Sessile Drop Evaporation in Relation to Leidenfrost Phenomenon (B.Sc. Thesis Report)

i

Sessile Drop Evaporation in Relation to Leidenfrost Phenomenon

A thesis

Submitted to

Department of Mechanical Engineering

Bangladesh University of Engineering and Technology

by

Md. Zahabul Islam (Student No: 0510030)

Shuvra Banik (Student No: 0510094)

Under the supervision of

Dr. Aloke Kumar Mozumder

In partial fulfillment of the

Requirement for the Degree

of

Bachelor of Science in Mechanical Engineering.

February, 2011

ii

DECLARATION

This to certify that the presented paper is the outcome of the accomplishment of the project and

thesis on “Sessile Drop Evaporation in Relation to Leidenfrost Phenomenon” carried out by

the students of Mechanical Engineering Department, BUET, Dhaka under the supervision of Dr.

Aloke Kumar Mozumder, Associate Professor, Mechanical Engineering Department, BUET,

Dhaka and it has not been submitted anywhere for any award of degree or diploma, nor it has

been published in any technical journal.

Name Student Number Signature

1. Md. Zahabul Islam 0510030

2. Shuvra Banik 0510094

SUPERVISOR

-----------------------------------------------

Dr. Aloke Kumar Mozumder

Associate Professor

Dept. of Mechanical Engineering

BUET, Dhaka-1000.

iii

ACKNOWLEDGEMENTS

The authors are grateful to Dr. Aloke Kumar Mozumder, Associate Professor, Department of

Mechanical Engineering, Bangladesh University of Engineering and Technology, Dhaka for his

guidance, close supervision, inspiration and constructive suggestions to attain the desired

experimental goal.

The authors also acknowledge their gratitude to the Department of Mechanical Engineering,

Bangladesh University of Engineering and Technology (BUET) for providing necessary

financial aid and other facilities to conduct the research. The authors also express their

thankfulness to the personnel of different shops and laboratories for their help during the

fabrication of the experimental setup.

iv

CONTENTS

Declaration ii

Acknowledgements iii

List of Tables viii

List of Figures ix

Abstract xii

Nomenclature xiv

1 Introduction 1-3

2 Literature Review 4-11

2.1 Experiment Conducted by Leidenfrost 4

2.2 Stability of Leidenfrost phenomenon 5

2.3 Momentum, Heat and Mass transfer processes 6

2.4 Application 6

2.5 Boiling and Leidenfrost Effect 7

3 Development of Model 12-23

4 Experimental setup and procedure 24-30

4.1 Introduction 24

4.2 Schematic diagram of experimental setup 24

4.2.1 Metal Blocks 25

4.2.2 Stand 26

4.2.3 Heater 27

4.2.4 Thermocouple 27

4.2.5 Variac 28

4.2.6 Syringe 28

4.3 Working Fluids 29

v

4.3.1 Water 29

4.3.2 NaCl solution 29

4.3.3 Methanol 29

4.3.4 Ethanol 29

4.4 Experimental Procedure 29

5 Results and Discussions 31-82

5.1 Analysis of Theoretical model 31

5.2 Analysis of Experimental data 38

5.2.1 Liquid Variation 38

5.2.1.1 Effect of latent heat of vaporization 38

5.2.1.2 Effect of specific heat, thermal

conductivity and density of liquid

39

5.2.1.3 Effect of boiling temperature of liquid 39

5.2.2 Diameter Variation 39

5.2.3 Material Variation 46

5.3 Experimental Boiling Curve 52

5.3.1 Experimental Boiling curve of water 53

5.3.2 Experimental Boiling curve of methanol 55

5.3.3 Experimental Boiling curve of ethanol 57

5.4 Inverse boiling curve 59

5.5 Engineering Correlation of experimental data 61

5.5.1 Experimental Correlation for Aluminum 62

5.5.2 Experimental Correlation for Brass 63

5.5.3 Experimental Correlation for Copper 64

5.6 Comparison of Theoretical and Experimental result 66

5.6.1 Comparison curve for distilled water on different

metal surfaces

66

5.6.2 Comparison curve for methanol on different metal

surfaces

71

5.6.3 Comparison curve for ethanol on different metal

surfaces

75

vi

6 Conclusions 80-82

6.1 Conclusions 80

6.2 Further Work 81

6.3 Recommendations 81

REFERENCE 83-84

APPENDICES 85-107

A Saturation Properties of Liquid 86

A.1 Saturation Properties of Methanol 86

A.2 Saturation Properties of Ethanol 87

A.3 Saturation Properties of Water 88

B Experimental Data 89

B.1 Evaporation time of Distilled water on Aluminum

Surface

89

B.2 Evaporation time of NaCl Solution on Aluminum

Surface

90

B.3 Evaporation time of Ethanol on Aluminum Surface 90

B.4 Evaporation time of Methanol on Aluminum

Surface

91

B.5 Evaporation time of Distilled water on Brass

Surface

91

B.6 Evaporation time of NaCl Solution on Brass

Surface

92

B.7 Evaporation time of Ethanol on Brass Surface 92

B.8 Evaporation time of Methanol on Brass Surface 93

B.9 Evaporation time of Distilled water on Copper

Surface

93

B.10 Evaporation time of NaCl Solution on Copper

Surface

94

B.11 Evaporation time of Ethanol on Copper Surface 94

B.12 Evaporation time of Methanol on Copper Surface 95

B.13 Evaporation time of Distilled water on Mild Steel

Surface

95

B.14 Evaporation time of NaCl Solution on Mild Steel

Surface

96

B.15 Evaporation time of Ethanol on Mild Steel Surface 96

vii

B.16 Evaporation time of Methanol on Mild Steel

Surface

97

C Summary of Theoretical and Experimental Result

98

C.1 Comparison for small diameter liquid droplet 98

C.2 Comparison for large diameter liquid droplet 99

C.3 Comparison of Leidenfrost point temperature for

for different liquid droplets (small and large

diameter)

different liquid droplets

100

D Program Code 101

D.1 Estimation of theoretical time 101

D.2 Engineering Correlation of experimental data 103

viii

LIST OF TABLES

B1 Evaporation time of Distilled water on Aluminum Surface 89

B2 Evaporation time of NaCl Solution on Aluminum Surface 90

B3 Evaporation time of Ethanol on Aluminum Surface 90

B4 Evaporation time of Methanol on Aluminum Surface 91

B5 Evaporation time of Distilled water on Brass Surface 91

B6 Evaporation time of NaCl Solution on Brass Surface 92

B7 Evaporation time of Ethanol on Brass Surface 92

B8 Evaporation time of Methanol on Brass Surface 93

B9 Evaporation time of Distilled water on Copper Surface 93

B10 Evaporation time of NaCl Solution on Copper Surface 94

B11 Evaporation time of Ethanol on Copper Surface 94

B12 Evaporation time of Methanol on Copper Surface 95

B13 Evaporation time of Distilled water on Mild Steel Surface 95

B14 Evaporation time of NaCl Solution on Mild Steel Surface 96

B15 Evaporation time of Ethanol on Mild Steel Surface 96

B16 Evaporation time of Methanol on Mild Steel Surface 97

ix

LIST OF FIGURES

2.1 A Leidenfrost drop in cross section 4

2.2 (a) A bubble forms in the crevice of a scratch along the bottom of a

pan of water. (b–f ) The bubble grows, pinches off, and then ascends

through the water

8

2.3 Boiling curve for water 9

2.4 Drop lifetimes on a hot plate 11

3.1 Geometry of sessile droplet for the model 12

3.2 Determination of radiation shape factor at side surface of liquid

droplet

19

4.1 Schematic diagram of the experimental setup 24

4.2 Metal Block 26

4.3 Stand 26

4.4 Heater 27

4.5 K type thermocouple meter. 27

4.6 Variac 28

4.7 Syringes used in the experiment 28

5.1 Experimental evaporation time and model predicted Leidenfrost time

for small diameter Methanol on Copper surface

32


for small diameter Methanol on Aluminum surface

32


for large diameter Methanol on Aluminum surface

33


for small diameter Ethanol on Brass surface

35


for large diameter Ethanol on Brass surface

36

5.6 Experimental evaporation time and model predicted large diameter 36

x

Leidenfrost time for Ethanol on Mild steel surface

5.7 Comparison curve of Droplet Evaporation Time of Distill Water,

NaCl solution, Methanol, Ethanol on Aluminum surface

40


NaCl solution, Methanol, Ethanol on Brass surface

42


NaCl solution, Methanol, Ethanol on Copper surface

44


NaCl solution, Methanol, Ethanol on Mild steel surface

45

5.11 Comparison of Droplet Evaporation Time of Distilled water on four

different surfaces

47

5.12 Comparison of Droplet Evaporation Time of NaCl solution on four

different metal surfaces

49

5.13 Comparison of Droplet Evaporation Time of Methanol on four

different surfaces

50

5.14 Comparison of Droplet Evaporation Time of Ethanol on four different

surfaces

51

5.15 Boiling curve of Water on different material surfaces 54

5.16 Boiling curve of Methanol on different material surfaces 56

5.17 Boiling curve of Ethanol on different material surfaces 58

5.18 Schematic of a typical Inverse boiling curve and boiling curve of a

Liquid

59

5.19 Empirical correlation of total evaporation time for Aluminum surface 62

5.20 Empirical correlation of total evaporation time for Brass surface 63

5.21 Empirical correlation of total evaporation time for Copper surface 64

5.22 Empirical correlation of total evaporation time for Mild steel surface 65

5.23 Comparison graph of total evaporation time (τ) vs surface temperature

(𝑇𝑠) of water on Aluminum surface

67


(𝑇𝑠) of water on Brass surface

68

5.25 Comparison graph for total evaporation time (τ) of Water vs surface 69

xi

temperature (𝑇𝑠) on Copper surface


(𝑇𝑠) of water on Mild steel surface

70


(𝑇𝑠) of methanol on Aluminum surface

71


(𝑇𝑠) of methanol on Brass surface

72


(𝑇𝑠) of Methanol on Copper surface

73

5.30 Comparison graph of total evaporation time (τ) vs. surface

temperature (𝑇𝑠) of methanol on Mild steel surface

74


(𝑇𝑠) of ethanol on Aluminum surface

76

5.32 Comparison graph of total evaporation time (τ) vs surface

temperature (𝑇𝑠) of ethanol on Brass surface

77


(𝑇𝑠) of ethanol on Copper surface

78

5.34 Comparison graph of total evaporation time (τ) vs surface

temperature (𝑇𝑠) of ethanol on Mild steel surface

79

xii

ABSTRACT

A model for the prediction of evaporation time in film boiling region of a sessile drop of liquid

on a hot metallic surface has been developed in the present study. The droplet is assumed to have

a stable vapor film formed beneath the droplet and is supported by the excess vapor pressure of

the film. Heat is assumed to be transferred to the liquid droplet by conduction and radiation

through vapor film. The model develops an iterative process for the refinement of calculated

mass transfer rate from the bottom surface of the droplet. Sessile drop of four different liquids

such as distilled water, saturated NaCl solution, methanol and ethanol having two different

diameters (2.5 and 2.75mm) were used to conduct an experiment for a wide range of solid

surface temperatures (60-400 oC) which verifies the proposed model at Leidenfrost point. Four

solid surfaces copper, aluminum, brass and mild steel were used to conduct the experiment. The

Leidenfrost time (complete evaporation time corresponding to Leidenfrost temperature)

predicted from the proposed model has been compared with the experimental value; the

predicted time is 50-80 % of the experimental one in most of the cases. In the present study heat

flux has been determined. Using these heat fluxes, boiling curves have been generated for each

liquid on different material surfaces. By using experimental data correlation constants have been

developed for four different metal surfaces (aluminum, copper, mild steel and brass) considering

four liquids on each metal surfaces. A comparison has been made above Leidenfrost temperature

between experimental data and correlated data using these correlation constants; correlated time

is 80-95% of the experimental one in most of the cases.

xiii

NOMENCLATURE:

A Projected base area of droplet (m2)

Al Bottom surface area of liquid (m2)

Ap Test surface area (m2)

As Side surface area of liquid (m2)

C1

Correlation constant from experimental data [ - ]

C2 Correlation constant from experimental data [ - ]

cp Specific heat of vapor (J. Kg−1. K−1)

C Concentration of liquid (Kg/m3)

D Diffusivity of liquid (m2/s)

Fpl Non dimensional radiation shape factor

between test surface and liquid

[ - ]

g Gravitational acceleration (m/s2)

hg Latent enthalpy of vaporization of liquid droplet (J/Kg)

h* Reduced latent heat of vaporization (J/Kg)

kv Thermal conductivity of vapor (W. m−1. K−1)

m b Evaporation rate of mass from bottom surface

of the liquid

(Kg/s)

m s Evaporation rate of mass from side surface of

the liquid

(Kg/s)

M Molecular mass of liquid (Kg/mol)

p Pressure at the bottom of the droplet (Pa)

xiv

po Atmospheric pressure (Pa)

ps Saturation pressure of liquid (Pa)

q Time averaged heat flux (W/m2)

Q Cb (p→l) Heat flux from test surface to bottom surface of

liquid by conduction

(W/m2)

Q Rb (p→l) Heat flux from test surface to bottom surface of

liquid by radiation

(W/m2)

Q Rs (p→l) Heat flux from test surface to side surface of

liquid by radiation

(W/m2)

Q b Total heat flux from test surface to bottom

surface of liquid

(W/m2)

Q s Total heat flux from test surface to side surface

of liquid

(W/m2)

ro Initial radius of liquid droplet (m)

ro′ Radius of spherical liquid droplet considering

spherical coordinate

(m)

rp Radius of test surface (m)

r Radius of liquid droplet at any time (m)

R Universal gas constant (J. mol−1. K−1)

T Variable temperature (⁰C)

TL Leidenfrost point Temperature (⁰C)

Tp Test surface temperature (⁰C)

Ts Saturation temperature of liquid (⁰C)

xv

∆T = ( Tp − Ts) (⁰C)

u Average radial velocity of vapor (m/s)

U Radial velocity of vapor (m/s)

v Vertical velocity of vapor (m/s)

V Volume at any time (m3)

Vo Initial volume of the liquid droplet (m3)

Z Vertical coordinate (m)

Greek symbols

δ Vapor film thickness at the bottom (𝑚)

𝜏 Total evaporation time of liquid droplet (𝑠)

𝜌𝑙 Density of liquid (𝐾𝑔/𝑚3)

𝜌𝑣 Density of vapor (𝐾𝑔/𝑚3)

𝜇𝑣 Viscosity of vapor (𝑁. 𝑠/𝑚−2)

𝜀𝑙 Non dimensional emissivity of liquid

𝜀𝑝 Non dimensional emissivity of test surface

𝜎 Stefan-Boltzmann constant (𝑊.𝑚−2.𝐾−4)

𝜆′ =ℎ𝑔+0.5𝐶𝑝*∆T (J/Kg)

xvi

Subscripts

B Bottom surface of liquid droplet

C Conduction heat transfer

L Liquid phase

P Plate or test surface

R Radiation heat transfer

S Saturation phase of liquid droplet

V Vapor phase

1

CHAPTER

INTRODUCTION 1

When a sessile drop of liquid comes into contact with a very hot metal surface, nucleate boiling

is not usually found because a thin vapor film at the contact surface of the droplet and hot metal

surface is formed instantly. The higher the metal surface temperature, the thicker is the vapor

layer and at a certain temperature a stable vapor film is formed. This stable film impedes the

conductive heat transfer through it as its thermal conductivity is much lower compared to that of

the liquid. So the evaporation time reaches to a maximum. This phenomenon was first

investigated by Johann Gottlob Leidenfrost [1] in 1756 and is named the Leidenfrost

phenomenon in honor of him. The temperature at that point is known as Leidenfrost temperature

and the corresponding evaporation time is known as Leidenfrost time. After Leidenfrost

temperature, the heat transfer rate to the liquid droplet again increases with the increase in

temperature because radiation heat transfer starts to dominate which in turn decrease the

evaporation time considerably. This point is practically significant because it states that a higher

metal surface temperature doesn‟t guarantee the higher amount of heat transfer to the liquid

which can be utilized in the design of boiler, cooling tower and many other heat addition and

removal equipments.

