discovered characteristics of the transient nucleate

Discovered Characteristics of the Transient Nucleate Boiling Process to Be

Widely Used for Testing of Materials and New Technologies Development

NIKOLAI KOBASKO

IQ Technologies Inc., Akron, USA and Intensive Technologies Ltd, Kyiv, Ukraine

www.intensivequench.com

Abstract: - The nucleate boiling processes are in use in everyday people’s activity; and they were carefully

investigated mainly for steady state condition. The transient nucleate boiling process takes place during quenching of

steels and alloys and it is not enough deeply investigated yet. During last decades the new characteristics of the

transient nucleate boiling process were discovered which can be formulated as follows. The duration of the transient

nucleate boiling process is directly proportional to squared size of a component and inversely proportional to thermal

diffusivity of a given material, depends on configuration of component, initial temperature and thermal properties of

liquid. The surface temperature of a component during the nucleate boiling process is maintained at the level of

boiling point of liquid until heat flux densities during nucleate boiling and convection become equal. These

characteristics were widely discussed at the WSEAS Conferences. In present paper, the possibilities of use of the

discovered characteristics in the heat treating industry are widely discussed. Namely, they can be used for testing of

materials and new intensive technologies development to improve mechanical properties of quenched components.

Key –Words:- Nucleate boiling, Characteristics, Practical application, New technologies, Simplified calculations,

Environment.

1 Introduction

During quenching of steel parts in cold water, salt or

alkali solutions of optimal concentration in many

cases film boiling is absent and main modes are

transient nucleate boiling process and convection. To

predict absence of film boiling, hyperbolic heat

conductivity equation (1) should be used. In contrast

to parabolic heat conductivity equation, the hyperbolic

equation provides finite initial heat flux density during

immersion of steel parts into cold liquid which can be

less than the first critical heat flux. In this case film

boiling is absent and temperature field during

quenching in steel parts can be calculated using

equations (1) – (4) [1]:

( ) ggradTdivT

rT

a&+=

∂

∂∗+

∂∂

λττ

λ2

2

(1)

( ) 0=

−+

∂∂

=Rr

m

S

m

TTr

T

λβ

(2)

( ) oTrT =0, (3)

0=∂∂r

T (4)

Here 3

10=m ; β is constant which depends on

physical properties of liquid; Ts is saturation

temperature [1].

Transition from nucleate boiling to convection is

calculated from the condition:

convnb qq = (5)

Recent Advances in Fluid Mechanics, Heat & Mass Transfer and Biology

ISBN: 978-1-61804-065-7 15

Here nbq is heat flux at the end of nucleate boiling;

convq is heat flux at the beginning of convection.

During convection, boundary condition is linear and

has a form:

( ) 0=

−+∂∂

=Rr

mTTr

T

λα

(6)

From boundary condition (2) and (6) follow that

transition temperature from nucleate boiling to

convection can be calculated fron equation (7):

(7)

The equation for determining the duration of transient

nucleate boiling process was first received by

generalization of experimental data, and then derived

from the analytical equation solution taking into

account boundary condition (2), and has the following

form [2]

a

Dkk WFnb

2

Ω=τ (8)

where value Ω depends on initial temperature of a

steel part and condition of cooling. For initial

temperatures of 850oC it can be within 3.6–4.17 (see

Table 1). Coefficient Fk depends on configuration of

the steel part (see Table 2). For plate-shaped forms,

1013.0=Fk ; for cylinder-shaped forms,

0432.0=Fk ; for spherical-shaped forms,

0253.0=Fk ; Wk is a dimensionless coefficient

which depends on liquid flow velocity. For motionless

liquid, .1=Wk For high flow velocity of liquid which

prevents nucleate boiling, .0=Wk That is why for

different condition we have .10 ≤≤ Wk D is the

thickness of the component: diameter of cylinder,

sphere, or thickness of the plate; a is thermal

diffusivity of a material.

