Journal homepage: www.fia.usv.ro/fiajournal
Journal of Faculty of Food Engineering,

Ştefan cel Mare University of Suceava, Romania
Volume XIII, Issue 1 – 2014, pag. 14 - 22

INTENSIFICATION OF THE HEAT TRANSFER

THROUGH CORRUGATED WALL
*Donka STOEVA1

1University of Food Tehnologies, MAFI Department,

26 Maritsa Blvd; 4000 Plovdiv; BULGARIA
bodurova@gmail.com
*Corresponding author

Received February 17th 2014, accepted March 14th 2014

Abstract: The corrugation of the smooth steel tubes increases the heating surface per length unit. The
advantages compared to smooth pipe bodies are the lower relative mass at same thermal power and
the smaller volume. The aim of the present research is to trace the temperature alteration near to a
specially corrugated wall with baffles. The baffles have variable step towards the flow direction at two
different heights. We observe developed turbulent air flow at temperature 353К (80oC) through a
corrugated tube with inside diameter d=0.08m and length 0.2m. The tube wall is heated to 453K
(180oC). The heat transfer between the tube and the flowing fluid has been modulated at two different
corrugation grades of the tube – Х1 and Х2 – equation (9) and with four different Reynolds numbers.

Key words: CFD, boundary layer , surface baffles, turbulization, circulation zone.

1. Intorduction

The intensity of the heat transfer can be
influenced by alteration of the geometric
dimensions of the channel, alteration of the
velocity of the heat carrier and the form of
the heat transfer surface, which defines the
temperature field [1, 2, 3].
One of the ways for intensification of the
heat flows is by increasing the velocity of
the heat carrier or by corrugating the
surfaces.
When flowing onto hard wall there is a
boundary layer forming. It is the main
thermal resistant. The thicker the boundary
layer is, the lower the heat transfer is [4, 5,
6].
The decreasing of the boundary layer
thickness and the increasing of the transfer
coefficients
For moment and heat is the essence of the
heat transfer intensification.

Most profitable hydrodynamic regime
regarding the heat transfer is the
transitional and turbulent regime in the
boundary layer. This can be achieved by
artificial turbulization of the flow in the
boundary layer or destroying of the
boundary layer near the wall. This enforces
the application of artificial methods for
intensification of the heat transfer.
The methods for intensification of heat
transfer are divided in two groups: passive
and active.
Passive methods are the ones that do not
need direct use of outer energy source.
Active are those, who use outer source.
There are two methods used for
intensification of the heat transfer: increase
of the heat flow, regardless of the costs and
increase of the heat flow at defined power
of the heat carrier [1, 2, 3, 4]. The most
frequently used passive method is
intensification through surface baffles,

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

such as rough surfaces and equally
distributed roughness [5, 6].
The configuration of the baffles is chosen
is such a way, so that it destroys the
viscosity sub-layer and increases the
turbulence near the wall [7, 9, 10].
One of the most important conditions for
choosing of method is the hydrodynamic
structure of the flow in which we need
alteration in the temperature field
distribution. Knowing this structure, we
can reduce the areas in which the increase
of the intensification of the turbulent
pulsations will make greatest influence on
the heat transfer intensification [1, 7, 8, 9].
The analysis and the visualization of the
flow in such tubes are of great importance

because they have wide application in the
heating equipment and many other spheres.
The aim of the present research is to trace
the temperature alteration near to a
specially corrugated wall with baffles. The
baffles have variable step towards the flow
direction at two different heights.

2. Materials and Methods

The model researches are carried out at
four different Reynolds numbers (Re). We
have used the equation for fluid movement
for turbulent regime (equation 1) and we
have added two equations for kinetic
energy (equation 2)– k and kinetic energy
dissipation (equation 3)

22ji i ti t
i j j i i k i j

UU U vk k k
U v ( ) ( v ) v( )

x x x x x x x



      

             
(1)


2k

Cvt  (2)

k
C

x
U

v
k

C
x

v
v

xx
U

i
t

ii
i

21 )()(





 




























(3)

The constants are:

1 2 1 2
2

1 92
1 44 1 92

1 0 9
.

