Journal homepage: www.fia.usv.ro/fiajournal

Journal of Faculty of Food Engineering,

Ştefan cel Mare University of Suceava, Romania

Volume XVII, Issue 1-2018, pag. 9 - 19

HEAT TRANSTER AT EVAPORATIVE CONCENTRATION OF DOWN FLOWING

IN VERTICAL PIPES SOLUTIONS IN ANNULAR REGIMES

Valentin PETRENKO
1
, *Yaroslav ZASIADKO1

1Department of Termal Engineering and Industrial Refrigeration,

National University of Food Technologies,

68, Volodymyrska St.; 01601 Kyiv; Ukraine

*Corresponding author iaroslav@nuft.edu.ua
Received 20th November 2017, accepted 19th March 2018

Abstract: In many branches of food processing, particularly in sugar production, the solution

concentration takes place within industrial multi effect evaporator; here, the solution moves down as a
liquid film forming annular descending flow in vertical heated pipes. It should be noticed that within

the evaporation station the liquid which is being evaporated significantly changes its physical

properties due to the fact that the concentration of the solution increases by the range of 14…65% of
dry matter. The operational process parameters (pressure, temperature, etc.) also change to a

noticeable degree. These factors determine a wide range of liquid films flow patterns, namely film

thickness, surface wavy structures, velocity distribution across the films, interphase shear stress and,
as a result of these, the making of a certain heat transfer mechanism including bubble boiling or its

suppression. Unfortunately, the reliable methods of prediction and calculation of heat transfer

coefficients are unavailable, which seriously hampers the designing and calculation of efficient

evaporators and other heat transfer equipment. The work presents the results of modeling heat
transfer to saturated liquid films of solutions flowing down inside the vertical pipes as in the regime of

evaporation from the interphase surface and in that of surface boiling. The correlations given allow

calculating the heat transfer coefficients for liquid films being concentrated in the vertical pipes of
industrial evaporators

Keywords: heat flux, heat transfer coefficient (HTC), depression, interphase surface, nucleate boiling

1. Introduction

An extensive analysis of the mechanisms

of heat transfer to the saturated turbulent

and laminar liquid films of sugar solutions

in the regime of evaporation from the

developed wavy structures in given in

[1,2]. The analyzed pattern of film

movement is considered to be dominant in

the long vertical pipes of industrial

evaporators [3]. The data presented in [1,2]

and respective correlations for calculation

heat transfer coefficients (HTC) for

laminar and turbulent films adequately

reflect the mechanisms of heat transfer in

long vertical pipes of industrial

evaporators within the regime of

evaporation from film free surface. At the

same time in [4-7] it has been shown that

the regime of heat transfer which has been

identified as that of evaporation from the

interphase surface can be realized only to

the certain limiting value of heated wall

superheat related to the local saturation

temperature, above which the mechanism

of heat transfer undergoes a drastic change

as being affected by pulses resulted by

appearing and move of steam bubbles.

http://www.fia.usv.ro/fiajournal
mailto:iaroslav@nuft.edu.ua

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

Valentin PETRENKO, Yaroslav ZASIADKO, Heat transfer at evaporative concentration of down flowing in vertical
pipes solutions in annular regimes, Food and Environment Safety, Volume XVII, Issue 1 – 2018, pag. 9 – 19

Nomenclature

 – film thickness;

v
Г – volumetric liquid flux;

a –temperature conductivity;

 –cinematic viscosity coefficient;

sat
t –saturation temperature;

w
t – wall temperature;

i
t – interphase temperature

 –heat conduction of liquid;

q – heat flow;

 –liquid density;

2
 –steam density;

 – surface tension;

C – mass concentration

u – average liquid film velocity

2
u − steam velocity;

g –acceleration of gravity;

Г
Pe

v 


44
– the Peclet number;


 v

Г
Re

4
– the Reynolds number.

In [6], the intensifying effect of the

nucleate boiling upon the heat transfer at a

free down flowing water films on the

outside of a cylinder and a constant along

the channel heat flux has been determined

as a multiplier:



























 


36.1

05.01
incip

incipw

qq
(1)

to the basic equation for HTC

determination at the regime of evaporation

from the film free surface. In Eq.(1) the

subscripts denote: w-related to wall, incip-at

bubble boiling inception.