To simplify problem, in the paper motionless

quenchants are considered. For such condition Eq. (9)

is true:

a

DkFnb

2

Ω=τ (9)

This simple law of boiling process can be used for

evaluation of thermal properties of materials and

developing new technologies for strengthening of

materials. Below is proposed simple method for

evaluating thermal diffusivity of steel. Eq. (9) can be

used also for development a new method of

austempering.

Table 1 Coefficients Ω depends on initial

temperature and properties of quenchants at 20 oC

Quenchant Ω

Water, 20oC 4.17

30-50% CaCl2 4.78

5 – 12% NaOH 3.6

6 – 8% NaNO3 3.76

Note: Initial temperature is fixed at 850oC;

Table 2 Coefficients Fk for bodies of different shapes

Shape of a

body Fk Equation

Plate 0.1013 2−π

Cylinder 0.0432

24

1

ν

Sphere 0.0253

24

1

π

Round plate

with hight Z

and dia D =

nZ; n = 1

0.0303

224

1

πν +

n = 2 0.0639

22

1

πν +

n = 5 0.0926

22 254

25

πν +

Finite cylinder

with dia D and

Z = nD; n = 1

0.0303

224

1

πν +

n = 2 0.0391

2216

4

πν +

n = 5 0.0425

22100

25

πν +

Notes: 4048.2=ν and is a root of the first kind of

Bessel function; 1416.3=π , Z is height of a

cylinder or round plate.

3.0)]([1

uhIIconvII ϑϑαβ

ϑ +=


ISBN: 978-1-61804-065-7 16

2 The thermal diffusivity evaluation of

different kinds of solid materials

Evaluation the thermal diffusivity of solid materials is

important for the practice. Authors [3] developed an

analytical method for calculation of average value of

thermal diffusivity of solid materials. To measure

average value of thermal diffusivity, accurate

temperature measurement of tested probe is needed [1,

3]. Using correlation (9), it is possible to evaluate

average diffusivity of material by controlling duration

of transient nucleate boiling process [4]. In this case

Eq. (9) should be rewritten as:

nb

F

Dka

τ

2

Ω= (10)

Here a is average value of thermal diffusivity (m2/s);

Ω is available from Table 1. Fk is coefficient which

depends on configuration of probe and is available

from Table 2; D is size of probe (m); nbτ is duration

of transient nucleate boiling process (sec);

Fig.1 Core cooling rate of cylindrical Ø10 × 50 mm

specimen made of AISI 304 steel and noise intensity

during quenching in 6% water Na2CO3 solution at

20oC (1 are frequencies 100 - 1000 Hz; 2 are

frequencies 1.0 - 2.0 kHz) [4]

Cylindrical probe 10 mm diameter is cooled from

850oC in 6% water salt solution at 20

oC . Transducer

of noise control system detected the cooling time of

nucleate boiling which is equal to 3.2 seconds (see

Fig. 1). The coefficient Fk for cylinder is equal to

0.0423. Using these data, the thermal conductivity can

be evaluated using Eq. (10), i.e.

( )s

m

s

ma

26

2

1099.42.3

01.00425.076.3 −×=××=

Thermal diffusivity of AISI 304 steel, depending on

temperature, is provided in Table3.

Table 3 Thermal diffusivity of AISI 304 steel and

Inconel 600 in m2/s vs. temperature.

Material 100oC 200 400 600 800

Steel 304, 610×a [m

2/s]

4.55 4.63 4.95 5.65 6.19

Average value of thermal diffusivity of steel AISI

304, according to Table 3, is 4.95 x10-6

m2/s. Proposed

method of evaluation provides 4.99 x10-6

m2/s that

agree very well with the data presented in Table 3.

It means that average value of thermal diffusivity can

be measured by detecting duration of transient

nucleate boiling process. The method is easy in use

and results of measuring can be more accurate as

compared with the temperature measurement of probe

during quenching.