C . ; C .
( . A A ) 

  


(4)

For solving the heat transfer system of
equations we add the equation for energy
of the following type:

eff j j eff hj
( E ) .( v( E p )) .( k T h J ( )) S

t
   


       




 
(5)

Where effk is the effective conductivity,

tk is the turbulent conductivity defined

by the used turbulent model, and jJ


is a
diffusion of the flow type j . The first
three nominals at the right side of the
equation present the energy transfer
through conductivity, the specific diffusion

and the viscous dissipation. hS includes
heat from chemical reactions and others, if
such are defined.

2
p v

E h


   (6)

where the enthalpy h for an
incompressive fluids is calculated by
equation (7) :

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

j jj

p
h Y h


  (7)

In the above equations jY is the mass
fraction of the type j .

j p , jTref
h C dT 

(8)
where Tref =298.15К

For the two-dimension case the mash
contains 16500 cells, 33350 faces and
16581 knots as a preliminary test for
independence of the solution from the
mash thickness has been performed [3, 4,
9, 10].

We observe developed turbulent air flow at
temperature 353К (80oC) through a
corrugated tube with inside diameter
d=0.08 m and length 0,2 m. The tube wall
is heated to 453K (180o C). The heat
transfer between the tube and the flowing
fluid has been modulated at two different
corrugation grades of the tube – Х1 and Х2
– equation (9) and with four different
Reynolds numbers (we achieve that by
setting four different initial velocities at the
boundary conditions – equation (10)). The
graphic relations are shown for central
section in the geometric body and for the
outgoing section.

1
0 002

0 025
0 08

h .
X .

D .
   ; 22

0 004
0 05

0 08
h .

X .
D .

   (9)

1 5

0 75 0 08
3353 1

1 7894 10в х

V .D . .
Re .

. 


  


22 5

1 0 08
4470 8

1 7894 10в х

V .D .
Re .

. 


  



33 5
2 0 08

8941 5
1 7894 10в х

V .D .
Re .

. 


  


544 5

2 8 0 08
0 125 10

1 7894 10в х

V .D . .
Re .

. 


   


(10)

Fig. 1 Geometric model of observed area from the corrugated tube with threshold height h1=2 mm.

The steps between two thresholds are
different. For the first drawing (Fig 1) the
height of the threshold is h1=2 mm. The
dimensionless ration between the height of

the threshold and the distance between the
two thresholds calculated by equation (11)
is:

1
1

0 045
22 5

0 002
P ,

Y ,
h ,

   ; 22
2

0 085
42 5

0 002
P ,

Y ,
h ,

   (11)

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

Fig. 2 Geometric model of observed area from the corrugated tube with threshold height h2=4 mm

On (Fig.2) the height of the threshold is
h2=4 mm. The distance between the
thresholds is different. The dimensionless

ration between the height of the threshold
and the step P – equation (12) is:

3
1

0 045
11 25

0 004
P .

Y .
h .

   ; 24
2

0 085
21 25

0 004
P .

Y .
h .

   (12)

3. Results and Discussions

-0,07 -0,06 -0,05 -0,04 -0,03

350

360

370

380

390

400

410

420

430

440

450

Y-coo rdina te (m )

T X
1
=0.025

T X
2
=0.05

T
em

pe
ra

tu
re

[K
]

Twall=453K,Ta ir=353K, Re
1
=355 3.1

Fig.3 Temperature gradient in cross-section in
the center for Re1=3353.1

at two different thresholds Х1 and Х2

-0,07 -0,06 -0,05 -0,04 -0,03
340

360

380

400

420

440

460

T
em

pe
ta

tu
te

[K
]

Y-coordinate ( m)

Re
4
=0.125×105; X

1
=0.025

Re
4
=0.125×105; X

2
=0.05

Fig. 4. Comparison of the temperature gradient

in cross-section at Re4=0.125×105 at two
different thresholds Х1 and Х2

-0,07 -0,06 -0,05 -0,04 -0,03
340

360

380

400

420

440

460

Y-coordinate ( m)