Since Leidenfrost published the phenomenon, a numerous number of research papers and

technical notes have been published. Gottfried et al. [2] investigated the behavior and

evaporation rate of small droplet of liquid on a hot flat surface experimentally with no evident of

bouncing, spitting or hissing. They developed an analytical model to predict evaporation rate of

droplets. In their model they assumed the liquid droplet to be separated from the heating surface

by a vapor film which also provided the excess vapor pressure to support the liquid mass. Starov

and Sefiane [3] proposed a theoretical description of evaporation of sessile drop. They described

linear dependency of evaporation rate on droplet‟s base radius. Their analysis showed that most

of the evaporation was concentrated near the contact line.

2

Baumeister et al. [4] analyzed water droplets of volume 0.05 to 1 cc. In this volume range, they

suggested an analytical model based on flat disk geometry. The droplet was assumed to be in a

steady state condition and using momentum, energy, continuity equation along with boundary

conditions, they derived a formula to find the droplet evaporation time. Chatzikyriakou et al. [5]

used CFD simulations of both sessile droplets resting upon a vapor cushion and droplets

bouncing off a hot solid surface. Experimentally they found that the droplet can rebound from

the vapor layer. A good agreement with the experimental observations was found with their

simulation. Wachters et al. [6] developed an theoretical model for heat transfer from hot

horizontal plate to sessile water drops in spheroidal state. They neglected radiation heat transfer

in their model and only put concentration on conduction heat transfer to the bottom surface of

liquid through the vapor film. Xie and Zhou [7] conducted a theoretical analysis for liquid

droplet impinging on a solid wall near Leidenfrost point. They divided the evaporation process

into two stages recoil stage and spherical stage and built heat transfer models on both stages

respectively. The maximum contact radius was also calculated by a theoretical model. Crafton

and Black [8] observed and quantified the evaporation rates of small liquid droplets of Water and

n-Heptane on Aluminum and Copper surfaces. From the measured quantities, they calculated

contact angle and evaporation rate. They used these results to predict the heat transfer on surface

and compared it with experimental results.

Nguyen and Avedisian [9] presented a numerical solution for the problem of film evaporation of

a liquid droplet on a horizontal surface. They assumed the horizontal surface having a constant

surface temperature which was considered to be isolated from the ambience. There are many

other scientists and researchers who conducted experiment on this phenomenon [10-12]. Yao and

Cai [13] studied the dynamics of water drops impacting at small angles on hot surfaces. The

Experiments were conducted using a monosize droplet stream and a rotating disk. When the

impact angle was decreased, the Leidenfrost temperature was found to be reduced. Correlations

were established for the description of this behavior. Nagai and Nishio [14] studied Leidenfrost

temperature on a very smooth surface. The Leidenfrost temperature was measured on single-

crystal and metal plates. The maximum surface roughness of the former was 0.03 μm, and that of

the latter was 1.25 μm. Results of the experiment showed that the Leidenfrost temperatures on

these two surfaces did not differ from each other as long as the surfaces were the same in

wettability and thermal conductivity (or thermal diffusivity). Based on the theory of Baumeister

3

et al. [4], I. Michiyoshi, K. Makino [16] determine time averaged heat flux. They studied the heat

transfer characteristics of evaporation of a single droplet of pure water placed on smooth surfaces

of copper, brass, carbon steel and stainless steel at temperature ranging 80⁰C to 450⁰C .They

analyzed heat transfer characteristics by correlating heat flux with ∆T=( 𝑇𝑝 − 𝑇𝑠).

In the present study, an analytical model will be proposed for the prediction of sessile drop

evaporation time at Leidenfrost temperature on hot solid surface. The model will be verified with

some experimental data. In the proposed model, conduction and radiation heat transfer along

with mass diffusion have been successfully included. It was roughly observed in the experiment

that for small droplet diameter, the liquid droplet usually flattens on the hot metal surface having

a thin vapor cushion beneath it. In the proposed model, it is considered that the liquid droplet on

the heated surface to have an almost cylindrical shape with a very little height. The vapor layer

thickness is considered to be uniform during the entire vaporization process and the vertical

velocity of the vapor leaving the bottom surface of the droplet has been considered to be

uniform. Heat is assumed to be transferred at the bottom surface of the liquid by conduction and

radiation. The side surface is assumed to get the heat energy by radiation only. Mass diffusion is

also considered from side surface of droplet in the analysis.

A correlation was developed in reference [18] considering only the heat is transferred from the

hot surface to the droplet by conduction through the vapor film and by radiation. Mass of the

droplet is removed by evaporation and diffusion. The droplet evaporation time of a specific

liquid on different plates depends upon the thermo-physical properties of the corresponding

plate. Evaporation times of different liquids on different solid surfaces are compared in this

dissertation by graphical presentation. The experimental data has been correlated in terms of

dimensionless groups resulting from the analytical model by Lee. In the present study heat

transfer characteristics of evaporation of small droplets of distilled water, saturated NaCl

solution, methanol and ethanol settled on aluminum, copper, mild steel and brass surface with

temperature ranging from 60 to 400⁰C will be studied. The experimental data has been plotted to

obtain evaporation time (τ) versus surface temperature (Ts) curve, which has an inverse trend of a

typical boiling curve and can be called as Inverse Boiling Curve. By determining heat flux,

boiling curve for different liquids (water, methanol and ethanol) has been generated.

4

CHAPTER

LITERATURE REVIEW 2

2.1 Experiment Conducted by Leidenfrost

Figure 2.1 A Leidenfrost drop in cross section

Leidenfrost conducted his experiments with an iron spoon that was heated red-hot in a fireplace.

After placing a drop of water into the spoon, he timed its duration by the swings of a pendulum.

He noted that the drop seemed to suck the light and heat from the spoon, leaving a spot duller

than the rest of the spoon. The first drop deposited in the spoon lasted 30 s while the next drop

lasted only 10 s. Additional drops lasted only a few seconds.

Leidenfrost misunderstood his demonstrations because he did not realize that the longer-lasting

drops were actually boiling. When the temperature of the plate is less than the Leidenfrost point,

the water spreads over the plate and rapidly conducts energy from it, resulting in complete

vaporization within seconds.

When the temperature is at or above the Leidenfrost point, the bottom surface of a drop

deposited on the plate almost immediately vaporizes. The gas pressure from this vapor layer

5

prevents the rest of the drop from touching the plate (Fig. 4). The layer thus protects and

supports the drop for the next minute or so. The layer is constantly replenished as additional

water vaporizes from the bottom surface of the drop because of energy radiated and conducted

through the layer from the plate. Although the layer is less than 0.1 mm thick near its outer

boundary and only about 0.2 mm thick at its center, it dramatically slows the vaporization of the

drop.

2.2 Stability of Leidenfrost Phenomenon

The question of the stability of the Leidenfrost phenomenon usually quickly reduces to a

discussion of the Leidenfrost point and how it was determined, since most workers are agreed

that film boiling becomes increasingly stable relative to nucleate and mixed modes at increasing

surface temperatures. However, very little agreement exists between various workers on the true

value of the Leidenfrost point for any given set of conditions.

Baumeister [4] report maintaining stable film boiling for small droplets in air down to a surface

temperature less than a degree above saturation, while Wachters [20] found a similar for water

droplets in film boiling in dry air at a surface temperature as low as 75ºC. In fact, Wachters

argues that the absolute minimum surface temperature for the Leidenfrost phenomenon is equal

to the wet-bulb temperature of the surrounding atmosphere; to quote his explanation

“When the drop bottom temperature has a value below the boiling point, the narrow layer under

the drop contains a mixture of vapor and air. In this mixture the vapor concentration is in

equilibrium with the drop bottom temperature. However, at the outer rim of the drop bottom the

dry surroundings. This is a one-way diffusion which involves a drift velocity of the gas mixture

and generates a radial pressure gradient, higher than the atmospheric pressure”.

The explanation appears plausible, but the quantitative expressions have not been worked out.

Baumeister and Wachters both emphasize the need for extremely smooth surface and

suppression of disturbances in the droplet to achieve these extremely low temperatures. The

6

droplets are initially deposited on quite hot surfaces which are then cooled to low temperatures.

Too rapid cooling of the surface leads to premature collapse, presumably because the droplet

oscillations have not been adequately damped out in this time. With care, a wire can be inserted

into the droplet to damp out the oscillations; the droplet is then partially supported by surface

tension on the wire, and the unconstrained force balance is upset. Both of these workers also

used test surfaces that were slightly concave underneath the droplet, and this undoubtedly

contributed to droplet stabilization.

2.3 Momentum, Heat and Mass transfer processes

A number of attempts have been made to analyze quantitatively the momentum, heat and mass

transfer processes during the Leidenfrost phenomenon. Several of these contain errors of

assumption or execution. All of these analyses assume that vapor is generated on the lower

surface of the drop by heat conduction through the vapor layer, that the vapor is in laminar flow

under the droplet, and that the integrated product of the local excess pressure (above

atmospheric) and the horizontal projection of the droplet lower surface is equal to the droplet

weight.

2.4 Application

Failure of tube walls of steam boiler is a common problem. In a nuclear reactor with boiling

coolant, the transition from nucleate to film boiling occurs at constant heat flux and can be

accompanied by a very large increase in wall temperature, most descriptively called burnout.

Conversely, once a reactor has had a coolant flow failure and surface has become very hot, film

boiling will occur, and one way to make a small amount of coolant contact a large amount of

surface is to spray it in as a fog. This technique, spray or fog cooling, has been tested, and it is a

variant of the convective Leidenfrost phenomenon in that major interest is attached to the impact

characteristics of the droplets on the surface.

7

Several other applications of the phenomenon are closely related in basic mechanism to those

above

The use of a water spray to cool steel billets or the rolls in rolling mill operations.

Water spray during continuous casting.

The design of quick response steam generators by spraying liquid on a hot surface.

The stable operation of a steam iron with a changing water inventory.

Film cooling of a rocket nozzle, either by breakdown of a continuous liquid film or direct

spray injection.

Cool-down of cryogenic liquid storage tanks and transfer lines during filling. An

interesting corollary problem is the possibility of minimizing cryogenic liquid loss by

deliberate production of a vapor film next to the wall by film boiling.

Use of air-dropped solutions to control forest fires.

2.5 Boiling and Leidenfrost Effect

Let us consider a pan where water to be heated from below by a flame or electric heat source. As

the water warms, air molecules are driven out of solution in the water, collecting as tiny bubbles

in crevices along the bottom of the pan (Fig. 1a). The air bubbles gradually inflate, and then they

begin to pinch off from the crevices and rise to the top surface of the water (Figs. 1b–f ). As they

leave, more air bubbles form in the crevices and pinch off, until the supply of air in the water is

depleted. The formation of air bubbles is a sign that the water is heating but has nothing to do

with boiling.

8

Figure 2.2 (a) A bubble forms in the crevice of a scratch along the bottom of a pan of water. (b–f

) The bubble grows, pinches off, and then ascends through the water

Water that is directly exposed to the atmosphere boils at what is sometimes called its normal

boiling temperature TS . For example, TS is about 100ºC when the air pressure is 1 atm. Since the

water at the bottom of your pan is not directly exposed to the atmosphere, it remains liquid even

when it superheats above TS by as much as a few degrees. During this process, the water is

constantly mixed by convection as hot water rises and cooler water descends.

9

Figure 2.3 Boiling curve for water.

If the pan‟s temperature is continuing to increase, the bottom layer of water begins to vaporize,

with water molecules gathering in small vapor bubbles in the now dry crevices, as the air bubbles

do in Fig. 1. This phase of boiling is signaled by pops, pings, and eventually buzzing. The water

almost sings its displeasure at being heated. Every time a vapor bubble expands upward into

slightly cooler water, the bubble suddenly collapses because the vapor within it condenses. Each

collapse sends out a sound wave. Once the temperature of the bulk water increases, the bubbles

may not collapse until after they pinch off from the crevices and ascend part of the way to the top

surface of the water. This phase of boiling is labeled „„isolated vapor bubbles‟‟ in the boiling

curve.

10

If the pan‟s temperature is more increased, the clamor of collapsing bubbles first grows louder

and then disappears. The noise begins to soften when the bulk liquid is sufficiently hot that the

vapor bubbles reach the top surface of the water. There they pop open with a light splash. The

water is now in full boil.

If the pan‟s temperature is further increased the vapor bubbles next become so abundant and

pinch off from their crevices so frequently that they coalesce, forming columns of vapor that

violently and chaotically churn upward, sometimes meeting previously detached „„slugs‟‟ of

vapor.

The production of vapor bubbles and columns is called nucleate boiling because the formation

and growth of the bubbles depend on crevices serving as nucleating sites (sites

of formation).

If the pan‟s temperature is raised past the stage of columns and slugs, the boiling enters a new

phase called the transition regime. Then each increase in the pan‟s temperature reduces the rate

at which energy is transferred to the water. The decrease is not paradoxical. In the transition

regime, much of the bottom of the pan is covered by a layer of vapor. Since water vapor

conducts energy about an order of magnitude more poorly than does liquid water, the transfer of

energy to the water is diminished. The hotter the pan becomes, the less direct contact the water

has with it and the worse the transfer of energy becomes.

At this stage, the whole of the bottom surface is covered with vapor. Then energy is slowly

transferred to the liquid above the vapor by radiation and gradual conduction. This

phase is called film boiling.

Jearl Walker of Cleveland State University performed an experiment for finding an elementary

relationship between lifetime of drops and pan temperature. Drops of water having uniform size

were released from a syringe to the hot plate and the survival time of the drop was measured.

The data was plotted and the graph shows a curious peak.

11

Figure 2.4 Drop lifetimes on a hot plate

When the plate temperature was between 100 and about 200ºC, each drop spread over the plate

in a thin layer and rapidly vaporized. When the plate temperature was about 200ºC, a drop

deposited on the plate beaded up and survived for over a minute. At even higher plate

temperatures, the water beads did not survive quite as long. The temperature corresponding to

the peak in a graph is generally known as the Leidenfrost point.

12

ro

Projected area = 𝜋𝑟𝑜2

Total surface area = 4𝜋𝑟𝑜

2

r

z

v

Profile of u

ro Thin vapor film

𝑄𝑅𝑠 (𝑝→𝑙)

𝑄𝐶𝑏(𝑝→𝑙) + 𝑄𝑅𝑏(𝑝→𝑙) Hot test surface

δ u

CHAPTER

DEVELOPMENT OF MODEL 3

Considering a droplet of liquid to be a sphere and of radius, 𝑟𝑜 , when dropped very gently on a

solid surface from a syringe, it takes heat from the solid surface and evaporates. For the proposed

model it is considered that the droplet becomes flattened when it falls on the hot test surface. So

the liquid droplet on the metal surface will be considered as a cylinder with a very little height. It

will be assumed that this flattened liquid will occupy a contact surface area equal to the projected

area of the initial spherical droplet. A schematic view of the geometry for the proposed model is

given in Fig. 3.1.