3 Real and effective heat transfer

coefficients during quenching in liquid

media As is well known, thermal scientists consider

real HTC during nucleate boiling as the ratio q/(Tsf –

Ts) because overheat (Tsf – Ts) is responsible for

bubble growth and their numbers [5, 6, 7]. Many

thousands of bubbles are acting like micro-pumps.

Each micro-pump pushes out overheated liquid from

the boundary layer with the frequency 62 Hz (see

Table 4). During this process tremendous turbulence

and vaporization of liquid occur [8, 9] which causes

dramatically increase of HTC. Since HTC during

nucleate boiling is several times greater as compared


ISBN: 978-1-61804-065-7 17

with convective HTC, a self – regulated thermal

process is established during which the surface

temperature of steel parts maintains a long time at the

level of boiling point (see Fig. 2) [1, 2].

Fig. 2 Temperature vs. time during quenching in 5%

NaOH water solution at 20oC of sphere 38 mm

diameter made of stainless steel.

This fact can be written as [6, 10]:

constTTT Ssf ≈∆+= (11)

To evaluate real HTC (see Fig. 3 and Fig. 4), it is

important to relate the heat flux density during boiling

to the difference Ssf TTT −=∆ , instead of difference

msf TTT −=∆ which is used at convection and

provides effective HTC during nucleate boiling. Here

sfT is the temperature of a wall (a surface to be

cooled); ST is a saturation temperature; and mT is the

temperature of the medium (quenchant). Therefore, as

it was already mentioned, formation of nucleating

centers depends on the overheat of a boundary layer,

Ssf TTT −=∆ , which is determined by Eq. (12) [1,

9]:

Tr

TR S

cr ∆=

"'

2

ρσ

(12)

Fig. 3 Real and effective HTC vs. time during

quenching of spherical probe 38 mm diameter in 5%

NaOH water solution at 20oC.

Fig. 4 Real and effective HTC vs. time during

quenching of spherical probe 38 mm diameter in 5%

NaOH water solution at 20oC.

Fig. 5 Kondratjev number Kn versus Fourier number

Fo for cylinders 20 mm (1); 30 mm (2), and 40 mm

(3) quenched in 5% water alkaline solution [6].

According to Tolubinsky [9], the number n of

nucleating sites increases in direct proportion to the

cube of the temperature difference: 3Tnc ∆⇒

It is also well known that the average heat flux density

during nucleate boiling is proportional to the cube of

temperature difference:

3Tq ∆⇒

Tolubinsky has reported that the average heat flux

density per one nucleating center 0q , in the case of

full nucleate boiling, is constant [9]:

.0 constn

qq

c

≈=


ISBN: 978-1-61804-065-7 18

Fig. 6 A model of pumping effect of growing bubble

(PEGB), according to Shekriladze [11] .

Table 4 Comparison of parameters of boiling

process for water and aqueous salt solutions at normal

pressure [1,9] Substance )(,0 mmd )(Hzf )/(" smW

Water 2.5 62 0.155

25% NaCl

solution

2.4 64.5 0.155

29%

Na2CO3

solution

2.4 65 0.156

Table 5 Effect of heated surface material on bubble

departure diameter and release frequency in the case

of boiling water at normal pressure [1, 9]. Material )(,0 mmd )(Hzf )/(" smW

Permanite 2.5 61 0.153

Brass 2.3 67 0.157

Copper 2.8 56 0.157

Average 2.5 62 0.155

Effect of heated surface material on bubble departure

diameter and release frequency in the case of boiling

water at normal pressure is shown in Table 5. From

presented Tables 4 and Table 5 follow that inner

characteristics of boiling process don’t depend on

material of probe and concentration of water solution

[8, 9]. The author [9] underlined many times that

inner characteristics of boiling process also don’t

depend on size of heater (size of steel part). Such

conclusion is very important for understanding what is

effective HTC during transient nucleate boiling

process. This issue is widely discussed in Ref [1, 9],

In contrast to real HTC, effective HTC depends on

size of steel part (see Fig. 5, Fig. 6, and Fig. 7.) and it

can be used only for core cooling time and cooling

rate calculations and are not valid for temperature

field calculations like shown in Fig. 8 [14].