The minimum value of the heat flux at

which the bubble boiling starts effect the

heat transfer mechanism has also been

found. According to [6], the heat flux at

which the bubble boiling starts in some

inception points is recommended to

determine as
2

2.14
m

kW
q

incip
 . At the same

time, it has been noted that the onset of

boiling is influenced by liquid convection,

therefore a much more adequate factor

which reflects the beginning of boiling as

well as its effect upon the intensity of heat

transfer would be a complex
ur

presented in [4] in which the onset of

boiling is identified as:

3.0

24.0

4
Pr105.1











 


 a

q
. (2)

It should be marked that the complex in

Eq. (2)
ur

q
does not account for the

effect of pressure or vacuum upon the

critical heat flux at which the surface

nucleate boiling starts. On top of this,

neither
incip

q in Eq. (1), nor
ur

q
account

for the local roughness of heat transfer

surface, which presents a decisive factor in

the determination of a critical value of the

wall superheat leading to the onset of

bubbles generation. It is necessary to stress

specifically, that the majority of

experimental works deal with the heat

transfer processes in the liquid films heated

to the saturation temperatures in

experimental stands which model the

conditions that occur in the industrial

evaporators. In these conditions of

simultaneous effect of mutually

regulating factors, it is practically

impossible to separate and distinguish

effect of any individual factor.

Therefore the recommended expressions

which are used for calculations of heat

transfer intensity in the saturated liquid

films have a limited applicability due to the

narrow range of the regime parameters, in

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

which they are valid, as well as due to

their applicability only to some

geometrical configurations. Due to the

above mentioned, they hardly may be

applied to determine the conditions of the

bubble boiling onset in the pipes of real

industrial evaporators.

2. Materials and methods

A direct experimentation of heat transfer in

down flowing liquid films of sugar

solutions heated to the saturation

temperatures has been carried out in the

experimental unit with the independent

formation of phases’ mass flow rates and

heat flux. The main core of the

experimental unit is formed by a stainless

still pipe with the inside diameter of 20 mm

and 1.8 m long. The experimental tube was

separated into the initial 1.5 m stabilization

section and 0.3 m measurement section.

The down flow of water (sugar solutions)

film has been formed by means of

overflowing over the tube’s upper rim. In

the event of steam-liquid flow modelling,

dry saturated steam has been supplied in

co-current regime. The liquid falling film

has been heated by dry saturated steam

which was supplied into outside heating

sections attached to the experimental tube.

The heating chambers were designed in a

way as to provide an individual heating of

the stabilization section and the

experimental one. The said sections were

hooked up to the individual vacuum-

condensation sections which allowed for

the keeping of different pressures in each

chamber. Such arrangements allowed also

maintaining vacuum down to 0.85 bars and

thus, vary the temperature head between

the heating steam temperature and

evaporation temperature. Special probes

for taking samples of liquid to determine

its concentration and measurements of

temperatures were positioned directly after

the measurement section. A detailed

description of the experimental unit is

given in [11].

The experimental unit closely reflects the

actual operational conditions of sugar

industrial film evaporators. The installation

consist of heat transfer pipe from stainless

steel, 9 m long with internal diameter of 30

mm partitioned in 20 section each of 40

mm long. Each section was equipped with

the special chamber which allowed

collecting condensate which was generated

on the respected section. The experimental

pipe and condensate chambers were

positioned into the heating jacket. Then

this condensate was transferred to the

adiabatic measurement glasses which

allowed measurements of the condensate

collected from each test section and thus to

determine the heat flux acting on the

respective section. The heating of the

experimental pipe has been done by means

of supplying dry saturated steam into the

pipe’s heating jacket. Between each of 20

test section a special probe for taking

samples of liquid and static pressure were

installed. The wall temperature of each

section and the temperature at the access of

the pipe were taken by means of copper-

constantan thermo-couple (type T). A

detailed description of the experimental

unit is given in [4].