Fig. 3.1 Geometry of sessile droplet for the model

13

Heat transfer from a hot surface to a liquid is a very complex process and several physical

processes occur simultaneously. For simplicity of analysis, the following assumptions are made

throughout the theoretical development.

i. Heat is transferred to the bottom surface of the liquid droplet by conduction and

radiation through the vapor film.

ii. The side surface of the droplet is heated by radiation heat transfer only.

iii. The vapor flow at the bottom of the droplet is laminar and viscous.

iv. A stable vapor layer of uniform thickness is considered throughout the theory.

v. Mass diffusion from the droplet has been considered only on the side surface.

vi. As the vapor layer is very thin, it is assumed that the vertical velocity will not

influence the heat transfer to the bottom of the liquid droplet. Vertical velocity has

been considered to be constant in the analysis.

vii. Though actually the bottom surface of the liquid is not completely flat, for simplicity

of analysis it has been considered as a flat surface.

viii. As the vapor layer is considered to have an extreme radius at r = 𝑟𝑜 it is considered that

at this point the pressure will be the atmospheric pressure, 𝑝𝑜 .

Now, conduction heat transfer through bottom surface of the liquid can easily be found by

considering the steady state one dimensional Fourier‟s heat conduction equation

𝛿2𝑇

𝛿𝑧2 = 0 (3.1)

By integrating and putting boundary conditions at z=0, T=Tp, and at z=δ, T=Ts, the temperature

profile beneath the droplet is found. Substitution of this temperature profile in the differential

conduction heat transfer formula yields in conduction heat flux through the bottom surface,

Integrating, ∫𝛿(𝛿𝑇

𝛿𝑧)=∫0. 𝛿𝑧

𝛿𝑇

𝛿𝑧 =c1

∫𝛿𝑇= c1∫δz

14

T=c1z+c2 ∙∙∙∙∙∙∙∙∙∙ (3.a)

Boundary conditions, at z=0, T=Tp, and at z=δ, T=Ts

For, z=0, Tp=0+c2 i.e. c2= Tp

So, from equation (a), T=c1z+ Tp ∙∙∙∙∙∙∙∙∙∙ (3.b)

And, from equation (3.b)

For z=δ, T=c1δ+ Tp,

c1=𝑇𝑠−𝑇𝑝

𝛿

Now, from equation (b), T=𝑇𝑠−𝑇𝑝

𝛿𝑧 +Tp ∙∙∙∙∙∙∙∙∙∙ (3.c)

So, conduction heat transfer from hot metal surface to bottom surface of liquid is

Qcb(p→l)=-kv𝐴𝑙𝛿𝑇

𝛿𝑧

Qcb(p→l)=-kv𝐴𝑙 𝛿

𝛿𝑧 (

𝑇𝑠−𝑇𝑝

𝛿𝑧 +Tp) ……………[from eqn (3.c)]

Qcb(p→l)=-kv𝐴𝑙 𝑇𝑠−𝑇𝑝

𝛿

Qcb(p→l)=kv 𝐴𝑙 𝑇𝑝−𝑇𝑠

𝛿

QCb (p→l)

𝐴𝑙= kv

𝑇𝑝−𝑇𝑠

𝛿

𝑄 𝐶𝑏(𝑝→𝑙) = kv

𝑇𝑝−𝑇𝑠

𝛿 (3.2)

We will consider this initial heat flux will continue up to last for the ease of calculation.

Now, radiation heat flux from hot metal surface to bottom of liquid droplet may be expressed by

the following equation [15],

QRb(p→l)= 𝐸𝑝 −𝐸𝑏𝑙

1−εp

휀𝑝 𝐴𝑝+

1

𝐴𝑝 𝐹𝑝𝑙+

1−휀𝑙휀𝑙𝐴𝑙

𝑄𝑅𝑏(𝑝→𝑙)=𝜍(𝑇𝑝

4 −𝑇𝑠4)

1−εp

휀𝑝 𝐴𝑝+

1

𝐴𝑝 𝐹𝑝𝑙+

1−휀𝑙휀𝑙𝐴𝑙

15

𝑄𝑅𝑏(𝑝→𝑙)= 𝜍(𝑇𝑝

4 −𝑇𝑠4)𝐴𝑙

1−εp

휀𝑝

𝐴𝑙𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑙𝐴𝑝

+1−휀𝑙

휀𝑙

𝑄𝑅𝑏 (𝑝→𝑙)

𝐴𝑙=

𝜍(𝑇𝑝4 −𝑇𝑠

4)1−εp

휀𝑝

𝐴𝑙𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑙𝐴𝑝

+1−휀𝑙

휀𝑙

𝑄 𝑅𝑏 𝑝→𝑙 =

𝜍 𝑇𝑝4 –𝑇𝑠

4 1−휀𝑝

휀𝑝

𝐴𝑙𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑙𝐴𝑝

+1−휀𝑙

휀𝑙

(3.3)

We will consider this initial heat flux will continue up to last for the ease of calculation.

Radiation shape factor for bottom surface, 𝐹𝑝𝑙 can be found using formula of shape factor

between two parallel coaxial disks given by reference [15],

𝐹𝑝𝑙 = 𝑋− 𝑋2 −4

𝑅2𝑅1

2

12

2 (3.4)

Where, 𝑅1 =𝑟𝑝

𝛿 , 𝑅2 =

𝑟𝑜

𝛿 and 𝑋 =

1+(1+𝑅22)

𝑅12

As the droplet is of very little volume, these two heat fluxes 𝑄 𝐶𝑏(𝑝→𝑙) and 𝑄

𝑅𝑏 𝑝→𝑙 will be

considered to retain their value to be constant up to the complete vaporization of the droplet.

So, total heat flux at bottom,

𝑄 𝑏 = kv

𝑇𝑝−𝑇𝑠

𝛿 +


4)1−휀𝑝

휀𝑝

𝐴𝑙𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑙𝐴𝑝

+1−휀𝑙

휀𝑙

(3.5)

From Eq. (5), it is evident that total heat flux at the bottom of the droplet is only a function of

vapor layer thickness, 𝛿.

This 𝑄 𝑏 vaporizes the liquid at bottom and superheats the vapor at an average temperature of

𝑇𝑝 +𝑇𝑠

2 . So,

𝑄𝑏 =𝑚 𝑏𝑕𝑔+𝑚 𝑏𝑐𝑝(𝑇𝑝 +𝑇𝑠

2 - 𝑇𝑠)

16

𝑄𝑏 =𝑚 𝑏𝑕𝑔+𝑚 𝑏𝑐𝑝(𝑇𝑝 −𝑇𝑠

2)

𝑄𝑏 = 𝑚𝑏

𝑡(𝑕𝑔+𝑐𝑝

𝑇𝑝 −𝑇𝑠

2 )

𝑄𝑏

𝐴𝑙 =

𝑚𝑏

𝑡𝐴𝑙(𝑕𝑔+𝑐𝑝


2)

𝑄 𝑏=

𝑚𝑏𝛿

𝑡𝐴𝑙𝛿(𝑕𝑔+𝑐𝑝


2)

𝑄 𝑏 =

𝑚𝑏𝛿

𝑉 𝑡(𝑕𝑔+𝑐𝑝


2)

𝑄 𝑏 = 𝜌𝑣 𝑣(𝑕𝑔+𝑐𝑝


2) (3.6)

Again, we will consider this initial heat flux will continue up to last for the ease of calculation.

Eqs. (5) and (6) yield,

𝑣 =

𝑘𝑣 𝑇𝑝−𝑇𝑠

𝛿 +


4)

1−휀𝑝휀𝑝

𝐴𝑙𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑙𝐴𝑝

+1−휀𝑙

휀𝑙

𝜌𝑣 (𝑕𝑔+𝑐𝑝𝑇𝑝 −𝑇𝑠

2)

(3.7)

Now, simplified from of Navier-Stokes equation for cylindrical vapor layer at bottom, is given

by,

𝛿𝑝

𝛿𝑟 = 𝜇𝑣

𝛿2𝑢

𝛿𝑧2

By integrating twice and considering no slip condition at the bottom vapor layer (Fig. 3.1),

average velocity can be obtained as follows,

By Integrating,

∫𝛿

𝛿𝑧(

𝛿𝑢

𝛿𝑧) 𝛿𝑧=

1

𝜇𝑣

𝛿𝑝

𝛿𝑟∫ 𝛿𝑧

𝛿𝑢

𝛿𝑧=

1

𝜇𝑣

𝛿𝑝

𝛿𝑟𝑧+𝑐3

Again integrating,

17

𝑢=1

𝜇𝑣

𝛿𝑝

𝛿𝑟

𝑧2

2+𝑐3𝑧 +𝑐4 ……… (3.d)

Boundary condition at the vapor layer

Here, 𝑢 = 𝑓(𝑟, 𝑧)

At no 𝑠lip condition,

𝑢 𝑟, 0 = 0 ……… (3.e)

𝑢 𝑟, 𝛿 = 0 ……… (3.f)

For condition (e), using equation (3.d)

0=1

𝜇𝑣

𝛿𝑝

𝛿𝑟

02

2+𝑐3. 0 +𝑐4

𝑐4=0

𝑢=1

𝜇𝑣

𝛿𝑝

𝛿𝑟

𝑧2

2+𝑐3𝑧 ……… (3.g)

For condition (3.f), using equation (3.g)

0=1

𝜇𝑣

𝛿𝑝

𝛿𝑟

𝛿2

2+𝑐3𝛿

𝑐3=- 1

𝜇𝑣

𝛿𝑝

𝛿𝑟

𝛿

2

𝑐3=- 1

2𝜇𝑣

𝛿𝑝

𝛿𝑟𝛿

So from equation (3.g)

𝑢=1

𝜇𝑣

𝛿𝑝

𝛿𝑟

𝑧2

2−

1

2𝜇𝑣

𝛿𝑝

𝛿𝑟𝛿. 𝑧

𝑢=1

2𝜇𝑣

𝛿𝑝

𝛿𝑟(𝑧 − 𝛿)𝑧

Now average velocity can be obtained from the above equation as follows

𝑢 =1

𝛿∫ 𝑢 𝛿𝑧

𝛿

0

𝑢 =1

𝛿∫

1

2𝜇𝑣

𝛿𝑝

𝛿𝑟 𝑧 − 𝛿 𝑧 𝛿𝑧

𝛿

0

18

𝑢 =1

𝛿

1

2𝜇𝑣

𝛿𝑝

𝛿𝑟[𝑧3

3−

𝑧2

2𝛿]0

𝛿

𝑢 =1

𝛿

1

2𝜇𝑣

𝛿𝑝

𝛿𝑟[𝛿3

3−

𝛿3

2]

𝑢 = - 𝛿2

12𝜇𝑣

𝛿𝑝

𝛿𝑟 (3.8)

Balance of flow rate at bottom gives,

2𝜋𝑟𝛿𝑢 =𝜋𝑟2𝑣

Substitution of 𝑢 in it from Eq. (3.8) and integration using boundary conditions at r=0, pressure

is 𝑝 and at r = 𝑟𝑜 pressure is 𝑝𝑜yield in,

2𝜋𝑟𝛿(−𝛿2

12𝜇𝑣

𝛿𝑝

𝛿𝑟)=𝜋𝑟2𝑣

𝛿𝑝

𝛿𝑟 =−

6𝜇𝑣𝑟𝑣

𝛿3

∫ 𝛿𝑝 =𝑝

𝑝𝑜 −

6𝜇𝑣𝑣

𝛿3 ∫ 𝛿𝑟𝑟

𝑟𝑜

𝑝 − 𝑝𝑜 = −3𝜇𝑣𝑣

𝛿3 (𝑟2 − 𝑟𝑜2)

𝑝 − 𝑝𝑜 =3𝜇𝑣𝑣

𝛿3 (𝑟𝑜2 − 𝑟2) (3.9)

This is the pressure distribution of vapor film at the bottom.

Force balancing at bottom at initial condition gives,

𝜌𝑙𝑔𝑉𝑜=∫ (𝑝 − 𝑝𝑜)2𝜋𝑟𝛿𝑟𝑟𝑜

0

Here, 𝑉𝑜=4

3 𝜋𝑟𝑜

3=Initial droplet volume

𝜌𝑙𝑔𝑉𝑜=∫3𝜇𝑣𝑣

𝛿3 (𝑟𝑜2 − 𝑟2) 2𝜋𝑟𝛿𝑟

𝑟𝑜

0

𝜌𝑙𝑔4

3 𝜋𝑟𝑜

3 =2𝜋3𝜇𝑣𝑣

𝛿3 ∫ r(𝑟𝑜2 − 𝑟2) 𝛿𝑟

𝑟𝑜

0

19

Vapor surface

Hot test surface

Liquid surface

Imaginary surface used for

finding Radiation shape factor

for side surface, 𝐹𝑝𝑙

2

1

4

3

2′

3′

4′

3

2𝑔𝜌 𝑙𝑟𝑜3𝛿3

9𝜇𝑣𝑣 =

𝑟𝑜

4

𝛿 = [9

8

𝜇𝑣𝑟𝑜𝑣

𝜌 𝑙𝑔 ]

1

3 (3.10)

This is the final expression of vapor film thickness, δ. It can be determined by iterations using a

computer program.

Now, radiation heat flux from hot metal surface to side surface of liquid droplet can be expressed

by the following Eqn. [3.15]

𝑄 𝑅𝑠(𝑝→𝑙) =


4)1−εp

휀𝑝

𝐴𝑠𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑠𝐴𝑝

+1−휀𝑙

휀𝑙

(3.11)

Radiation shape factor for side surface, 𝐹𝑝𝑙 can be found using formula of shape factor [3.15]

between two finite, coaxial cylinders and two parallel, coaxial disks.

Fig. 3.2 Determination of radiation shape factor at side surface of liquid droplet

Figure 3.2 provides required configuration for determination of desired shape factor. For lower

half of the image, considering symmetry and reciprocal relation, the following relation can be

obtained,

𝐹12 =𝐴2

2𝐴1(1 −

𝐴4

𝐴2𝐹42) (3.12)

20

Here,

𝐹42 =1

𝑋−

1

𝜋𝑋 𝑐𝑜𝑠−1(

𝐵

𝐴 −

1

2𝑌 [𝐴2 + 4𝐴 − 4𝑋2 + 4]

1

2 𝑐𝑜𝑠−1 𝐵

𝐴𝑋 + 𝐵 𝑠𝑖𝑛−1(

1

𝑋) −

𝜋𝐴

2 }

(3.13)

Where, =𝑟𝑝

𝑟𝑜 , 𝑌 =

𝛿

𝑟𝑜, 𝐴 = 𝑋2 + 𝑌2 − 1 and 𝐵 = 𝑌2 − 𝑋2 + 1 and

𝐴2 = 2𝜋𝑟𝑜𝛿, 𝐴1 = 𝜋(𝑟𝑝2 − 𝑟𝑜

2)

Again for complete image [Fig. 3.2]

𝐹1→22′=

𝐴22 ′2𝐴1

(1−𝐴44 ′𝐴22 ′

𝐹44 ′→22 ′) (3.14)

𝐹1→22′ can be found by using the Eq. (3.13)

Where, =𝑟𝑝

𝑟𝑜 ,𝑌 =

𝛿+4

3𝑟𝑜

𝑟𝑜, 𝐴 = 𝑋2 + 𝑌2 − 1 , 𝐵 = 𝑌2 − 𝑋2 + 1 and 𝐴44 = 2𝜋𝑟𝑝(𝛿 +

4

3𝑟𝑜),

𝐴22′ = 2𝜋𝑟𝑜(𝛿 +4

3𝑟𝑜)

Here, 4

3𝑟𝑜 is the height of the liquid droplet on the test surface as the volume of the initial

spherical liquid droplet is equal to the volume of the cylindrical shaped droplet on the test

surface.