Te
m

pe
ta

tu
te

[K
]

Re4 X
1
=0.025 Re4 X

2
=0.05

Re1 X
1
=0.025 Re1 X

2
=0.05

Fig. 5 Temperature gradient at the two heights
of the threshold Х1 and Х2

for Re1=3353.1 and Re4 =0.125×105

The change in the flow character near the
wall reflects in the distribution of the
temperature and velocity towards the flow
direction and perpendicular to the flow.
The temperature profile change is most
sensitive at the higher threshold (Х2=0.05)
at the same Reynolds number.

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

-0,070 -0,065 -0,060 -0,055 -0,050
340

360

380

400

420

440

460

em
pe

ra
tu

re
[

K
]

Y-coordinate [m]

Re1=3353.1; Re2=4470.8

Re3=8941.5; Re4=0.125×10
5

Fig.6. Influence of the Reynolds number on the

temperature distribution at cross direction at Х1.

On Figure 6 we can follow the influence of
the Reynolds criteria on the temperature
distribution at geometric model with
relative height of the threshold – Х1=0.025.
By increasing the value of Re the
temperature profile is changed as it nears

the wall. The temperature profile at Re4 is
nearest to the wall, which means that at
high Re values there will be the best heat
transfer and the heat transfer surface will
used in the most effective way.
The observation of the location and the
size of the circulation zone give
opportunity for optimization of the shape
and geometrical parameters of the
threshold. After modulation and analysis of
the circulation zone we can estimate the
best solution for maximal effective heat
transfer, which is the final goal of the
numerical modulation. Every observation
is performed after testing of the calculating
mash for adequacy and after proving the
independence of the solutions from the
thickness of the calculating mash.

Fig.7 Constant temperature lines – isotherms, X1=0.025 and Re1=3353.1

Fig.8 Constant temperature lines - isotherms, X1=0.025 and Re1=3353.1

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

Lines with constant temperature –
isotherms have been calculated and drawn.
The visualization of the isotherms near the
flowed wall is of great interest regarding
the intensification. The isotherms are
drawn for equal temperature intervals – by
20 degrees. The most intensive heat
transfer we have near the wall, not in the
centre of the flow that is why it is
important to show the temperature
distribution exactly at this place. After
comparison of the isotherms (Fig. 8 and
Fig. 9) at the two heights of the thresholds
we can make a conclusion for the

temperature gradient alteration. We can see
that at the higher threshold the higher
temperature isotherms are further from the
wall. The prove for that statement is the
visible difference in the temperature
profiles near the wall (Fig. 11 and Fig. 12)
at the two heights of the threshold and at
same Reynolds number. This means that at
higher threshold there is better heat
transfer. The increase of the threshold
dimension can not be done infinitely and
there is a maximal value, up to which it
can be increased.

Fig. 9 Constant temperature lines - isotherms, X2=0.05 and Re1=3353.1

Fig.10 Constant temperature lines – isotherms, X1=0.025 and Re4=0.125×105

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

Fig. 11 Constant temperature lines – isotherms, X1=0.025 and Re4=0.125×10

Fig. 12 Constant temperature lines – isotherms, X2=0.05 and Re4=0.125×10

We can see on Figures 7, 11 and 12 the
simultaneous impact of the higher
threshold as well as of the higher Reynolds
number. The correct choice of these two
significant factors defines the good heat
transfer between the heated surface and the
cool fluid. At the exit on Fig. 12 there is
the smallest cold sector, which means that
the best heat transfer will be achieved if
the height of the threshold is 4mm and
Re4=0.125×105.
By comparison of the shape of the
temperature profiles we can estimate the

influence of the corrugation and the
velocity of the fluid on the temperature
distribution in Y direction. At the highest
values of the Reynolds number (Re4) we
have the highest value of the temperature
of the heated fluid (air) at the outlet in
perpendicular to the flow direction. We
achieve better heat transfer at higher values
of Reynolds number. If we combine
enough high threshold and velocity of the
flowing fluid at the outlet we can achieve
the least cold zone. That is the important
role of the calculating hydrodynamics and

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

the methods for modulation of such
processes – because these modern
calculation tools help making the right

choice for the best solution amongst the
many variants of the given problem.