Fig. 7 Effective HTC vs. diameter of cylindrical

specimens quenched in 12% water solution of NaOH

at 20oC [6, 12].

Fig. 8 Temperature gradients in cylindrical

specimens 20 mm and 40 mm diameter vs. time

during transient nucleate boiling process [2, 6]

New approach in providing

austempering of high carbon steels and

irons

Austempering is an isothermal heat treatment that is

applied to high carbon steels and ductile iron. In steel

it produces a lower bainite microstructure whereas in

cast irons it produces a structure of acicular ferrite and

high carbon, stabilized austenite known as ausferrite.

This combination of mechanical properties is achieved

by the formation of ‘ausferrite’, which is a


ISBN: 978-1-61804-065-7 19

microstructure consisting of aggregates of bainitic

ferrite sheaves and carbon enriched retained austenite

matrix free of cementite. As a rule this process is

fulfilled in molten salts or molten alkalis. Temperature

of molten salt or molten alkali is above martensite

start temperature MS to prevent martensitic

transformation. Shortcoming of such technology is

slow cooling in molten salt resulting in not enough

fine microstructure after finishing austempering

process. To solve this problem, a new method of

cooling in cold liquids, combined with tempering, is

proposed. The process is similar to austempering

process, however cooling rate is ten times higher and

even more as compared with cooling in molten salts.

Fig. 9 Effect of pressure Comparison

Fig. 10—Effect of pressure on the quenchant on

quench crack formation for bearing rings made of

ShKh15 (AISI 52100) steel [1]: 1, 208/01 bearing

ring; 2, 308/01 bearing ring. Temperature of the water

quenchant was 30–40oC.

Using self- regulated thermal process , Eq. (11), one

can use pressure or high concentration of salt (alkali)

solutions to increase boiling point of liquid used as a

quenchant. In this case, using effect shown in Fig. 9

a), it is possible to perform austempering combining

with intensive cooling. To be more understandable,

examples are provided below showing how it can be

done. It should be noted also that pressure decreases

probability of crack formation (see Fig. 10) [1].

Fig. 11 Martensite start temperature (MS) and

martensite finish temperature (MF) versus content of

carbon in steel.

Fig. 12 Installation for simulation the austempering

process: I, loading point for steel parts to the

conveyor; II, chute with intensive cooling devices; III,

quenching tank with two conveyors; IV, unloading

point of steel parts from heater HT2; TR1–TR4, speed

control units for conveyor belts 1, 2, 3, 4; PM1,

pump; CL1, cooler.

Example 1. Cylinders 30 mm diameter and 120 mm

long are made of ultra carbon steel containing 1.6 C;

0.35 Si and 0.15 Mn. Martensite start temperature MS

for this steel is 100oC (see Fig. 11). One should

prevent martensite transformation during intensive

cooling to provide condition similar to austempering.

It can be done by the following. First, cylinders are

quenched in 6% Na2CO3 water solution at 20oC where

the duration of nucleate boiling process, according to

Eq. (9), is:

ssm

mnb 3.29

/1085.4

03.0042.076.3

26

22

≈×

××=−

τ


ISBN: 978-1-61804-065-7 20

And then, if length of conveyor is 1.2 m, should be set

speed of conveyor 0.04 m/s to deliver the steel part to

tempering furnace HT2 in proper time (see Fig. 12).

Temperature in the tempering furnace is 1800C where

steel part will be tempered during one hour. Such

technology provides fine microstructure and high

mechanical properties of material [13, 14].

Example 2. Ultrahigh carbon steel (UHCS)

containing 1.9% C, 0.15% Si and 0.2% Cu was

intensively cooled from the molten state for receiving

very fine carbides using special technology [15, 16].