And, finally,

𝐹𝑝𝑙 = 𝐹1→22′ − 𝐹12 (3.15)

Where 𝐹1→22′ and 𝐹12 can be found using Eqs. (3.14) and (3.12) respectively.

So, total radiation heat transfer from hot metal surface to side surface of liquid droplet,

21

𝑄 𝑠 = 𝑄

𝑅𝑠(𝑝→𝑙)

𝑄 𝑠 =


4)1−εp

휀𝑝

𝐴𝑠𝐴𝑝

+1

𝐹𝑝𝑙

𝐴𝑠𝐴𝑝

+1−휀𝑙

휀𝑙

(3.16)

For mass diffusion from side surface of liquid droplet steady state mass diffusion equation for

cylindrical coordinate could be used. For simplicity of calculation spherical coordinate has been

used with an equivalent cylindrical surface area.

Now, for spherical coordinate, steady state mass transfer equation

𝛿

𝛿𝑟 𝑟2 𝛿𝐶

𝛿𝑟 = 0 (3.17)

Having boundary conditions At 𝑟 = 𝑟𝑜′ , 𝐶 =

𝑝𝑠𝑀

𝑅𝑇𝑠 and at 𝑟 = ∞, 𝐶 = 0

By integrating,

𝑟2 𝛿𝐶

𝛿𝑟=𝑐5

𝛿𝐶

𝛿𝑟=

𝑐5

𝑟2

Again integrating,

𝐶 = −𝑐5

𝑟+ 𝑐6 ……… (3.h)

From equation (3.21) for the second boundary condition,

0 = −𝐶5

∞+ 𝐶6

𝐶6 = 0

Putting the value of 𝐶6 in equation (3.h)

𝐶 = −𝐶5

𝑟 ……… (3.i)

22

Now, from equation (3.22) at the first boundary condition,

𝑝𝑠𝑀

𝑅𝑇𝑠 =−

𝐶5

𝑟𝑜′

𝐶5 = −𝑝𝑠𝑀𝑟𝑜

′

𝑅𝑇𝑠

So, from equation (3.i), we get

𝐶 =𝑝𝑠𝑀𝑟𝑜

′

𝑅𝑇𝑠𝑟

So, rate of mass transfer from the side surface of the liquid to atmosphere is

𝑚 𝑠 = −𝐷𝐴𝑠 𝑑𝐶

𝑑𝑟 𝑟 = 𝑟𝑜

′

𝑚 𝑠 = −𝐷𝐴𝑠 𝑑𝑑𝑟

(𝑝𝑠𝑀𝑟𝑜

′

𝑅𝑇𝑠𝑟 ) 𝑟 = 𝑟𝑜

′

𝑚 𝑠 = 𝐷𝐴𝑠 𝑝𝑠𝑀

𝑅𝑇𝑠

1

𝑟𝑜′

𝑚 𝑠 =𝐷𝐴𝑠𝑝𝑠𝑀

𝑅𝑇𝑠𝑟𝑜′ (3.18)

Now we will develop a relationship between cylindrical coordinate and spherical coordinate as

follows

2𝜋𝑟𝑜 ∗4

3𝑟𝑜 = 4𝜋𝑟𝑜

′2

𝑟𝑜′ =

√2𝑟𝑜

√3

So, from eqn (3.18)

𝑚 𝑠 =√3𝐷𝐴𝑠𝑝𝑠𝑀

√2𝑅𝑇𝑠𝑟𝑜 (3.19)

For a refined value of 𝑚 𝑏 , total heat balance should be considered as,

𝑄 𝑏𝐴𝑏 + 𝑄

𝑠𝐴𝑠 = 𝑚 𝑏(𝑕𝑔 +𝑐𝑝

2 (𝑇𝑝 − 𝑇𝑠)) +𝑚 𝑠𝑕𝑔

𝑚 𝑏 =𝑄 𝑏𝐴𝑏 +𝑄 𝑠𝐴𝑠−𝑚 𝑠𝑕𝑔

𝑕𝑔+𝑐𝑝

2 (𝑇𝑝−𝑇𝑠)

(3.20)

23

Again balancing the total evaporation rate,

−𝜌𝑙𝑑𝑉

𝑑𝑡= 𝑚 𝑏 + 𝑚 𝑠

Now integrating,

∫ 𝑑𝑉0

𝑉𝑜= −

𝑚 𝑏 +𝑚 𝑠

𝜌 𝑙∫ 𝑑𝑡

𝜏

0

Which gives,

𝜏 =𝜌 𝑙

𝑚 𝑏 +𝑚 𝑠𝑉𝑜 (3.21)

Writing a computer program, total vaporization time, 𝜏 can be found from Eq. (3.21). Value of

𝑚 𝑏 and 𝑚 𝑠 can be found using Eqs. (3.20) and (3.19) respectively.

24

CHAPTER

EXPERIMENTAL SETUP AND 4 PROCEDURE

4.1 Introduction

The sessile drop apparatus was used to study the evaporation characteristics of droplet on a

heated surface. In particular, the liquid-solid interface temperature corresponding to the

Leidenfrost Temperature was determined from droplet evaporation curve for different materials

of different liquid.

4.2 Schematic diagram of experimental setup

Fig. 4.1 Schematic diagram of the experimental setup

Insulator

Thermocouple

Variac

AC supply

Test surface

Stand

Cartridge

heater

Syringe

25

The experimental setup is shown in Figure 4.1 which consists of the following components

• Metal blocks

• Stand

• Heater

• Variac

• Thermocouple

• Dropper

The working liquids that are used in the in the experiment are as follows

• Water

• NaCl solution

• Methanol

• Ethanol

4.2.1 Metal Blocks

Four different metal blocks are used to find out the Leidenfrost Temperature and variation of

drop evaporation time. They are as follows

• Mild steel

• Copper

• Aluminum

• Brass

26

(a) Top view (b) Side view

Figure 4.2 Metal Block

Each block has same dimension. The height and diameter of the blocks were 3 in and 3.5 in

respectively. A thermocouple was installed 2 mm below the test surface. Two cartridge heaters

were used. The first one is located 1 inch beneath and second one was 4 inch beneath the test

surface of each block. The test surfaces of the blocks are polished by emery paper (1200 grade

(000) and 1600 grade (0000)).

4.2.2 Stand

A supporting structure shown in Figure 4.2 is used in experiment to hold the metal blocks above

the earth surface. The dimensions of the stand are 1 ft × 1 ft × 3 ft. Stand hold the block above 2

ft from the earth surface. Four glass plates of 1 ft × 1 ft are attached with the stand to protect

from the air flow over the test surface.

Figure 4.3 Stand

27

4.2.3 Heater

Heater is used for heating the metal blocks. 500 Watt cartridge (Figure 4.4) heater is used. Heater

is placed 1 in beneath the test surface by drilling the block.

Figure 4.4 Heater

4.2.4 Thermocouple

K-type thermocouple is used (Figure 4.5) to determine the center temperature of the testing

surface. A thermocouple was installed 5 mm in below the test surface. But we should installed

the thermocouple at the center of the test surface where liquid droplet falls. We installed the

thermocouple at the center of the test surface, heat may conduct with the thermocouple wire and

evaporation time should vary and we will not get correct evaporation temperature.

Figure 4.5 K type thermocouple meter.

28

4.2.5 Variac

The heat supplied to the metal block through joule heating. A cartridge heater is fitted in the

blocks. Regulated electrical energy is supplied to the heater during the experiment. The

resistance element that output is controlled by variac connected to the 220 Volt laboratory

power.

Figure 4.6 Variac

4.2.6 Syringe

A couple of syringes were used to drop gently the liquid droplets on the test surface. Two

different types of needles were used with the syringe to produce two different droplet diameters;

2.50 mm and 2.75 mm. The syringe was held perpendicular to the horizontal test surface and

droplets were released from about two inches from the surface.

Figure 4.7 Syringes used in the experiment

29

4.3 Working Fluids

The working fluids used in this experiment are Water(H2O), NaCl solution(H2O+NaCl),

Methanol(CH3OH) and Ethanol(C2H5OH). Fluid is heated up on the test surface, boils and

evaporate. and we measure the drop evaporation time. Some important properties of working

fluids are mentioned below.

4.3.1 Water

Water is available in nature. But natural water is not pure. Many salts are dissolved in natural water.

Water used in experiment is distilled water from BUET boiler lab. It boils at 373.15 K at 101.325 kPa.

4.3.2 NaCl Solution

We use NaCl solution in experiment. We add (2± 0.01) gm NaCl salt in 100 ml distilled Water.

4.3.3 Methanol

Methanol is a colorless, flammable liquid. Pure methanol melts at 175.2 K, boils at 327.85 K and

molecular weight is 32. The commercial use of methanol has sometimes been prohibited. Large amount

of it are used in the synthesis of formaldehyde. Methanol is often called wood alcohol because it was once

produced mainly as a byproduct of destructive distillation of wood. Methanol is also used as a solvent for

varnishes and lacquers as antifreeze and as gasoline extender in the production of gasohol.

4.3.4 Ethanol

Ethanol can be produced by formation of carbohydrates, which occur naturally and abundantly in some

plants like sugarcane and from starchy materials like potato and corn. It boils at 351.3 K. Ethanol and

methanol both also used as fuels in SI engines.

4.4 Experimental Procedure

As seen from the Fig. 4.1, the test surface was heated from the bottom by using two cartridge

heaters. The power supply to the block was regulated using the variac to reach desired surface

temperature of the test surface. When the temperature reached at a predetermined value, a droplet

of working liquid was dropped gently to the center of the heating surface with a syringe; complete

evaporation time was measured using a stopwatch. The droplet temperature was equal to the

30

room temperature (30⁰C±5%) when it was dropped. The surface temperature was sensed by the

thermocouple, whose bead was located 3 mm beneath the center of the test surface and the digital

temperature reading was taken from the meter. Few numbers of observed phenomena during the

droplet evaporation was captured using a video camera. The droplet‟s initial diameter was

calculated from the total measured volume of 30 droplets at room temperature considering each

droplet to be a little sphere. To reduce error, this was done three times and the average diameter

was taken.

When the plate temperature reached at steady state the syringe was filled with liquid and

mounted. Bottom end of the syringe was pressed slowly and a droplet formed on the tip of the

needle of the syringe until the droplet weight becomes sufficient to detach from the tip. The

stopwatch was used to record the time of evaporation of droplets and its accuracy was 0.01sec. To

minimize the measured time error, three evaporation times were recorded for each temperature

and then averaged together. The experiment conducted for the test surface temperature with an

increment of 10⁰C up to ten surface temperature of 100⁰C and later the increment was changed to

25 ºC up to the test surface temperature 400⁰C.

31

CHAPTER

RESULTS AND DISCUSSIONS 5

5.1 Analysis of Theoretical model

Experimental droplet vaporization time (taken for complete evaporation) has been investigated

as a function of test surface temperature for four test metal surfaces, four different liquid and two

different droplet diameters (2.5mm and 2.75 mm). A numerous number of graphs have been

found within a temperature range from 60 to 400 oC. Resulting graphs are found to have shapes

just opposite of a typical boiling curve, as expected which is defined as the „Inverse Boiling

Curve‟ in the present study. It is because in typical boiling curve, heat flux is plotted as a

function of temperature difference. And in this experiment, evaporation time has been plotted as

a function of test surface temperature. The droplet getting higher heat flux will evaporate

quickly, and so the time and heat flux relationship is just opposite and it has become an evident

in the experimental graphs. Leidenfrost temperatures are easily determined from the graphs

where maximum vaporization time is required in the film boiling region. Based on the prescribed

model, a computer program has been generated. Theoretical Leidenfrost time has been estimated

from this program. For comparison purposes some experimental and theoretical (at Leidenfrost

point) times have been presented in graphs from Figs. 5.1-5.6. The lower temperature than the

Leidenfrost point in the boiling curve has not been included in the present model. This is because

the theory has been developed considering a stable vapor film beneath the liquid droplet. But,

before the Leidenfrost temperature, the film developed is not in a stable condition and gradually

increases in thickness of the vapor film with the increase in time up to Leidenfrost point.

32

Fig. 5.1 Experimental evaporation time and model predicted Leidenfrost time for small diameter

Methanol on Copper surface


Methanol on Aluminum surface

0

5

10

15

20

25

30

35

40

0 100 200 300 400

Vap

oriz

tion

tim

e (s

ec)

Temperature (⁰C)

Methanol (Small diameter) on Copper surface

Theoritical Experimental

MethanolCopper2.50 mm

0

5

10

15

20

25

0 100 200 300 400 500

Vap

oriz

tion

tim

e (s

ec)

Temperature (⁰C)

Methanol (Small diameter) on Aluminum surface


MethanolAluminum2.50 mm

33

Fig. 5.3 Experimental evaporation time and model predicted Leidenfrost time for large diameter

Methanol on Aluminum surface

Figure 5.1 shows experimental vaporization time of Methanol for do = 2.5 mm on copper surface

along with theoretical approximation of Leidenfrost time. The resulting graph with experimental

data has a shape just opposite of a typical boiling curve and the reason has been described earlier.

For surface temperature around 100 oC, the evaporation time is very small might be because of

nucleate boiling. With the increase of temperature, the vapor layer develops and the heat flux to

the droplet falls eventually. As a result, total vaporization time increases. It expresses the partial

film boiling (transition boiling from nucleate to stable film boiling) region (From temperature

about 100 to 175 oC). A stable vapor layer forms at around 175

oC and it is the Leidenfrost

temperature where the vaporization time is the maximum. After 175 oC, the radiation heat

transfer becomes dominating mode which increases the heat flux and decreases the total

vaporization time. So the region in the graph from 175 to about 400 oC is film boiling region.

The Leidenfrost time from experiment as shown in the Fig. 5.1 is around 33 sec whereas, this

value is about 17 sec as predicted from the analytical solution [Eqn. 21]. The theoretical value is

about 50% of the experimental one.

0

5

10

15

20

25

30

0 100 200 300 400

Vap

oriz

tion

tim

e (s

ec)

Temperature (⁰C)

Methanol (Large diameter) on Aluminum surface


MethanolAluminum2.75 mm

34

Figure 5.2 shows experimental vaporization time of Methanol for do = 2.5mm on Aluminum

surface along with the theoretical approximation of Leidenfrost time. The shape of the graph is

opposite to the shape of boiling curve as described earlier. Here the nucleate boiling region is

again at the vicinity of 100 oC. The region between 100 to 225

oC is partial film boiling region.

The Leidenfrost temperature here is around 225 oC. The graph between 225 to 400

oC shows the

film boiling region where radiation heat transfer is dominating. The Leidenfrost time from

experiment as shown in the Fig. 5.2 is around 22 sec whereas, this value is about 17 sec as

predicted from the analytical solution [Eqn. 21]. The theoretical value is about 80% of the

experimental one.

