooth tube.  

 

Figure 1: Heating area F at different hydraulic diameters Dh    

Comparing different channels, the heat transfer area Fs3, of a heat exchanger with smooth tubes at Dh = 3 mm  

is taken as a benchmark, and the specific performance index (SPI) can be written by Eq(12): 

𝑆𝑃𝐼 =
𝐹

𝐹𝑠3
                                                                                                                       (12) 

 

Figure 2: Performance evaluation index (SPI) at different hydraulic diameters Dh  

The SPI index enables a more rigorous estimation of the channel performance, as it is nondimensional and, for 

the examined channel, depends only on the temperature program, fluid properties and pressure drop. The heat 

transfer area F is otherwise affected by the heat load Q. The evolution of the SPI of the smooth tube with the Dh 

is depicted in Figure 2. Counting for uncertainty with Dh smaller than 1 mm, there is little chance to decrease 

the heat transfer area based on channels with smooth surfaces just by decreasing the hydraulic diameter. It 

would require employing other methods of heat transfer enhancement. One such method is used in crisscross 

flow channels of plate heat exchangers and primary surface recuperators of micro gas turbines (Figure 3). The 

0.01 0.1 1 10
0.1

1

10

100

Smooth tube

Crisscross flow channel

Hydraulic diameter Dh, mm

H
e
at

 t
ra

n
sf

er
 s

ur
fa

ce
 a

re
a 

F
, 
m

2

0.01 0.1 1 10
0.1

1

10

Smooth tube

Crisscross flow channel

Hydraulic diameter Dh, mm

S
p
ec

if
ic

 P
e
rf

o
rm

a
n
ce

 I
n
d
e

x
 (

S
P

I)

478



generalised correlations for friction factor and Nu number in such channels were proposed by Arsenyeva et al. 

(2012).  

 

Figure 3: Schematic drawing of a crisscross flow channel   

The results of calculations by these correlations for the channel with the corrugation inclination angle 60 degrees 

and aspect ratio 0.6 are presented in Figure 1, with index SPI in Figure 2 by the dashed lines. The performance 

index is changing from 0.43 at Dh = 3 mm to 0.307 at Dh = 1 mm, with the possibility of further decrease to 0.148 

at Dh = 0.1 mm. While the applicability of such conventional correlations at Dh < 1 mm needs to be studied, at 

Dh = 1 mm it can be granted. Xi et al. (2018) studied crossflow channels of primary surface recuperators with 

hydraulic diameters from 0.89 to 0.94 mm.  In that case, SPI=0.307, which even theoretically could be achieved 

with a smooth surface at a much smaller hydraulic diameter Dh = 0.08 mm. In such conditions, the Re number 

is equal to 82, corresponding to laminar flow in a smooth tube. In a crisscross flow channel at Dh = 1 mm Re 

number is equal to 685, which corresponds to a turbulent regime in these channels with heat transfer 

enhancement. It confirms the possibility of using crisscross flow channels for manufacturing efficient micro heat 

exchangers and emphasises the need for further studies with different heat transfer enhancement techniques. 

4. Conclusions 

Nowadays, compact heat exchangers with mini and micro channels can be regarded as the next generation of 

heat transfer equipment, accounting for enhanced heat transfer and reduction of weight, volume, and 

construction materials. This efficient type of equipment is finding a lot of applications in different industries. A 

large number of experimental and theoretical studies on heat transfer and hydraulic performance of such 

channels have been published in recent years. Some results of these studies for channels of hydraulic diameters 

less than 1 mm are not consistent. A method to estimate the performance of a heat exchanger with different 

mini and micro channels is proposed.  It is based on a developed equation for the estimation of fluid velocity in 

the channel that allows strict satisfaction of the specific conditions of the temperature program and pressure 

losses in a heat exchanger with channels of different hydraulic diameters. The Specific Performance Index (SPI) 

for comparison of channel performance in specific process conditions is introduced. It is shown that simple 

reduction of hydraulic diameter for channels with smooth walls can lead to an increase of required heat transfer 

surface area on some intervals of mini and micro sizes from hydraulic diameter about 3 to 0.3 mm. To get a 

monotonic decrease in heat transfer surface area with the diminishing hydraulic diameter, it is better to use 

channels with enhanced heat transfer. It is shown by an example of the crisscross flow channel, typically used 

in plate heat exchangers and primary surface recuperators of gas turbines. The SPI value of 0.30, which 

corresponds to 70 % reduction in heat transfer area, can be achieved at a moderate value of hydraulic diameter 

of about 1 mm. In future research, other methods of heat transfer enhancement in microchannels should be 

investigated and estimated with the proposed methodology. 

Acknowledgments 

The research has been supported by Czech Science Foundation GACR (project #24-14939 L) and Slovenian 

Research and Innovation Agency (project J2-60044). Olga Arsenyeva is grateful for receiving the Philipp 

Schwartz funding grant for threatened researchers from Paderborn University within the framework of the Philipp 

479



Schwartz Initiative of the Alexander von Humboldt Foundation and acknowledges Prof. Eugeny Kenig and Prof. 

Julia Riese for personal support.  

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	Selection of Heat Transfer Enhancement Technique for Compact Mini and Micro Heat Exchangers Design