3. Results and discussion

A generally accepted parameter for the

identification of the onset of nucleate

boiling in films has been suggested by

Chun and Seban [5]. The value of the

minimal superheat of a rough wall over

which a liquid film flows down looks a

reliable factor which may be used for

identification of the onset of steam bubbles

appearing. The value can be calculated

based upon the combining the Laplace and

Clapeyron-Clausius expressions, which

correlate the value of a wall critical

superheat
min

t with a certain radius of

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

indents and micro cracks
c

R at a certain

pressure (or vacuum):

sat
min

T
t




 , (3)

were
sat

T - absolute saturation temperature.

In the event of solution boiling, the wall

superheat will be bigger by the value of the

physical-chemical depression
fc

 , and thus

Eq.(3) is to be rearranged as:

sat
min

T
t 






2
. (4)

It is clear that the intensification of heat

transfer at the surface boiling is caused by

a gradual increase in the new centers of

steam bubbles generation along with the

growth of the temperature superheat, as it

is evidently follows from (3,4). Equally

this parameter adequately reflects the

effect of pressure upon the inception of

bubble appearing on the heated surface.

Therefore the parameter which may be

used to characterize the heat transfer

intensification might be developed by use

of the temperature head
min

tt  which

later will be presented as a multiplier to the

basic equation for calculation of HTC in

liquid films at evaporating from the

interphase surface as:

boil
t

tt
cK 
















min

min1 , (5)

where c and n- empirical coefficients

derived from the experimental data.

The basic equation for calculation the

intensity of teat transfer at the regime of

evaporation from the free interphase of

liquid films of water and sugar solutions

derived in [2] is extremely complex,

especially in case of co-current steam flow,

therefore its simplified version for

engineering calculations is given as Eq.

(6):

, (6)

where

boil
K - correction factor accounting

for the nucleate boiling,
L

K - correction

factor accounting for the channel length

and diameter.

A comparison of experimental and

calculated according to Eq.(6) data on

HTC to water and sugar solution free

flowing films in 20 mm diameter pipes at

the regime of evaporation from the free

intrerphase surface is given in figure 1 and

in case of co-current steam flow – on

figures 2, 3 and 4.

a
W

Кm2,

4000

1 2 3 4 5

3000

2000

10
- 4

s
m2

,Гv

3
4

Fig.1. Comparison of date calculated as per (6)

and experimental data [11]

1 – water, t = 100
о
С; 2, 3, 4, 5 – sugar solution;

2 –DM = 30%; 3 – 40; 4 – 50; 5 – 60

2
4000

6 12 18 24 30

4500

6000

5000

5500 2
1

3
4

a
W

Кm
2,

u
2
, /m s

Fig.2. Correlation  

2
uf . Comparison of

data calculated by Eq.(6)

with experimental data [11] water, t = 100
o
C. 1

– Гv = 0.1 10
-3

2 – 0.2; 3 – 0.3; 4 – 0.5

 
1/3

2
1/3 0.2 4 0.86 0.2

2
0.2

1.12 Re 0.85 0.01 4.5 10 Pr

1 7.5 10 Re
boil L

Pe Pe
g

K K

 





  



 
     

 

  
     
   

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

a
W

Km2,

2000
2400

2800

3200

3600

10 15 20 25 30 35

1
2
3

u2, /m s

Fig.3. Correlation  
2

uf . Comparison of

data calculated by Eq.(6) with experimental

data [11]Sugar solution, DM = 40%, t = 100
o
C ;

1 – Гv = 0.1 10
-3

2 – 0.2; 3 – 0.35

a
W

Кm2,

800

5 10 15 20 25 30

900

1000

1100

u , /
2
m s

1
2
3

Fig.4. Correlation  
2

uf . Comparison of

data calculated by Eq.(6) with experimental

data [11] Sugar solution DM = 70 %, t = 100
o
C,

1 – Гv = 0.1 10
-3

2 – 0.3; 3 – 0.55

Analysis of the obtained results shows that

a close concurrence may be achieved by

substituting into (3) the values of micro

cracks dimensions of 5105.0



c

R m,

which corresponds to the values of new

heat transfer pipes’ roughness. Respective

values of 4.0c and 1.2n  found from

experimental data are to be used in Eq. (5).