Figure 5.3 shows experimental vaporization time of Methanol for do = 2.75mm on Aluminum

surface along with theoretical approximation of Leidenfrost time. As shown in the Fig. 5.3, the

Leidenfrost temperature is here also 225oC. This reveals that the size of sessile drop does not

have any influence on Leidenfrost temperature (both are around 225 oC as shown in the Figs. 5.2

and 5.3) though it effects the Leidenfrost time (for do = 2.5mm, Leidenfrost time is about 22 sec

as shown in the Fig. 5.2 and for do = 2.75 mm Leidenfrost time is around 26 sec as shown in the

Fig. 5.3. The Leidenfrost time for larger droplet is more than that of smaller one. It is expected

because a larger droplet will require more heat and time to fully evaporate. The temperature

range for nucleate boiling, partial film boiling and film boiling for large diameter Methanol

droplet on Aluminum surface are almost same as those of small diameter Methanol droplet on

Aluminum surface as shown in Fig. 5.2. The Leidenfrost time as measured in the experiment (as

shown in the Fig. 5.3) is approximately 25 sec and on the other hand this value is around 20 sec

as predicted from the model [Eqn. 21]. The predicted value from the proposed model is around

80% of the experimental measured value.

If it is compared Figs. 5.1-5.3; Fig. 5.2 and 5.3 show a fair agreement between the Leidenfrost

time predicted from the proposed model and the experimental data. Figure 5.1 shows that the

agreement between the experimental Leidenfrost time and the theoretical Leidenfrost time is not

as good as compared to the other two as shown in the Figs. 5.2 and 5.3. It can be explained by

thermal conductivity of the test surface. Thermal conductivity of Copper is almost double than

that of Aluminum. A metal having higher thermal conductivity has higher capability to supply

intense heat to the liquid droplet on its surface. As a result a thicker vapor blanket will generate

35

instantly which will impede the conduction heat transfer to the liquid and in turn a higher

Leidenfrost time should be found. It is evident from Fig. 5.1. The Leidenfrost time for Methanol

on Copper surface (as shown in the Fig. 5.1) is more than the Leidenfrost time for the same

liquid and same droplet diameter on Aluminum surface (Fig. 5.2). For simplicity, thermal

conductivity of test metal surface has not been incorporated in present theoretical model. As a

result the experimental Leidenfrost time is higher than the theoretical prediction of the

Leidenfrost time on the copper surface. In future study, the solid surface material‟s conductivity

will be tried to include which will hope to more close agreement of the experimental data with

the model.


Ethanol on Brass surface

0

5

10

15

20

25

30

35

40

45

50

0 100 200 300 400

Vap

oriz

tion

tim

e (s

ec)

Temperature (⁰C)

Ethanol (Small diameter) on Brass surface


EthanolBrass2.50 mm

36

Fig. 5.5 Experimental evaporation time and model predicted Leidenfrost time for large diameter

Ethanol on Brass surface

Fig. 5.6 Experimental evaporation time and model predicted large diameter Leidenfrost time for

Ethanol on Mild steel surface

0

10

20

30

40

50

0 100 200 300 400

Vapo

riztio

n tim

e (s

ec)

Temperature (⁰C)

Ethanol (Large diameter) on Brass surface


EthanolBrass2.75 mm

0

5

10

15

20

25

30

35

0 100 200 300 400

Vap

oriz

tion

tim

e (s

ec)

Temperature (⁰C)

Ethanol (Large diameter) on Mild steel surface


EthanolMild stel2.75 mm

37

Figure 5.4 shows experimental vaporization time of Ethanol for do = 2.5 mm on Brass surface

along with theoretical approximation of Leidenfrost time. Leidenfrost temperature here is around

150 oC and the Leidenfrost time is about 43 sec for the experimental case and around 17 sec

predicted from the model. Figure 5.5 represents the experimental time of Ethanol for do = 2.75

mm on Brass surface along with the theoretical approximation of Leidenfrost time, the

Leidenfrost temperature here is around 150 oC. Here the experimental Leidenfrost time value is

more or less 46 sec and the predicted value is about 20 sec. Again it is an evident from these two

figures (Figs. 5.4-5.5) that droplet size does not have any influence on the Leidenfrost

temperature. Experimental Leidenfrost time as shown in the Fig. 5.4 is less than that of as shown

in the Fig. 5.5. This again depicts that the larger the droplet size, the larger the Leidenfrost time.

Figure 5.6 expresses comparison between experimental vaporization times of Ethanol with do =

2.75mm on Mild steel surface along with the theoretical approximation of Leidenfrost time. Here

the Leidenfrost temperature is about 175oC, the experimental Leidenfrost time is about 30 sec

and the predicted value is around 20 sec. For all the three conditions (Fig. 5.4-5.6), the deviations

of the model predicted time values from the experimental times vary from 40 to 65 %. Here,

among the three conditions (Figs. 5.4-5.6), the agreement for the Leidenfrost time between the

model predicted and the experimental is better for the case of mild steel as it has the lower

thermal conductivity.

Sessile drop evaporation on a hot metal surface is a very complex phenomenon. The droplet on

the hot metal surface goes through dancing and jumping or in another way touching and

detaching of the droplet on the metallic surface. When the vapor beneath the droplet makes

floating the droplet (due to reaction force of the vapor) on hot metallic surface, there forms a

vapor layer which results in drop of heat transfer. In this way, when the heat transfer reduces, the

vapor pressure no longer remains able to sustain the weight of the droplet on the solid surface.

Once the droplet touches the hot solid surface, a large amount of heat transfer occurs and the

vapor pressure again floats the droplet. So the heat transfer to the droplet occurs in an

interrupted way. This continues until the weight of the droplet is reduced due to evaporation and

it is then balanced by the vapor pressure beneath the droplet (vapor pressure is almost not

reducing practically because it may be assumed that the solid surface temperature remains more

or less constant during the evaporation of the droplet). It is to be mentioned here that the heat

capacity of the experimental solid block is infinite compared to liquid droplet. At Leidenfrost

38

temperature a stable vapor film is formed below the droplet. Based on this stable film layer,

present model has been developed. For simplicity of the model, the dancing and bouncing

phenomena have been discarded. The effect of radiation heat transfer has been successfully

inserted into the theory and has also been taken in account at the final calculation and the

theoretical approximation of Leidenfrost time has been found fair enough compared to the

experimental Leidenfrost time.

5.2 Analysis of Experimental data

The experimental total vaporization time results are shown in (Figure 5.7 to Figure 5.14). The

mean point are plotted and the range of experimental results. The temperature which gives

maximum evaporation time is presumed to be the minimum heat flux at which stable film boiling

can exist and is termed as Leidenfrost temperature. The Leidenfrost temperature is not a strong

function of size, as has been noted over a much wider size range.

In the present study, complete evaporation time of a sessile droplet of liquid as a function of test

surface temperature of four different materials for four different liquids with two different

droplet diameters are analyzed. A numerous number of graphs having different combinations are

obtained here due to involvement of various experimental parameters. The representative

characteristics among all the experimental conditions will be described here.

5.2.1 Liquid variation

In this experiment we have plotted evaporation time of different liquids on a specific metal

surface (Figure 5.7 to Figure 5.10). Different liquids on a specific metal surface took different

time to evaporate. The factors that affect the evaporation time of a liquid droplet are as follows

5.2.1.1 Effect of latent heat of vaporization

A liquid having a higher latent heat of vaporization should take more time to evaporate. This

phenomenon is verified in our experiment (Figure 5.7 to Figure 5.10). Water has the maximum

heat of vaporization compared to methanol and ethanol so it takes the highest time to evaporate

among the all liquids for different metal surfaces (Aluminum, Brass, Copper and Mild steel).

39

5.2.1.2 Effect of specific heat, thermal conductivity and density of liquid

Evaporation time and Leidenfrost point temperature of the liquid depends on the specific heat,

thermal conductivity and density of the liquid as shown in the model of Henry [17]. Higher the

specific heat, thermal conductivity and density of the liquid Leidenfrost temperature will also be

higher as we observe in the experiment (Figure 5.9). Droplet evaporation time is maximum for

copper and minimum for mild steel (Figure 5.8 and Figure 5.9).

5.2.1.3 Effect of boiling temperature of liquid

Evaporation time also depends on boiling temperature of the liquid. The liquid which has higher

boiling point will take more time to evaporate. In this experiment we observe this phenomenon

as water has highest boiling point (100⁰C) comparing to methanol (64.7⁰C) and ethanol (78.3⁰C)

so water takes highest time to evaporate (Figure 5.11 and Figure 5.13).

5.2.2 Diameter variation

For a specific liquid, larger diameter droplet should take more time to evaporate. This

phenomenon is verified in our experiment (Figure 5.7 to Figure 5.14). As diameter increases

volume and mass of the liquid also increases due to this total amount of heat required by larger

diameter liquid droplet to evaporate is higher than the smaller diameter liquid droplet. Although

the evaporation time for larger diameter liquid droplet is higher than smaller diameter liquid

droplet but Leidenfrost point temperature remain same for both diameters as Leidenfrost point

temperature is independent of diameter. This phenomenon has been also proved by experimental

data (as shown in Figure 5.7 to Figure 5.10).

40

(a)

(b)

Fig. 5.7 Comparison curve of Droplet Evaporation Time of Distill Water, NaCl solution, Methanol, Ethanol on Aluminum surface

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.50 mmAluminium:Dist water:Sd

Aluminium:NaCl sol:Sd

Aluminium:Ethanol:Sd

Aluminium:Methanol:Sd

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.75 mmAluminium:Dist water:Ld

Aluminium:NaCl sol:Ld

Aluminium:Ethanol:Ld

Aluminium:Methanol:Ld

41

Droplet evaporation time curve of water on Aluminum surface shows that the both droplet takes

maximum time to evaporate completely at a temperature of 200 ⁰C and corresponding time for

smaller diameter is around 55sec. The complete evaporation time for larger diameter droplet is

around 65 sec.

Droplet evaporation time curve of NaCl solution on Aluminum shows that the both droplet takes


smaller diameter droplet is around 45sec. The complete evaporation time for larger diameter

droplet is around 55 sec.

Droplet evaporation time curve of methanol on Aluminum shows that the both droplet takes




Droplet evaporation time curve of ethanol on Aluminum shows that the both droplet takes




42

(a)

(b)

Fig. 5.8 Comparison curve of Droplet Evaporation Time of Distill Water, NaCl solution, Methanol, Ethanol on Brass surface

0

20

40

60

80

100

120

140

0 100 200 300 400

Tim

e(s)

Temperature(°C)

Diameter: 2.50 mm Brass:Distill water:Sd

Brass:NaCl solution:Sd

Brass:Ethanol:Sd

Brass:Methanol:Sd

0

20

40

60

80

100

120

140

0 100 200 300 400

Tim

e(s)

Temperature(°C)

Diameter: 2.75 mm Brass:Distill water:Ld

Brass:NaCl solution:Ld

Brass:Ethanol:Ld

Brass:Methanol:Ld

43

Droplet evaporation time curve of water on Brass surface shows that the both droplet takes



around 120 sec.

Droplet evaporation time curve of NaCl solution on Brass shows that the both droplet takes




Droplet evaporation time curve of methanol on Brass shows that the both droplet takes maximum

time to evaporate completely at a temperature of 150 ⁰C and corresponding time for smaller

diameter droplet is around 40sec. The complete evaporation time for larger diameter droplet is

around 45 sec.

Droplet evaporation time curve of ethanol on Brass shows that the both droplet takes maximum



around 47sec.

(a)

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature (⁰C)

Diameter: 2.50 mm Copper:dist water sd

Copper:NaCl sol sd

Copper:Ethanol:sd

Copper:Methanol:sd

44

(b)

Fig. 5.9 Comparison curve of Droplet Evaporation Time of Distill Water, NaCl solution, Methanol, Ethanol on Copper surface

Droplet evaporation time curve of water on Copper surface shows that the both droplet takes



around 80 sec.

Droplet evaporation time curve of NaCl solution on Copper shows that the both droplet takes




Droplet evaporation time curve of methanol on Copper shows that the both droplet takes




Droplet evaporation time curve of ethanol on Copper shows that the both droplet takes maximum


0

20

40

60

80

100

120

0 100 200 300 400

Tim

e (s

)

Temperature( C)

Diameter: 2.75 mm Copper:Dist Water:Ld

Copper:NaCl sol:ld

Copper:Ethanol:Ld

Copper:Methanol:Ld

45


around 40 sec.

(a)

(b)

Fig. 5.10 Comparison curve of Droplet Evaporation Time of Distill Water, NaCl solution, Methanol, Ethanol on Mild steel surface

0

10

20

30

40

50

60

70

80

0 100 200 300 400

Tim

e(s)

Temperature(°C)

Diameter: 2.50 mmMild steel:Distill water:Sd

Mild steel:NaCl solution:Sd

Mild steel:Ethanol:Sd

Mild steel:Methanol:Sd

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400

Tim

e(s)

Temperature(°C)

Diameter: 2.75 mmMild steel:Distill water:Ld

Mild steel:NaCl solution:Ld

Mild steel:Ethanol:Ld

Mild steel:Methanol:Ld

46

Droplet evaporation time curve of water on Mild steel surface shows that the both droplet takes



around 55 sec.

Droplet evaporation time curve of NaCl solution on Mild steel shows that the both droplet takes




Droplet evaporation time curve of methanol on Mild steel shows that the both droplet takes




Droplet evaporation time curve of ethanol on Mild steel shows that the both droplet takes


smaller diameter droplet is around 25 sec. The complete evaporation time for larger diameter


5.2.3 Material variation

We kept the liquid fixed and changed the metal surfaces while plotting Fig. 5.11 to Fig. 5.14. For

each liquid, we have plotted the total droplet vaporization time as a function of surface

temperature of four different metal surfaces. We find a general trend that, vaporization time

required for a specific liquid at a specific temperature is different for different metal surfaces. It

happens due to different values of specific heat, thermal conductivity and density of the metal.

For all cases, according to the model of Henry [17] if specific heat, thermal conductivity and

density of metal is high Leidenfrost point temperature will be low.

From Fig. 5.9 and Fig. 5.10 we observe that Leidenfrost time for methanol on copper surface is

150°C and on mild steel surface is 200°C (as copper has the highest density and thermal

47

conductivity while mild steel has the lowest among these four metals). In this experiment, brass

takes the maximum time, then copper, aluminum and mild steel respectively. The effect of

diameter of liquid droplet is also verified from experimental results and graphs.

(a)

(b)

Fig. 5.11 Comparison of Droplet Evaporation Time of Distilled water on four different surfaces

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300 350 400

Tim

e(s

)

temperature(°C)

Diameter: 2.50mm Distilled water:copper:sd

Dist water:Mild steel:sd

Dis water:Aluminum:sd

Dist water:Brass:sd

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300 350 400

Tim

e(s

)

Temperature(℃)

Diameter: 2.75mm Dist water:copper:LD

Distwater:Mild steel:Ld

Dist water:Aluminum:Ld

Dist water:Brass:Ld

48

For both water droplets (small and large diameter) Figure 5.11(a-b) shows that, water droplet

evaporation time is maximum for Brass surface. Droplet evaporation time decreases in the order

of copper, aluminum and Mild steel. According to the model of Henry [17] if specific heat,

thermal conductivity and density of metal is high Leidenfrost point temperature will be low.

From Fig. 5.11 we observe that Leidenfrost temperature for distilled water on copper surface is

150°C and mild steel surface is 200°C (as copper has the highest density and thermal

conductivity while mild steel has the lowest among these four metals).

(a)

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.50mmNaCl sol:copper:sd

NaCl sol:Mild steel:sd

NaCl sol:Aluminum:sd

NaCl sol:Brass:Sd

49

(b)

Fig. 5.12 Comparison of Droplet Evaporation Time of NaCl solution on four different metal surfaces

For both NaCl solution droplets (small and large diameter) Figure 5.12(a-b) shows that, NaCl

solution droplet evaporation time is maximum for Brass surface. Droplet evaporation time

decreases in the order of copper, aluminum and Mild steel. From Figure 5.12(a-b) we observe

that Leidenfrost temperature for NaCl solution on copper surface is 200°C and mild steel surface

is 275°C (as copper has the highest density and thermal conductivity while mild steel has the

lowest among these four metals).