There is need to quench it from the austenite

temperature 850oC in cold 8% water salt solution at

20oC to improve additionally its mechanical

properties. Martensite transformation should be

prevented to eliminate crack formation during

quenching. Note that fine carbides are the main

parameters for improving mechanical properties of

UHCS. Assume that the test probes are cylinders 20

mm diameter and 100 mm long. Using Eq. (9), one

can calculate duration of nucleate boiling process and

speed of conveyor for the quenching system shown in

Fig. 12, i.e.

ssm

mnb 5.13

/1075.4

02.00425.076.3

26

22

≈×

××=−

τ

To deliver probes to the tempering furnace in right

time, the conveyor’s speed in this case should be

0.089 m/s.

Characteristics of transient nucleate boiling process

can be used for explanation what Grossmann factor

is [17-19], for optimizing of IQ -3 process [20], and

reducing distortion of steel parts during quenching

[21].

Summary

1 A method for determination of thermal diffusivity of

solid materials is proposed which is based on

detecting of noise effect initiated by the transient

nucleate boiling process.

2 Surface temperature of steel parts during transient

nucleate boiling process maintains at the level of

boiling point and during this time HTC are very high

due to pumping effect of growing bubbles and

vaporization.

3 During transient nucleate boiling process, the

number of vapor bubbles and intensity of cooling

depend on overheat Ssf TTT −=∆ and real HTC

doesn’t depend on size of steel part and thermal

properties of material if overheat is fixed.

4 The effective HTC depends on size of steel parts

thermal properties of materials and its value could be

several times less as compared with the real HTC.

That is why effective HTC cannot be used for

calculation of temperature gradients at the surface of

steel parts. Effective HTC can be used for simplified

calculation of core cooling time and core cooling rate

the different steel parts.

5 The new method of austempering for high carbon

steels and irons is proposed which consists in two step

operation. At the first step parts are cooled in liquid

quenchant boiling point of which is equal to

martensite start temperature or exceeds it. At the

second step the immediate tempering is provided at

the temperature higher than martensite start

temperature.

6 Further developments can be done in improving

austempering method based on use special salts

solutions or pressure which increase significantly

boiling point of quenchant.

7 Products made of high carbon steels and irons,

sensitive to quench crack formation, can be

strengthened by use of new method to provide fine

microstructure after austempering.

References:

[1] Kobasko, N.I., Aronov, M.A., Powell, J.A., and

Totten, G.E., Intensive Quenching Systems:

Engineering and Design, ASTM International,

West Conshohocken, 2010, 252 pages.

[2] Kobasko Nikolai, Transient Nucleate Boiling as a

Law of Nature and a Basis for Designing of IQ

Technologies, Proc. of the 7th IASME/WSEAS

Int. Conference on Heat Transfer, Thermal

Engineering and Environment (THE’09),

Moscow, Aug. 20 – 22, 2009, pp. 67 – 76.

[3] Rimshans Janis S., Guseynov Sharif E., Kaupuzs

Jevgenijs, On one approach for calculation of the

thermal conductivity coefficients for heat transfer:

Part I and Part II, Recent Advances in Fluid

Mechanics, Heat & Mass Transfer and Biology,

Alexander Zemliak, Mastorakis Nikos (Eds.),

WSEAS Press, Athens, 2011, pp. 147 – 157.


ISBN: 978-1-61804-065-7 21

[4] Kobasko, N.I., Moskalenko, A.A., Mazurenko,

E.A., Medvedev, A.M., Intensive quenching of

tools in water salt solutions, Computers and

Simulation in Modern Science, Vol. V, Mastorakis

Nikos, Demiralp Metin, Mladenov Valeri M.,

Zaharim Azami (Eds.), WSEAS Press, Athens,

2011, pp. 136 – 141.

[5] Krukovskyi, P.G., Kobasko, N.I., and Yurchenko,

D., Generalized equation for cooling time

evaluation and its verification by CFD analysis ,

Journal of ASTM International, Vol. 6, No

5,2009.