An additional factor affecting the accuracy

and singularity of the experimental data on

heat transfer to the solutions processing

would be a unevenness of the

concentration distribution across the film.

As a result of the gradual evaporation of

solvent (water in case of sugar solutions or

fruit juices) from the liquid film, there

appears a thin layer adjacent to the

interphase in which the concentration of

solution is somewhat bigger than that in

the bulk of the film. If only the molecular

diffusion had caused the equalizing of the

concentration field, the process would have

taken an extremely long time. In fact, the

surface of the film is covered by a complex

wavy structure, which even at low

Reynolds numbers exerts turbulence

penetrating the bulk of the film, which in

turn results in an uncertain form of the

concentration distribution across the film.

The temperature of liquid film of solution

being concentrated at a regime of

evaporation from the free surface
i

t should

be equal to the saturation temperature of

the solvent at a given pressure and

physical-chemical depression at a

concentration on the interphase surface
i

C ,

thus  
ifcsati

Сtt  . Keeping in mind

stated above concerning the uncertainties

in the concentration field across the film, it

would be grounded enough to suggest that

the waves equalize the concentrations in

the bulk of the film, so that the mean film

temperature will be  Сtt
fcsati

 .

Using this value as a reference temperature

and determining HTC as )/( iw ttq  ,

one may obtain:

  Ctt
q

fcsatw


 , (7)

where C - mean across the film solution

concentration.

Since the film temperature profile is

nonlinear (usually in the laminar stationary

film it is parabolic), the mean film

temperature
mav

t
.

in general may be

derived as Eq.(8):

 
 

2
0

.
iw

mav

tt
dy

yu
ytt


 



, (8)

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

where    yuyt , - temperature and velocity
profiles, respectively.

At the same time, the results of direct

measurements have proven that the

experimental mean mass film temperature

of solution exp
m.av

t , which had been measured

in the adiabatic calorimeter immediately at

the exit of the experimental stand

correlates with Eq.(8) only at conditions of

free down flowing at the absence of

interphase shear stress. The schematic of

measurements is given in figure 5.

ex p

.mav
t

sat
t

w
t

u2
q

Fig. 5. Schematics of calorimetric temperature

measurements in flowing down liquid films

In case of a co-current flow of steam above

the film, the experimental mean mass

solution temperature exp
m.av

t turned out

lower than that determined by Eq.(8)
exp

.. mavmav
tt  . The deviation observed was

the bigger the bigger was the steam flow

velocity and liquid mass flow rate.

Since the experimental temperature exp
m.av

in the contrast to
i

t adequately reflects any

change in the regime parameters and being

the value which is directly measured in the

experiments, then the HTC to solutions are

to be correctly defined as Eq.(9):

exp

.mavw

m
tt


 , (9)

which will adequately reflect the effect of

phases mass flow rates change. This

immediately yields
m

 .Since HTC

determined as per Eq.(6) led to the

generalized correlation Eq.(9), the

calculation of heat flux (or as a result

evaporation capacity) should take into

consideration the value of the mean

concentration of the solution in the liquid

film and thus appearing effect of physical-

chemical temperature depression. It is

necessary to stress specifically that since

the correlation presents data of the

discreet-local character, which means that

they were obtained within comparatively

short sections of the channel, in which it

was acceptable to assume a constancy of

all regime parameters, phase flow rates and

their properties. This determines a

successive-iterative method of channel

evaporative capacity calculations. A

channel being under the calculation is to be

split into a number of sections, and the

calculation process starts from the upper

inlet of the channel. Insofar as it can be

seen from Eqs.(6) and (11), the local

values of heat flux do not affect HTC

directly, there is no need to initial guess of

q to start iterative calculations to reach a

convergence of guessed and obtained q

values. Rather, it would be necessary to

first calculate the local value of heat flux

on the first section as a first approach, then

to calculate the amount of steam generated

in this section, and after this – determine

all parameters dependent on the steam

velocity. The next iteration would be

calculation of a new value of HTC by

Eq.(6) and (11) with the respective new

values of heat flux and obtained in the

previous calculation q and eventually -

steam velocity, phase flow rates,

concentrations, etc. The values of the local

heat flux are to be determined with taking

account of local value of physical-chemical

temperature depression as well as its

suppression by the concurrent steam flow

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

  tCttq
fcsatwm

 , (10)

where    
iwmavw

ttttt 
exp

.
-a

function which accounts for the

suppression effect of interphase shear

stress.