0

20

40

60

80

100

120

140

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.75mmNaCl sol:copper:Ld

NaCl:Mild steel:Ld

NaCl sol:Aluminum:Ld

NaCl sol:Brass:Ld

50

(a)

(b)

Fig. 5.13 Comparison of Droplet Evaporation Time of Methanol on four different surfaces

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.50mm

Methanol:Copper:sd

Methanol:Mild steel:sd

Methanol:Aluminum:sd

Methanol:Brass:sd

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.75mmMethanol:Copper:Ld

Methanol:Mild steel:Ld

Methanol:Aluminum:Ld

Methanol:Brass:Ld

51

For both Methanol droplets (small and large diameter) Figure 5.13(a-b) shows that, Methanol

droplet evaporation time is maximum for Brass surface. Droplet evaporation time decreases in

the order of copper, aluminum and Mild steel. From Figure 5.13(a-b) we observe that

Leidenfrost temperature for methanol on copper surface is 175°C and mild steel surface is 200°C

(as copper has the highest density and thermal conductivity while mild steel has the lowest

among these four metals).

(a)

(b)

Fig. 5.14 Comparison of Droplet Evaporation Time of Ethanol on four different surfaces

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.50 mmEthanol:copper:Sd

Ethanol:Mild steel:sd

Ethanol:Aluminum:sd

Ethanol:Brass:sd

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(℃)

Diameter: 2.75mmEthanol:copper:Ld

Ethanol:Mild steel:Ld

Ethanol:Aluminum:Ld

Ethanol:Brass:Ld

52

For both Ethanol droplets (small and large diameter) Figure 5.14(a-b) shows that, Ethanol

droplet evaporation time is maximum for Brass surface. Droplet evaporation time decreases for

copper, aluminum and Mild steel respectively. From Figure 5.14(a-b) we observe that both for

copper and mild steel surfaces Leidenfrost temperature of ethanol is identical and its value is

175⁰C.

Leidenfrost temperature values were obtain for water, NaCl solution, methanol and ethanol on

aluminum, copper, brass and mild steel surface. The Leidenfrost temperature is nearly identical

for aluminum, brass and mild steel surfaces but is slightly higher for the copper surface

[Bernardin and Mudawar, 1999]. The higher Leidenfrost value of copper surface is speculated to

be the result of surface roughening which accompanied large amounts of surface oxidation

during heating. The higher drop evaporation value of copper surface is speculated to be the result

of higher conductivity than other metal. Higher conductivity means higher heat transfer through

the metal. It means, when liquid touch the metal, large amount vapor will produce due to higher

heat transfer rate and surface is completely covered by a vapor blanket and then heat transfer

from the surface to the liquid occurs by conduction through vapor. Droplet was supported by the

vapor film slowly boil away.

5.3 Experimental boiling curve

Boiling curve of water, methanol and ethanol on four metal surfaces (aluminum, brass, copper,

mild Steel) as a function of test surface temperature are presented in Figure 5.15 to Figure 5.17.

Michiyoshi, Makino [16] have simplified the time averaged heat flux based on the theory of

Baumeister et. al [4]. Combining heat balance and time averaged heat transfer coefficient, time

averaged heat flux can be determined. According to Baumeister et al. [4] heat transfer coefficient

is

α= 1.1×1.5(𝐾𝑣

3𝜌𝑙𝜌𝑣 𝑕∗𝑔

µ𝑣𝑉13∆𝑇

)1

4 (5.22)

Here, h*= 𝑕𝑔 [1 + (7

20)𝐶𝑝(

∆𝑇

𝑕𝑔)]−3

53

From the heat balance the following equation can be obtained,

𝜌𝑙 𝑕𝑔 𝑑𝑉

𝑑𝑡= α (V) A (V) ∆T (5.23)

The resulting equation for the time averaged heat flux is

q= 1.5

τ×

ρl hg

1.813× 3 × Vo

1

3 (5.24)

By inserting complete droplet evaporation time in Eqn (5.24), heat flux is determined and by

plotting this heat flux with respect to surface temperature boiling curve is obtained.

5.3.1 Experimental Boiling curve of water

By using Eqn (5.24), heat flux during sessile drop evaporation has been estimated as shown in the

Figure 5.15(a-b) (for all the experimental conditions, the working pressure remain constant as of

atmospheric pressure. The experiments were started from 60⁰C of test surface for all the cases and the

experiment were conducted up to 400⁰C. Depends on the wall superheat (=surface temperature˗ liquid

saturation temperature) different mode of heat transfer could be obtained.

(a)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 50 100 150 200 250 300 350 400 450

Hea

t fl

ux

(W/m

2)

Surface Temperature (⁰C)

Boiling curve of distilled water(diameter: 2.50mm)

ALUMINUM

BRASS

COPPER

MILD STEEL

54

(b)

Fig. 5.15 Boiling curve of Water on different material surfaces

Immediate after the 60⁰C of test surface temperature and before 100⁰C, convection boiling can

be predicted as the dominating mode of heat transfer for water evaporation as shown in Figure

5.15(a-b). Above 100⁰C of test surface temperature, nucleate boiling becomes the dominating

mode and consequently sharp increase of heat flux is observed for all the materials (aluminum,

brass, copper and mild steel). At around 105-130⁰C (5-30⁰C of wall superheat for water) the heat

flux reaches the maximum value (it is defined as critical heat flux).

In the transition boiling region all curves deviates from each other. This can be explained by

considering thermal diffusivity. We consider the two cases mild steel and copper as the former

has lowest thermal diffusivity and the later one has the maximum thermal diffusivity.

The film boiling region starts at the Leidenfrost point temperature; at this point heat flux is

minimum. Above this temperature heat flux increases as radiation heat transfer gradually

dominates, this is true for all liquids for different material surface. If the thermal diffusivity of

1.E+04

1.E+05

1.E+06

1.E+07

0 100 200 300 400

Hea

t flu

x (W

/m2)

Temperature(⁰C)

Boiling curve of water (diameter: 2.75 mm)

Aluminum

Brass

Copper

Mild Steel

55

the material is high Leidenfrost point temperature TL will start at low ∆T. Leidenfrost point

temperature depends on material. The higher the thermal diffusivity of material lower the

Leidenfrost temperature which has already established in our experimental graph. We have

noticed in our experimental graph that the Leidenfrost point temperature of higher thermal

diffusivity material (copper, aluminum) is lower and ranging between 200-225⁰C, and for lower

thermal diffusivity material (mild steel) is higher (>225⁰C).

5.3.2 Experimental Boiling curve of methanol

(a)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 50 100 150 200 250 300 350 400 450

Hea

t fl

ux

(W/m

2)


Boiling curve of methanol(diameter: 2.50mm)

ALUMINUM

BRASS

COPPER

MILD STEEL

56

(b)

Fig.5.16 Boiling curve of Methanol on different material surfaces

In the nucleate boiling region Figure 5.16(a-b) we find that the curve linearly increases for all the

material and they almost merges (not perfectly) to each other. The maximum heat flux is

obtained at a temperature above 25-40⁰C above the saturation temperature. Material with higher

thermal diffusivity has critical heat flux (CHF) at lower surface temperature (for copper ~90⁰C),

similarly material with lower thermal diffusivity has CHF at higher surface temperature (for

Mild steel ~100⁰C). CHF is maximum for mild steel surface and the numerical value is

approximately 15.26 MW/𝑚2.

In the transition boiling region all curves deviates from each other. This can be explained by

considering thermal diffusivity. We consider the two cases mild steel and copper as the former

has lowest thermal diffusivity and the later one has the maximum thermal diffusivity. The curve

for mild steel deviates at higher ∆T ranges than for copper plate.

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 100 200 300 400

Hea

t flu

x(W

/m2

)

Temperature(⁰C)

Boiling Curve of Methanol(diameter: 2.75 mm)

Aluminum

Brass

Copper

Mild Steel

57

The film boiling region starts at the point where heat flux is minimum is known as Leidenfrost

point temperature. Above this temperature heat flux also increases as radiation heat flux

gradually dominates, this is true for all liquids for different material. The higher the thermal

diffusivity the lower ∆T at TL . We know that Leidenfrost point temperature depends on material

surface. The higher the thermal diffusivity of material lower the Leidenfrost temperature which

has been also established in our experimental graph. We noticed in our experimental graph that

Leidenfrost point temperature of higher thermal diffusivity material (such as copper) is lower

and ranging between 175-200⁰C, and for lower thermal diffusivity material (such as mild steel)

is higher (200-225⁰C).

5.3.3 Experimental Boiling curve of ethanol

(a)

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 50 100 150 200 250 300 350 400 450

Hea

t fl

ux

(W/m

2)


Boiling curve of ethanol(diameter : 2.50 mm)ALUMINUM

BRASS

COPPER

MILD STEEL

58

(b)

Fig. 5.17 Boiling curve of Ethanol on different material surfaces

Starting at the nucleate boiling region we find that the curve Figure 5.17(a-b) linearly increases

for all the material and they almost merges to each other. The maximum heat flux (CHF) is

obtained at a temperature above 20-30⁰C above the saturation temperature. CHF is maximum for

mild steel surface and the numerical value is approximately 10.55 MW/𝑚2.

In the transition boiling region all curves deviates from each other as happen in the previous

cases. This can be explained by considering thermal diffusivity. Considering two cases mild steel

and copper as the former has lowest thermal diffusivity and the later one has the maximum

thermal diffusivity. The curve for mild steel deviates at higher ∆T ranges than for copper plate.

The film boiling region starts at the Leidenfrost point temperature; at this point heat flux is

minimum. Above this temperature heat flux also increases as radiation heat flux gradually

dominates, this is true for all liquids for different material surface. The higher the thermal

diffusivity the lower ∆T at TL .Leidenfrost point temperature depends on material. The higher the

thermal diffusivity of material lowers the Leidenfrost temperature which has been also

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

0 100 200 300 400

Hea

tflu

x(W

/m2

)

Temperature(⁰C)

Boiling Curve of Ethanol(diameter: 2.75 mm)

Aluminum

Brass

Copper

Mild Steel

59

established in our experimental graph. We noticed in our graph that Leidenfrost point

temperature of higher thermal diffusivity material is lower and ranging between175-200⁰C, and

for lower thermal diffusivity material is higher (200-225⁰C).

5.4 Inverse boiling curve

In this experiment we have plotted evaporation time versus metal surface temperature thus we

have obtained curves (Figure 5.7 to Figure 5.10) which is inverse of boiling curve may be called

as inverse boiling curve. A typical inverse boiling curve Figure 5.18 is classified into four

regimes film evaporation, nucleate boiling, transition boiling and film boiling.

Fig. 5.18 Schematic of a typical Inverse boiling curve and boiling curve of a Liquid

The region a-b is known as film evaporation region which is below the saturation temperature of

liquid. As point „b’ is the saturation temperature, below this temperature there is no boiling,

Tim

e / H

eat

flux

Surface temperature( C)

Typical inverse boiling and boiling curve

Inverse boiling

curve

Boiling curvea

b

c

d

60

liquid droplet evaporates at atmospheric pressure. Gradually less time required for boiling when

the temperature approaches to the saturation point. This is due to the increase in heat flux as

temperature increases. The trend of the graph in this region is downward as shown in Figure 18.

The region b-c is known as nucleate boiling region. This region starts from saturation point up to

the point at which heat flux is maximum. As the surface temperature is increasing above

saturation point heat flux also increases due to the combined effect of liquid entrainment and

evaporation. In this region evaporation time gradually decreases and reaches a minimum value at

CHF (critical heat flux). This region is the most desirable region in boiling phenomenon.

The region c-d is transition boiling region also known as unstable film boiling. In this region heat

flux decreases for further increase in temperature due to the large fraction of heater surface is

covered by vapor film. As heat flux in this region in decreasing order so evaporation time must

be in increasing order which has been already established by experimental data.

The region above d is known as film boiling region. The point „d‟ is known as Leidenfrost point

at which heat flux is minimum. At this point metal surface is completely covered by vapor film.

As heat flux at this point is minimum so evaporation time at this point is maximum which is

undesirable. So during boiling this point must be avoided. Above point d heat flux is increasing

as the surface temperature is increasing. The heat transfer rate increases with increasing excess

temperature above saturation point as a result of heat transfer from the heated surface to the

liquid through the vapor film by radiation heat transfer which become significant at higher

temperature.

In our experimental curve (which is similar to Figure 5.18), we notice that from saturation

temperature up to temperature at which heat flux is maximum, the required vaporization

decreases. This happens due to the less vapor bubble or absence of vapor film under the droplet.

So, the total heat is transferred to the droplet from the hot metal surface by conduction. As the

temperature increases, a vapor layer is formed beneath the droplet and increases in thickness and

consequently the vaporization time also increases. This happens up to the Leidenfrost point. At

Leidenfrost point, the film thickness reaches to its maximum value and this lessens the

conductive heat transfer rate to its minimum value. So the time required for vaporization reaches

to its maximum value. After this point radiation heat transfer starts to dominate which gradually

decrease the vaporization time as heat flux increases.

61

5.5 Engineering Correlation of experimental data

The theoretical development in reference [2] is purely analytical. It does not require any

experimental data (except physical properties) in the prediction for droplet evaporation time. Due

to the complicated iterative computations to obtain the correct values for droplet evaporation

time, it is necessary in engineering calculations relatively simple equation which would imply

the correct functional dependence upon variables and allow a prediction for droplet evaporation

time without any time consuming iteration. In order to obtain such an empirical correlation of the

experimental data, a functional equation between the dependent variables and the independent

variables must be obtained.

From the theoretical development, we find in reference [2] that heat is transferred from the plate

to the droplet by conduction and radiation, neither one of which may be neglected in general.

The evaporation rate per unit area for a spherical droplet is on the order of L 𝑟𝑜/𝜏 and this

quantity is equal to the sum of the heat transferred by conduction and radiation divided by .

Functional arguments are developed in detail in reference [18], but the resulting equation is

𝜌𝑙𝑟𝑜

𝜏 = 1C [

𝑘∆𝑇𝑟𝑜𝑔𝜌𝑣(𝜌𝑙−𝜌𝑣)

µ𝑣𝜆 ′]

1

2 + 2C [𝜍𝜖𝑝 𝑇𝑝

4−𝑇𝑠4

𝜆 ′] ……………………….. (25)

Where, 1C and 2C are constants to be evaluated from the experimental data.

The first and second part of the above equation represents the conduction and radiation heat

transfer respectively.