Fig.13 Influence of the threshold height on the temperature distribution

We can see on Fig. 13. the lines with the
equations, which describe them for the size
of the zone with temperature 353К. At the
high threshold (Х2) at the outlet the section
with temperature 353К is 0.0026m and at
the lower threshold (Х1) it is 0.012m. We
have mathematically described the
dimensions of the zones with temperature
353К. The cold zone at the higher
threshold is smaller, which means there is
a better mixing and turbulization of the
flow.

4. Conclusion

On the base of the result, we can make the
following conclusions:

1. The uneven step of the baffles leads
to better picture of the wall
flowing.

2. By increasing the criteria of Re we
reduce the size of the non-flowing
zone after the baffles, which leads
to increasing the heat transfer.

3. The increasing of the temperature
under the influence of the baffles is
highly expressed in the direction of
the flow.

4. The higher the threshold – the
better the heat transfer.

5. There is a better heat transfer at
higher Reynolds number values.

6. If we combine high enough
threshold and velocity of the fluid
at the outlet, we achieve the
smallest cold zone.

7. This research can be used for
finding optimal values of the
Reynolds number regarding the
conditions for heat transfer.

5. References

[1]. KOSTOV P., K. ATANASOV, N.
KRASTEV, D. ANGELOVA. „Universal velocity
profiles of twisted injected jet“, Scientific works
tome LX “food science, technology and processes –
2013“ 18-19 October 2013, Plovdiv, pp.1531-1535.
(in bulgarian)
[2]. KOSTOV P, KRASTEV N, ANGELOVA D,
Observation of injected radial jet at isothermal
conditions – National Conference with international
participation “Machine science”- 2012 – Sliven.
Heat Technology 3, Year 3, Book 1 ISSN 1314-
2550 pp. 8-11. (in bulgarian)

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava
Volume XIII, Issue 1 – 2014

Donka STOEVA , Intensification of the heat transfer through corrugated wall, Volume XIII, Issue 1 - 2014, pag. 14 – 22

[3]. KOSTOV P., KRASTEV N., ANGELOVA
D., DIMITROV I. „Estimation of temperature
fields from flat-flame burner”, XVII scientific
conference with international participation EMF
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sofia.bg/faculties/emf/confer/documents/tom_1.pdf
(in bulgarian)
[4]. BERGLES, A. E. ExHFT for fourth
generation heat transfer technology, Exp. Thermal
Fluid Sci., Vol. 26, Nos. 2-4, pp. 335-344, (2002).
[5]. BERGLES, A. E. ExHFT for fourth
generation heat transfer technology, Exp. Thermal
Fluid Sci., Vol. 26, Nos. 2-4, pp. 335-344, (2002).
[6]. CATCHPOLE, J.P., DREW, B.C.E.,
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condensers, Steam Turbine Condenser, Report of a
Meeting at NEL, Glasgow, UK, pp. 68-75, (1974).
[7]. MANGLIK, R.M., BERGELS, A. E,
Enhanced Heat transfer in the New Millenium: A
Review of the 2001 Literature, Thermal Fluids and
Thermal Processing Laboratory, Laboratory report
№ TFTPL-EB01, University of Cincinnati, OH,
(2002).

[8]. V. ZIMPAROV, Enhancement of heat transfer
by a combination of a single – start spirally
corrugated tubes with a twisted tape, Experimental
thermal and Fluid Science 25 (2002) 535-546.
[9]. V. ZIMPAROV, Prediction of friction factors
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corrugated tubes combined with twisted tape
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(2004) 385-393.
[10]. Ő. AĞRA, H. DEMIR, Numerical
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