The suppression effect may be explained

by the fact that the steam being generated

from the film has the temperature of the

saturated solvent (water), whereas the

upper layer of the film has local

temperature sufficiently higher due to the

concentration growth of the soluble

substance. Being in the contact with the

steam flow at a lower temperature, the

surface of the film cools down; this leads

to the decrease in physical-chemical

temperature depression.

Analysis of the experimental data on the

heat transfer to liquid films of sugar

solutions with the concentrations up to

70% DM (Dry Matter) in the regimes of

evaporation from the interphase surface as

well as at bubble boiling with the

concurrent steam flow allowed deriving a

temperature function as Eq.(11):

  
fx

PeWet 
 32103.2exp1 .(11)

The comparison of HTC calculations by

Eq.(6) with the experimental data on the

heat transfer to the free down flowinh

liquid films and films flowing co-currently

with the steam at a velocity of 25 m/s of

water and sugar solutions with the

concentartion up to 75% within the

regimes of evaporation from the free

surface and nucleatete boiling are shown in

figures 6 and 7. The transition to the

regime of nucleate boiling is identified by

the beginning of upward line  qf on
the graphs. It is clearly seen from the data

given above that the transition to regime of

nucleate boiling with the steam flow

growth shifts towards to greater heat

fluxes, which satisfactorily is identified by

Eqs. (4) and (5).

For rough pipes ( mR
c

5
105.0


 ), for

example, after cleanning with the hard

metal brushing or superimposin an

artificial roughness according to Eq. (3) the

transition to the nucleate boiling regime

accompanied with the respective heat

transfer intensification at lower values of

heat flux.

Apart from the mentioned above factors,

the heat transfer intensity is greatly

affected by geometry of the channel, since

as the height as well as the diameter of the

channel determines the character of wavy

structure on the film surface. Namely, in

the 9 m boiling tubes of industrial

evapolators along with the distance from

the film distributor down to 3…4 m takes

plase an increase in heat transfer intensity

comared to that in the short pipes at the

same regime parameters and mass flow

rates. On top of this, it has been found in

[8,9] that an increase in pipe diameter

entails the increase in length and amplitude

of big waves that significantly intensifies

the mixing in films.

Unfortunately, it is impossible to separate

the effect of certain factors on the intensity

of heat transfer within the system under

consideration. It is necessary to mark

specifically that within the experimental

stands, which simulate the conditions of

actual film evaporators, all working and

regime parameters manifest themselves in

the unseparable mutually regulating unity.

For example, at a certain set of regime

parameters and initial solution flow rate,

down the Therefore, modelling of heat

transfer to free falling films in such

conditions becomes possible only within

the upper sections of experimental pipe.

Here the velocity of cocurrent steam is

negligibly low but, at the same time, the

wavy structure will be undeveloped.The

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

data for films with the developed waves

might be taken at the middle or exit

sections of pipes, but here the film flow

will be affected by the strong shear stress

fron the steam flow.

Fig. 6. Correlation  qf for free falling films of water and sugar solutions,
( m.R,Ct

o 5
1050100


 ). Data[11].

а. water, 1 – Гv = 1∙10
-4

m2/s; 2 – 2∙10
-4

; 3 – 3∙10
-4

; 4 – 5.5∙10
-4

;

b. sugar solution, DM = 30 %, 1 – Гv = 1∙10
-4

m2/s; 2 – 1.6∙10
-4

; 3 – 2.2∙10
-4

; 4 – 4.5∙10
-4

;

c. sugar solution, DM = 50 %, 1 – Гv = 0.7∙10
-4

m2/s; 2 – 1.5∙10
4
; 3 – 2.2∙10

-4
; 4 – 4∙10

-4
;

d. sugar solution, DM = 70 %, 1 – Гv = 0.5∙10
-4

m2/s; 2 – 2∙10
-4

; 3 – 3∙10
-4

; 4 – 5.5∙10
-4

Lines – calculated to Eq.(6) at the same mass flow rates.