62

5.5.1 Experimental Correlation for Aluminum

(a)

(b)

Fig. 5.19 Empirical correlation of total evaporation time for Aluminum surface

0 0.02 0.04 0.06 0.08 0.1 0.120

0.02

0.04

0.06

0.08

0.1

0.12

Obseved value

Calc

ula

ted v

alu

e

Correlation curve for Aluminum(Diameter 2.50 mm)

water

methanol

ethanol

equation

0 0.02 0.04 0.06 0.08 0.1 0.120

0.02

0.04

0.06

0.08

0.1

0.12

Obseved value

Calc

ula

ted v

alu

e

Correlation curve for Aluminum(diameter: 2.75 mm)

water

methanol

ethanol

equation

63

In both cases, twenty three data points representing the full range of experimental condition were

selected for aluminum and used to calculate C1 and C2 by least squares fitting. The resulting

correlation for four liquids on aluminum is-

𝜌 𝑙𝑟𝑜

𝜏 = 0.0206[

𝑘∆𝑇𝑟𝑜𝑔𝜌𝑣(𝜌 𝑙−𝜌𝑣)

µ𝑣𝜆 ′]

1

2 +1215 [𝜍𝜖𝑝 𝑇𝑝

4−𝑇𝑠4

𝜆 ′] ………………… (26)

5.5.2 Experimental Correlation for Brass

(a)

(b)

Fig. 5.20 Empirical correlation of total evaporation time for Brass surface

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Obseved value

Cal

cula

ted

valu

e

Correlation curve for Brass(Diameter 2.50 mm)

water

methanol

ethanol

equation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Obseved value

Cal

cula

ted

valu

e

Correlation curve for Brass(Diameter 2.75 mm)

water

methanol

ethanol

equation

64

In both cases, twenty seven data points representing the full range of experimental condition

were selected for brass and used to calculate C1 and C2 by least squares fitting (Fig. 5.13). The

resulting correlation for four liquids on brass is-

𝜌 𝑙𝑟𝑜

𝜏 = 0.0169[


µ𝑣𝜆 ′]

1

2 + 500[𝜍𝜖𝑝 𝑇𝑝

4−𝑇𝑠4

𝜆 ′] ………………… (27)

5.5.2 Experimental Correlation for Copper

(a)

(b)

Fig. 5.21 Empirical correlation of total evaporation time for Copper surface

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Obseved value

Cal

cula

ted

valu

e

Correlation curve for Copper( Diameter 2.50 mm)

water

methanol

ethanol

equation

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

Obseved value

Cal

cula

ted

valu

e

Correlation curve for Copper(Diameter: 2.75 mm)

water

methanol

ethanol

equation

65

Twenty five data points representing the full range of experimental condition were selected for

copper and used to calculate C1 and C2 by least squares fitting (Fig. 5.12). The resulting

correlation for four liquids on copper is-

𝜌 𝑙𝑟𝑜

𝜏 = 0.0160[


µ𝑣𝜆 ′]

1

2 + 1170[𝜍𝜖𝑝 𝑇𝑝

4−𝑇𝑠4

𝜆 ′] ………………… (28)

5.5.3 Experimental Correlation for Mild Steel

(a)

(b)

Fig. 5.22 Empirical correlation of total evaporation time for Mild steel surface

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.20

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Obseved value

Calc

ula

ted v

alu

e

Correlation curve for Mild Steel(Diameter 2.50 mm)

water

methanol

ethanol

equation

0 0.02 0.04 0.06 0.08 0.1 0.120

0.02

0.04

0.06

0.08

0.1

0.12

Obseved value

Cal

cula

ted

valu

e

Correlation curve for Mild Steel(diameter: 2.75 mm)

water

methanol

ethanol

equation

66

In both cases, twenty three data points representing the full range of experimental condition were

selected for mild steel and used to calculate C1 and C2 by least squares fitting. The resulting

correlation for four liquids on mild steel is-

𝜌 𝑙𝑟𝑜

𝜏 = 0.0158 [


µ𝑣𝜆 ′]

1

2 + 1440[𝜍𝜖𝑝 𝑇𝑝

4−𝑇𝑠4

𝜆 ′] ………………… (29)

5.6 Comparison of Theoretical and Experimental Result

Finally a comparison has been made for surface temperature above the Leidenfrost point

between data points obtained from correlation and data points obtained from experiment. This

comparison has been shown by plotting curve (Fig. 5.14 and Fig. 5.15). Correlated Equations

(Eqn 26 to Eqn 29) give very accurate time ranging maximum error limit 20 percents, in most of

the cases less than 10 percents.

5.6.1 Comparison curve for distilled water on different metal surfaces

(a)

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.50 mmCorrelation: Al-dist water

Experimental: Al-dist water

67

(b)

Fig. 5.23 Comparison graph of total evaporation time (τ) with surface temperature (𝑇𝑠) of water

on Aluminum surface

(a)

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.75 mmCorrelation: Al-dist water

Experimental: Al-dist water

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Brass -Dist waterExperimental: Brass-Dist water

68

(b)


on Brass surface

(a)

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Brass -Dist waterExperimental: Brass-Dist water

0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.50 mmCorrelation: Copper -Dist waterExperimental: Copper-Dist water

69

(b)

Fig. 5.25 Comparison graph for total evaporation time (τ) with surface temperature (𝑇𝑠) of Water

on Copper surface

(a)

0102030405060708090

100

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.75 mmCorrelation: Copper -Dist waterExperimental: Copper-Dist water

0

10

20

30

40

50

60

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Steel -Dist water

Experimental: Steel-Dist water

70

(b)


on Mild steel surface

Comparison curves above the Leidenfrost point for distilled water on four different material

surfaces (Aluminum, Brass, Copper and Mild steel) have shown in Figure 5.23 to Figure 5.26.

Above the Leidenfrost point experimental data and correlated data are well matched as shown in

Figure 5.23 to Figure 5.26. For Aluminum and Brass, variation between experimental data and

correlated data are 10% in both cases above the transition region. For Copper, variation between

experimental data and correlated data are 15% in both cases above the transition region. But for

Mild steel variation is higher than other three metal surfaces and it is within 20%.

0

10

20

30

40

50

60

70

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Steel -Dist water

Experimental: Steel-Dist water

71

5.6.2 Comparison curve for methanol on different metal surfaces

(a)

(b)

Fig. 5.27 Comparison graph of total evaporation time (τ) with surface temperature (𝑇𝑠) of

methanol on Aluminum surface

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.50 mmCorrelation: Al-methanol

Experimental: Al-methanol

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.75 mmCorrelation: Al-methanolExperimental: Al-methanol

72

(a)

(b)


methanol on Brass surface

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Brass -MethanolExperimental: Brass -Methanol

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Brass -Methanol

Experimental: Brass -Methanol

73

(a)

(b)


Methanol on Copper surface

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.50 mmCorrelation: Copper -Methanol

Experimental: Copper -Methanol

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.75 mm

Correlation: Copper -MethanolExperimental: Copper -Methanol

74

(a)

(b)

Fig. 5.30 Comparison graph of total evaporation time (τ) with surface temperature (𝑇𝑠) of methanol on

Mild steel surface

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Steel - Methanol

Experimental: Steel -Methanol

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Steel - Methanol

Experimental: Steel -Methanol

75

Comparison curves above the Leidenfrost point for methanol on four different material surfaces

(Aluminum, Brass, Copper and Mild steel) have shown in Figure 5.27 to Figure 5.30. Above the

Leidenfrost point experimental data and correlated data are well matched as shown in Figure

5.27 to Figure 5.30. For Aluminum and Brass, variation between experimental data and

correlated data are within10% in both cases above the transition region which is similar to

distilled water. For Copper and Mild steel, variation between experimental data and correlated

data are 15% in both cases above the transition region. Above Leidenfrost point as temperature

increases accuracy for both Copper and Mild steel increase.

5.6.3 Comparison curve for ethanol on different metal surfaces

(a)

0

5

10

15

20

25

30

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.50 mmCorrelation: Al-ethanol

Experimental: Al-Ethanol

76

(b)


ethanol on Aluminum surface

(a)

0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300 350 400 450

Tim

e(s)

Temperature(°C)

Diameter: 2.75 mmCorrelation: Al-ethanolExperimental: Al-Ethanol

0

5

10

15

20

25

30

35

40

45

50

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Brass -EthanolExperimental: Brass -Ethanol

77

(b)


ethanol on Brass surface.

(a)

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Brass -Ethanol

Experimental: Brass -Ethanol

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.50 mmCorrelation: Copper -EthanolExperimental: Copper -Ethanol

78

(b)


ethanol on Copper surface.

(a)

0

5

10

15

20

25

30

35

40

45

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(ᵒC)

Diameter: 2.75 mmCorrelation: Copper -EthanolExperimental: Copper -Ethanol

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.50 mmCorrelation: Steel -Ethanol

Experimental: Steel -Ethanol

79

(b)


ethanol on Mild steel surface.

Comparison curves above the Leidenfrost point for ethanol on four different material surfaces

(Aluminum, Brass, Copper and Mild steel) have shown in Figure 5.31 to Figure 5.34. Above the

Leidenfrost point experimental data and correlated data are well matched as shown in Figure

5.31 to Figure 5.34. For Aluminum, Brass and Copper, variation between experimental data and

correlated data are within 5% in all cases above the transition region. For Mild steel, variation

between experimental data and correlated data are within 10% above the transition region.

Above Leidenfrost point as temperature increases accuracy for all metal surfaces increases.

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300 350 400

Tim

e(s)

Temperature(⁰C)

Diameter: 2.75 mmCorrelation: Steel -Ethanol

Experimental: Steel -Ethanol

80

CHAPTER

CONCLUSIONS 6

6.1 Conclusions

Leidenfrost phenomenon is a very complex matter due to involvement of numerous numbers of

physical parameters. This makes the analysis of the most intrinsic details difficult. Here a model

has been proposed and verified with experimental results. From the experimental results, several

key conclusions concerning the influential parameters (Leidenfrost Temperature) can be drawn.

The fundamental understandings are summarized below:

1. The major contribution to the heat transfer is the conductive and radiative mode.

Conduction heat transfer mode is dominant below the Leidenfrost point and radiation

heat transfer becomes dominant above the Leidenfrost point.

2. Radiation heat transfer has been successfully included in the theoretical model and using

an iterative computer program, radiation effects on the droplet evaporation time has been

incorporated.

3. A stable layer of vapor has been considered beneath the droplet and the weight of the

droplet is balanced with the pressure beneath the droplet.

4. Size of droplet has been found to have no influence on the Leidenfrost temperature.

5. Data are well correlated, allowing prediction of total vaporization time to within ±20

percent. The comparison has been made between actual graph obtain in the experiments

and those obtained by correlation.

6. The heat flux is inversely proportional to the evaporation time. Heat flux increases after

the Leidenfrost point so evaporation time decreases.

81

7. The experimental curve (evaporation time versus temperature) curve is opposite to

boiling curve as heat flux is inversely related to the evaporation time.

8. Droplet size has been found to influence the Leidenfrost time. The larger the droplet size;

the higher is the total evaporation time.

6.2 Further Work

In this science era, faster growing technology promotes mankind to augment their standard of

living. The prerequisite for this technological development is the research and development in

the sector of science and technology. Human beings are eagerly waiting for the latest invention

which leads to the consequence that research and development are an endless job. In this context,

the research work delineated in this dissertation may serve as a primary foundation for some of

the phenomena which will lead to some future study :

1. The Leidenfrost phenomenon for two-component solutions.

2. The Leidenfrost phenomenon for cryogenic fluids.

3. The Leidenfrost phenomenon for various liquids on composite material.

4. The role played by heating surface conditions at the Leidenfrost point.

5.3 Recommendations

1. Instead of the four fluids used in the experiment other fluids can be chosen having

larger specific heat.

2. Detailed theoretical and experimental studies are needed to accurately predict the

behavior of the Leidenfrost Temperature.

82

3. During the evaporation period droplet always vibrated a little at their fundamental

frequency. In order to increase the accuracy this oscillation phenomenon should take in to

account.

4. Instead of 25˚C, temperature should be increased by 5˚C during the experiment for

accurate prediction of droplet evaporation time.

5. If the surface roughness of the metal is changed, detail behavior of the Leidenfrost

Temperature will be obtained.

83

REFERENCES

[1] J. G. Leidenfrost, De Aquae Communis Nonnullis Qualitatibus Tractatus, (A Tract About

Some Qualities of Common Water), Duisburg on Rhine (1756)

[2] B.S. Gottfried, C.J. Lee and K.J. Bell, The leidenfrost phenomenon: film boiling of liquid

droplets on a flat plate, International Journal of Heat and Mass Transfer, Volume 9, Issue 11,

November 1966, pp. 1167-1188

[3] Victor Starov and Khellil Sefiane, On evaporation rate and interfacial temperature of volatile

sessile drops, Colloids and Surfaces A: Physicochemical and Engineering Aspects, Volume 333,

Issues 1-3, 5 February 2009, pp.170-174

[4] Baumeister, K. J., Hamill, T. D., Schoessow, G. J., Schwartz, F. L., Film boiling heat transfer

to water drops on a flat plate, Jan 1, 1965 ,Technical report, NASA-TM-X-52103

[5] D. Chatzikyriakou, S.P. Walker, G.F. Hewitt, C. Narayanan and D. Lakehal, Comparison of

measured and modeled droplet–hot wall interactions, Applied Thermal Engineering, Volume 29,

Issue 7, May 2009, pp. 1398-1405

[6] L. H. J. Wachters, H. Bonne and H. J. van Nouhuis, The heat transfer from a hot horizontal

plate to sessile water drops in the spheroidal state, Chemical Engineering Science, Volume 21,

Issue 10, October 1966, pp. 923-936

[7] Heng Xie, Zhiwei Zhou, A model for droplet evaporation near Leidenfrost point, Technical

Note, International Journal of Heat and Mass Transfer, Volume 50, Issues 25-26, December

2007, pp. 5328-5333

[8] Elyssa F. Crafton, W. Z. Black, “Heat transfer and evaporation rates of small liquid droplets

on heated horizontal surfaces”, International Journal of Heat and Mass Transfer, Volume 47,

Issues 6-7, March 2004, pp. 1187-1200

84

[9] T. K. Nguyen, C. T. Avedisian, Numerical solution for film evaporation of a spherical liquid

droplet on an isothermal and adiabatic surface, International Journal of Heat and Mass Transfer,

Volume 30, Issue 7, July 1987, pp. 1497-1509

[10] K.E. Nicholds, Leidenfrost, Cryogenics, Volume 10, Issue 1, February 1970, pp. 45-47

[11] George S. Emmerson, The effect of pressure and surface material on the leidenfrost point of

discrete drops of water, International Journal of Heat and Mass Transfer, Volume 18, Issue 3,

March 1975, pp. 381-386

[12] J. Kistemaker, The spheroidal state of a waterdrop: The leidenfrost phenomenon, Physica,

Volume 29, Issue 2, February 1963, pp. 96-104

[13] Shi-Chune Yao, and Kang Yuan Cai, The dynamics and leidenfrost temperature of drops

impacting on a hot surface at small angles, Experimental Thermal and Fluid Science, Volume 1,

Issue 4, October 1988, pp. 363-371

[14] Niroh Nagai, Shigefumi Nishio, Leidenfrost temperature on an extremely smooth surface,

Experimental Thermal and Fluid Science, Volume 12, Issue 3, April 1996, pp. 373-379

[15] J. P. Holman, Heat Transfer, 8th

Edition, McGraw-Hill, INC., International Edition 1997,

Chapter 8, pp. 405 -413

[16] I. Michiyoshi, K. Makino, “Heat transfer characteristics of evaporation of liquid droplet on

heated surfaces”, Int. J. Heat Mass Transfer, Vol. 21, pp 605-613

[17] Henry, R. E. [1974], “A Correlation for the Minimum Film Boiling Temperature”, Chem.

Eng. Prog. Symp. Ser 70, 81–90.

[18] C. J. Lee, “A Theoretical and. Experimental Investigation of the Leidenfrost Phenomenon

for Small. Droplets.”Ph.D. Thesis, Oklahoma State University (1965).

[19] Hosler, E. R., and Westwater, J. W., "Film Boiling on a Horizontal Plate," ARS J., April

1962, pp. 553-558.

[20] Wachters, L. H. J., H. Bonne, and H. J. van Nouhuis, Chem. Eng. Sci., 21, 923-936 (1966).