[6] Kobasko, N.I., Discussion of the problem on

Designing the Global Database for Different

Kinds of Quenchants, In a book: Recent Advances

in Fluid Mechanics, Heat & Mass Transfer and

Biology, Zemlliak, A., Mastorakis, N. (Eds.),

WSEAS Press, Athens, 2011, pp. 117 – 125.

[7] Kobasko Nikolai I., Intensive Steel Quenching

Methods, In a book: Quenching Theory and

Technology, Second Edition, Liščić Bozidar,

Tensi Hans M., Canale Lauralice C.F., Totten

George E. (Eds.), CRC Press, Boca Raton,

London, New York, 2010, pp. 509 –568.

[8] Tolubinsky, V. I., Teploobmen pri kipenii (Heat

transfer at boiling), Naukova Dumka, Kyiv, 1980.

[9] Kutateladze, S. S., Fundamentals of Heat

Transfer, Academic Press, New York, 1963.

[10] Kobasko, N. I., Self-regulated Thermal Processes

During Quenching of Steels in Liquid Media,

International Journal of Microstructure and

Materials Properties, Vol. 1, No. 1, 2005, pp.

110–125

[11] Shekriladze Irakli, Boiling heat transfer: wide

fair discussion required (review), Journal of

ASTM International, Vol. 9, No. 1, 2012, Paper

ID JAI103387, Available online at www.astm.org

[12] Liščić, B., Filetin, T., Global Database of Cooling

Intensities of Liquid Quenchants, Proceedings of

the European Conference on Heat Treatment

2011, “Quality in Heat Treatment”, Wels,

Austria, 2011, pp. 40 – 49.

[13] Kobasko, N.I., Duration of the Transient Nucleate

Boiling Process and Its Use for the Development

of New Technologies, Journal of ASTM

International, Vol. 8, No. 7, 2011, Paper ID

JAI103485, Available online at www.astm.org

[14] Kobasko, N.I. Effect of Accuracy of Temperature

Measurements on Determination of Heat Transfer

Coefficient during Quenching in Liquid Media,

Journal of ASTM International, Vol. 9, No. 2,

Paper ID JAI104173

[15] N.I.Kobasko, Secondary intensive cooling of

melted materials for getting their fine

microstructures, Proc. of the 6th IASME/WSEAS

International Conference on HEAT TRANSFER,

THERMAL ENGINEERING and ENVIRONMENT

(HTE’08), Rhodes, Greece, Aug. 20 – 22, 2008,

pp.539 - 542.

[16] Kobasko Nikolai, An Explanation of Possible

Damascus Steel Manufacturing Based on

Duration of Transient Nucleate Boiling Process

and Prediction of the Future of Controlled

Continuous Casting, International Journal of

Mechanics, Issue 3, Vol. 5, 2011, pp. 182- 190.

[17] Lyman, T.Ed., Metals Handbook: 1948 Edition,

Americal Society for Metals, Cleveland, OH,

1948.

[18] Kondratjev, G.M., Thermal Measurements,

Mashgiz, Moscow, 1957.

[19] Aronov, M.A., Kobasko, N.I., Powell, J.A., and

Hernadez – Morales, J.B., Correlation between

Grossmann H-Factor and Generalized Biot

Number BiV, Proceedings of the 5th WSEAS

International Conference on Heat and Mass

Transfer (HTM’08), Acapulco, Mexico, January

25 – 27, 2008, pp. 122 – 126.

[20] Kobasko, N.I., US Patent # 6,364,974B1

[21] Kobasko, N.I., Aronov, M.A., Powell, J.A.,

Ferguson, B.L., Dobryvechir, V.V., Critical heat

flux densities and their impact on distortion of

steel parts during quenching, In a book: New

Aspects of Fluid Mechanics, Heat Transfer and

Environment, WSEAS Press, Athens, 2010, pp.


ISBN: 978-1-61804-065-7 22

discovered characteristics of the transient nucleate

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