10
3.5

4.5

4.0

5.0

5.5

20 30 40 50 60

2
33
4

kW
,

2


2
m

kW
,q

1
2
3
4

10
2.5

3.0

4.0

3.5

20 30 40 50 60

2
3

kW
,

2


2
m

kW
,q

1
2
3
4

10
1.5

1.8

2.1

2
4

kW
,

2


2
m

kW
,q

10 15
0.6

0.8

1.0

2
1 3

2
3

kW
,

2


kW
,q

a b

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

kW
,

2


2
m

kW
,q

4
4

2010
4.5

5.5

6.0

6.5

5.0

30 40 50

kW
,

2


2
m

kW
,q

2.6
10 20 30

3.0

3.4

2 3

1
2
3
4

kW
,

2


kW
,q

2
2 3

2.0

2.2

2.4

2.6

2.8

10 20 30

kW
,

2


2
m

kW
,q

1.4

1.0

1
2

3
4

1510

1.2

2 3

Fig.7. Correlation  qf at steam velocity
s

m
u 25

2
 , ( m.R,Ct

o 5
1050100


 ).

Data [11]

а. water, 1 – Гv = 1∙10
-4

m2/s; 2 – 2∙10
-4

; 3 – 3∙10
-4

; 4 – 5.5∙10
-4

;

b. sugar solution, DM = 40 %, 1 – Гv = 1∙10
-4

m2/s; 2 – 1.5∙10
-4

; 3 – 2∙10
-4

; 4 – 3.5∙10
-4

;

c. sugar solution, DM = 50 %, 1 – Гv = 1∙10
-4

m2/s; 2 – 2∙10
-4

; 3 – 3∙10
-4

; 4 – 6∙10
-4

;

d. sugar solution, DM = 70 %, 1 – Гv = 1∙10
-4

m2/s; 2 – 2∙10
-4

; 3 – 3∙10
-4

; 4 – 5.5∙10
-4

Lines – calculated to Eq. (6) at the same mass flow rates.

Therefore, the comparison and

generalization of the experimental data

obtained in long evaporating channels at

the local level (within a comparatively

short sections to suggest the constancy of

parameters) appear grounded only in the

event of equality all respective regime

parameters, flow rates and physical

properties of phases. In such case the data

can be compared and generalized with

those obtained in the stands allowing

individual formation of pfase flows and

thus providing for the comparable working

conditions. Data in figure 8 illustrate the

given above. It shows the fields of scatter

for data obtained in the experiments in

short and long pipes of different diameters

in the comparable conditions and their

comparison with the results of calculation

by Eq.(6).

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

The correction factor accounting for the

effect of pipe length and diameter on the

heat transfer was found by examining data

obtained in pipes of different geometries

but exclusively in the comparable

conditions as Eq.(12):

 3

0.35 0.06

1 0, 06 1 exp 0, 05

K L



 

 
  

 

   
           

 
 
 

,(12)

where md
o

02.0 ,
s

m
о

2
6

103.0


 ,

valid for L >1.0 m.

kW
2

,

m,L

1
3 2

2 4 6 8

4.5

5.5

6.0

5.0

kW
2

,

m,L

1.5

2.0

1 1 2

1.0

2 4 6 8

Fig. 8. Correlation  Lf .

а. water,
s

m
u 15

2
 ; b. sugar solution,

DM = 70 %,
s

m
u 30

2
 .

1 –data scatter field, d = 20 mm, L = 1.8 m[11];

2 – data scatter field [4] , d = 30 mm, L = 9 m;

3 – data scatter field [10] d = 32 mm, L = 4.9 m.

Lines – calculated by Eq.(6), 1 – d = 20 mm, 2 –

30 mm.

The comparison of calculated by Eq. (6)

values of heat flux along the height of a 9

m pipe with the experimental data [4] at

various temperature differences is given in

figure 9. As it is clearly seen from figure 9

the proposed correlations and methodology

allows quire closely predict the evaporative

capacity of boiling channels of induslrial

film evaporators with pipes up to 9 m

height within a vide range of working

parameters. Even at a big temperature

difference (wall – saturation) of 50C, figure

9(c) when the local values of heat flux

reach 35 kW/m2 at the lower sections and,

thus, one may expect rather significant

values of the cocurrent steam flow velocity

with affecting film surfacial wave

structure, its supressing effects, named

above, which manifest itself inseparably

with the local heat flux – the recommeded

method gives remarcably good coincidece

of measured and predicted data.

27 29 31 33 35 3718 20 22 24

9
4 6 8 10

q, kW m/
2

L,m

a b c

Fig.9. Heat flux distribution at a height of the

evaporative pipe

Lines – calculation by (6) (6 ); Dots-

experimental data [4].

a – Δt = 2.2
o
C, tw – tsat = 1.2; b – 7.5, tw – tsat =

3.7; c – 11, tw – tsat = 5.1;

Гv = 0.3 10
-3

m
2
/s, water, tsat = 100

o
С.

Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava

Volume XVII, Issue 1 – 2018

4. Conclusion

Equations (3) and (4) which take into

account the value of local wall superheat

and heating surface roughness are

recommended to be used as a factor

determining the onset of nucleate boiling

in films.

The temperature of liquid solution film at a

regime of evaporation from free surface

with the co-current steam flow is to be

determined with taking into account the

value of physical-chemical temperature

depression Eq. (11).

The Eq. (6) along with the methodology of

its application may be used for the

calculations of evaporative capacities of

boiling channels of industrial film

evaporators of sugar industry. The

methodology is valid in application to

water and sugar solutions with the

concentrations up to 70% DM, at regimes

of evaporation from free surface and

nucleate boiling, within the range of

vacuum up to 0.85 bar, heat fluxes up to 60

kW/m2, liquid mass flow rate density

0.05…600 m2/s, co-current steam flow

velocities up to 40 m/s, for evaporative

pipes 20…32 mm diameter.

5. References

[1]. PETRENKO V., ZASYADKO Y. Heat transfer

modeling in down-flowing laminar films with the
developed wavy structure with co-current steam

flow. Food and Environment safety, Vol 15, Issue

3, рр. 203 – 215, (2016)

[2]. PETRENKO V., ZASYADKO Y. Heat transfer

in down flowing turbulent evaporating liquid film

with developed wavy structure and co-current

steam flow. Food and Environment safety (FES),

Vol 15, Issue 4, 2016. рр. 284 – 298, (2016)

[3]. GANCHEV B. G. Cooling of nuclear reactor of

elements by film flow. Energoatomizdat, Moscow,

рр. 192, (1987)
[4]. ARDASHEV V.A. Investigation of heat

transfer at evaporation gravitationally falling liquid

film in a vertical pipe. – G.: pHD dissertation , 188

p.(1982)

[5]. Heat Transfer in Evaporating Liquid Films.

Heat Transfer, No. 4, pp. 71 – 77, (1971)

[6]. CERZA M., SERNAS V. Nucleate Boiling in

Thermally Developing and Fully Developed

Laminar Falling Water Films. Heat Transfer, No.4,

pp. 185 – 174. (1988)

[7]. FUJITA T., UEDA T. Heat Transfer to Falling

Liquids Films and Film Breakdown – Part ІІ.
Saturated Liquid Films With Nucleate Boiling Int.

J.Heat Mass Transfer, Vol. 21, No. 2, pp. 109 –

118.(1978)

[8]. KULOV N. N. Hydrodynamics and a mass

exchange in the film and disperse streams

descending, Dissertation, Moscow,409 p.(1984)

[9]. CHU K.J., DUKLER A.E. Statistical

characteristics of thin, wavy films. Pt 111, Structure

of the large waves and their resistance to gas flow.

AIChE.J., vol.21, N 3, pp. 583 – 593.(1975)

[10]. LEVERASH V.I. Experimental studies into
the heat transfer to liquid in the industrial

evaporators with falling films in application to the

conditions of distillation units. PhD

Dissertation.Moscow. Mosdow Power

Institute.1964

[11].RIABCHUK О. М., Thermal and

hydrodynamic processes evaporation in

downstream film flows of sugar solutions,

Dissertation, Kyiv , 167 р.(2013)

1. Introduction
4. Conclusion