85

APPENDICES

86

APPENDIX

SATURATION POROPERTIES A

OF LIQUID

A.1 Saturation Properties of Methanol

Chemical formula CH3OH

Molecular weight 32.00

Critical temperature 513.15 K

Critical Pressure 7950 kPa

Critical density 275 kg/m3

Table A.1 Saturation properties of methanol

87

A.2 Saturation Properties of Ethanol

Chemical formula CH3CH2OH


Critical temperature 516.25K

Critical Pressure 6390 kPa

Critical density 280 kg/m3

Table A.2 Saturation properties of ethanol

88

A.3 Saturation Properties of Water

Chemical formula H2O


Critical temperature 647.3 K

Critical Pressure 22,129 kPa

Critical density 351kg/m3

Table A.3 Saturation properties of water

89

APPENDIX

EXPERIMENTAL DATA B

Table B.1 Evaporation time of Distilled water on Aluminum Surface

Temperature(⁰C) Small diameter Large diameter

t1 t2 t3 𝑡𝑎𝑣𝑔 t1 t2 t3 𝑡𝑎𝑣𝑔

70 73.24 73.05 71.10 72.46 108.2 107.10 110.20 108.50

80 69.21 68.94 67.52 68.56 75.12 77.31 78.22 76.88

90 43.42 44.23 45.12 44.26 58.19 59.22 59.39 58.93

100 17.85 16.09 17.56 17.17 17.12 18.97 18.25 18.11

125 0.47 0.47 0.45 0.46 1.37 1.30 1.25 1.31

150 1.57 1.90 1.65 1.71 2.11 2.36 2.21 2.23

175 22.40 23.50 22.9 22.93 26.32 25.38 25.91 25.87

200 55.89 56.70 56.30 56.29 65.84 67.21 66.81 66.62

225 55.81 55.10 55.09 55.33 67.52 67.19 67.92 67.54

250 51.39 47.89 53.95 51.08 58.12 63.29 60.22 60.54

275 46.99 47.19 45.64 46.61 56.21 59.99 60.19 58.80

300 42.29 41.49 37.54 40.44 49.87 51.58 52.81 51.42

325 38.12 35.23 36.45 36.6 44.52 48.15 43.25 45.31

350 32.99 31.59 34.69 33.09 42.91 40.92 39.86 41.23

375 29.98 31.01 32.80 31.26 41.12 37.92 38.82 39.29

400 30.04 29.14 28.34 29.17 36.21 34.06 33.82 34.70

t1, t2, t3= Droplet evaporation time

𝑡𝑎𝑣𝑔 = Average value of t1, t2 and t3

90

Table B.2 Evaporation time of NaCl Solution on Aluminum Surface

Temperature(C) Small diameter Large diameter


70 108.60 104.90 107.10 106.86 132.19 128.98 129.54 130.24

80 69.23 70.64 70.21 70.03 86.21 84.34 90.61 87.05

90 45.81 51.23 50.19 49.08 61.42 58.23 57.19 58.95

100 27.98 28.86 29.68 28.84 33.78 34.91 34.31 34.33

125 0.51 0.48 0.42 0.47 0.50 0.47 0.44 0.47

150 0.75 0.97 0.61 0.78 1.22 1.07 1.1 1.13

175 23.05 22.89 22.95 22.96 23.21 24.12 21.84 23.06

200 40.15 40.56 40.29 40.33 50.20 48.49 52.55 50.41

225 47.59 48.69 46.15 47.48 54.22 54.58 55.19 54.66

250 44.98 46.89 45.69 45.85 52.11 54.51 51.18 52.60

275 42.12 43.01 42.44 42.52 47.58 51.19 52.22 50.33

300 36.59 38.10 39.99 38.23 40.11 43.59 44.95 42.88

325 35.95 36.86 35.42 36.08 38.84 39.55 42.11 40.17

350 31.18 32.51 29.45 31.05 33.94 37.86 36.84 36.21

375 30.05 28.22 28.5 28.92 29.84 31.14 30.99 30.65

400 22.98 24.54 25.83 24.45 25.87 29.95 26.88 27.57

Table B.3 Evaporation time of Ethanol on Aluminum Surface



70 7.37 7.83 6.92 7.37 9.39 9.83 8.83 9.35

80 4.31 4.19 4.83 4.44 5.73 5.23 4.82 5.26

90 1.65 1.70 1.43 1.59 1.92 1.53 2.21 1.89

100 0.34 0.37 0.35 0.35 0.56 0.47 0.43 0.49

125 0.84 0.85 0.82 0.84 1.37 1.65 1.51 1.51

150 2.52 2.48 2.51 2.50 2.49 2.72 2.61 2.61

175 11.65 12.47 12.15 12.09 12.78 12.31 12.56 12.55

200 24.33 25.00 25.19 24.84 28.12 29.02 28.93 28.69

225 22.39 22.52 22.19 22.37 26.45 26.86 25.23 26.18

250 22.3 18.55 19.45 20.10 22.12 23.54 23.82 23.16

275 15.65 17.10 18.12 16.96 21.01 20.86 21.54 21.14

300 13.99 15.11 14.25 14.45 17.88 15.59 18.11 17.19

325 13.15 14.21 13.24 13.53 16.11 15.21 14.55 15.29

350 13.21 9.41 12.55 11.72 14.20 12.55 13.12 13.29

375 9.55 10.52 10.11 10.06 12.31 10.80 10.50 11.20

400 7.88 8.11 9.95 8.65 9.56 10.12 8.95 9.54

91

Table B.4 Evaporation time of Methanol on Aluminum Surface



60 4.82 4.31 4.90 4.68 6.39 5.98 6.21 6.19

70 2.74 2.52 2.83 2.70 4.96 4.83 4.63 4.81

80 1.66 1.54 1.31 1.50 1.85 1.97 1.73 1.85

90 1.27 1.19 0.99 1.15 1.52 1.32 1.79 1.54

100 0.25 0.40 0.31 0.32 0.25 0.25 0.38 0.29

125 1.12 1.32 1.04 1.16 1.62 1.84 1.32 1.59

150 3.21 2.98 3.45 3.21 3.56 3.86 3.99 3.80

175 10.99 10.96 10.31 10.75 13.86 14.15 14.40 14.14

200 20.12 20.43 20.84 20.46 21.02 22.12 21.54 21.56

225 21.58 21.83 21.02 21.48 25.56 25.74 24.86 25.39

250 18.54 18.12 17.89 18.18 22.23 22.56 21.86 22.22

275 15.19 16.21 16.11 15.84 19.26 20.39 18.51 19.39

300 12.81 12.54 13.856 13.07 16.59 15.23 17.46 16.43

325 10.54 11.32 12.5 11.45 13.21 15.64 14.44 14.43

350 8.51 8.84 9.86 9.07 12.54 13.66 14.11 13.44

375 9.12 7.64 8.45 8.40 11.54 10.68 11.25 11.16

400 6.86 7.20 7.66 7.24 10.86 8.65 9.95 9.82

Table B.5 Evaporation time of Distilled water on Brass Surface



70 119.56 118.57 117.23 118.45 123.01 122.45 119.24 121.57

80 78.96 77.65 78.99 78.53 82.55 84.23 86.11 84.29

90 40.01 42.21 39.99 40.74 45.21 46.53 48.21 46.65

100 4.15 4.58 5.95 4.89 5.21 5.68 4.89 5.26

125 39.89 41.52 42.52 41.31 43.22 44.56 47.86 45.21

150 81.19 80.12 82.34 81.22 88.21 89.45 86.25 87.97

175 110.42 108.56 107.68 108.89 119.21 118.59 117.56 118.45

200 79.98 80.12 78.98 79.69 84.55 83.21 88.99 85.58

225 65.21 66.58 67.28 66.35 67.54 68.59 69.84 68.66

250 55.12 56.89 57.65 56.55 59.21 58.63 61.12 59.65

275 46.82 45.21 47.38 46.47 49.84 46.86 51.89 49.53

300 43.21 42.89 41.26 42.45 46.12 45.22 46.52 45.95

325 39.22 37.84 40.21 39.09 40.12 39.86 42.21 40.73

350 35.52 34.26 32.81 34.20 36.78 37.96 38.11 37.62

375 31.12 33.54 32.99 32.55 34.22 35.21 37.12 35.52

92

Table B.6 Evaporation time of NaCl Solution on Brass Surface



70 110.12 108.54 107.39 108.68 113.21 112.45 112.54 112.73

80 69.11 68.42 66.89 68.14 75.23 74.22 76.21 75.22

90 30.45 32.3 31.26 31.34 38.82 39.91 40.3 39.68

100 0.52 0.62 0.49 0.54 0.72 0.78 0.88 0.79

125 5.11 5.69 4.89 5.23 6.30 6.49 7.12 6.64

150 26.34 25.42 26.89 26.22 29.2 28.62 30.40 29.41

175 45.29 44.26 43.87 44.47 48.21 44.56 49.12 47.29

200 61.10 62.89 59.46 61.15 68.12 69.52 67.86 68.50

225 55.89 54.67 55.16 55.24 60.22 61.35 62.22 61.26

250 48.22 47.69 49.59 48.50 52.26 54.34 50.84 52.48

275 45.27 46.32 44.22 45.27 48.02 47.76 48.95 48.24

300 41.23 40.25 42.26 41.25 42.22 41.15 43.11 42.16

325 38.96 36.84 39.92 38.57 40.44 41.56 37.89 39.96

350 36.53 38.82 35.12 36.82 36.92 38.12 38.82 37.95

375 30.40 33.21 32.25 31.95 35.59 34.32 34.99 34.97

Table B.7 Evaporation time of Ethanol on Brass Surface



70 6.21 6.39 5.89 6.16 8.04 8.32 8.49 8.28

80 3.09 3.19 3.42 3.23 4.31 4.51 3.92 4.25

90 1.21 1.79 2.21 1.74 2.64 2.54 2.78 2.65

100 0.51 0.52 0.49 0.51 0.79 0.82 0.93 0.85

125 14.16 12.29 13.21 13.22 17.52 16.86 18.12 17.50

150 43.19 45.23 41.15 43.19 46.93 47.12 45.98 46.68

175 34.22 36.95 35.21 35.46 38.12 37.23 39.22 38.19

200 31.24 32.15 30.99 31.46 34.54 33.22 35.15 34.31

225 26.59 24.43 27.11 26.04 29.33 30.4 31.12 30.28

250 22.88 24.56 23.12 23.52 26.88 25.43 27.66 26.66

275 22.62 21.13 23.65 22.47 24.21 23.56 24.82 24.20

300 18.78 19.96 20.26 19.67 21.30 22.34 20.86 21.50

325 18.82 16.52 17.45 17.60 19.98 19.53 20.86 20.12

350 15.82 16.93 14.12 15.62 19.42 18.52 17.12 18.35

375 11.96 13.56 12.45 12.66 15.42 18.46 16.86 16.91

93

Table B.8 Evaporation time of Methanol on Brass Surface



60 5.64 5.24 5.42 5.43 7.11 7.19 6.60 6.97

70 4.51 4.29 4.11 4.30 5.75 5.53 5.21 5.50

80 1.24 1.39 1.58 1.40 1.92 2.01 1.83 1.92

90 1.18 0.92 0.93 1.01 1.83 1.45 1.51 1.60

100 0.40 0.42 0.49 0.44 0.67 0.79 0.59 0.68

125 12.71 11.98 13.42 12.70 14.83 13.21 15.23 14.42

150 39.18 40.22 38.45 39.28 44.23 45.89 44.85 44.99

175 30.99 31.24 32.86 31.70 38.21 39.12 37.54 38.29

200 27.89 25.32 26.22 26.48 31.12 32.23 33.42 32.26

225 24.86 22.13 25.86 24.28 29.98 30.44 28.45 29.62

250 22.83 21.45 24.44 22.91 28.01 27.05 26.98 27.35

275 19.86 18.92 21.45 20.08 23.45 24.52 22.12 23.36

300 18.72 19.24 17.92 18.63 20.54 21.23 19.82 20.53

325 15.69 14.23 16.32 15.41 18.82 17.64 16.98 17.81

350 11.63 12.87 13.14 12.55 16.62 15.42 14.23 15.42

375 9.50 10.55 11.10 10.38 11.99 12.45 13.86 12.77

Table B.9 Evaporation time of Distilled water on Copper Surface



70 98.23 96.54 98.99 97.92 110.23 108.74 106.54 108.50

80 78.25 80.23 75.44 77.97 84.56 86.23 87.23 86.01

90 54.12 56.22 59.42 56.59 60.22 62.45 63.11 61.93

100 32.13 31.12 34.12 32.46 49.23 48.15 50.23 49.20

125 40.32 39.73 41.51 40.52 55.12 56.31 54.23 55.22

150 46.95 48.33 49.13 48.14 63.22 66.18 64.37 64.59

175 61.11 63.43 65.43 63.32 70.13 69.35 68.13 69.20

200 70.13 70.79 71.93 70.95 79.87 83.12 80.90 81.29

225 59.10 61.15 58.24 59.50 65.43 67.84 70.26 67.84

250 50.92 49.85 51.41 50.73 60.35 59.87 58.85 59.69

275 47.34 45.13 44.21 45.56 57.36 54.33 55.83 55.84

300 40.13 41.13 42.27 41.18 50.41 49.81 47.90 49.37

325 38.13 37.35 36.56 37.35 43.13 42.22 40.95 42.10

350 33.14 34.91 35.16 34.40 35.60 37.83 36.92 36.78

375 28.72 29.10 27.63 28.48 30.13 31.95 29.24 30.44

94

Table B.10 Evaporation time of NaCl Solution on Copper Surface



70 90.12 89.85 86.99 88.99 105.66 106.21 104.44 105.44

80 70.12 69.89 71.12 70.38 80.22 81.11 81.19 80.84

90 52.12 49.53 50.11 50.59 54.23 56.81 59.12 56.72

100 35.63 34.93 33.17 34.58 38.36 40.16 39.9 39.47

125 8.42 9.33 10.16 9.30 9.84 11.16 13.18 11.39

150 14.16 15.99 13.23 14.46 19.16 20.11 21.5 20.26

175 50.13 52.32 51.31 51.25 55.13 57.95 58.14 57.07

200 59.73 58.82 60.18 59.58 63.13 64.93 65.81 64.62

225 51.32 54.23 52.31 52.62 59.18 57.83 56.97 57.99

250 45.16 46.33 44.19 45.23 52.19 52.96 51.12 52.09

275 43.59 42.11 42.05 42.58 51.24 50.86 51.65 51.25

300 39.54 40.21 39.86 39.87 49.11 48.11 47.33 48.18

325 34.31 33.99 36.11 34.80 41.26 43.25 40.21 41.57

350 35.13 34.36 32.23 33.91 38.95 37.26 35.10 37.10

375 30.12 29.29 28.29 29.23 30.16 31.27 32.94 31.46

Table B.11 Evaporation time of Ethanol on Copper Surface



70 4.51 4.19 3.99 4.23 4.74 4.93 5.11 4.93

80 4.04 3.70 3.65 3.80 4.25 4.42 4.11 4.26

90 1.73 1.42 1.39 1.51 2.31 2.59 2.05 2.32

100 1.05 0.89 0.78 0.91 1.31 1.49 1.79 1.53

125 5.11 4.95 6.36 5.47 6.12 5.95 6.35 6.14

150 14.95 15.16 13.24 14.45 17.23 19.36 18.43 18.34

175 36.93 34.82 35.18 35.64 39.32 40.53 41.95 40.60

200 34.11 33.28 31.13 32.84 37.38 36.43 35.93 36.58

225 30.17 32.16 29.32 30.55 33.26 31.19 32.92 32.46

250 26.33 24.56 25.93 25.61 28.33 27.56 26.93 27.61

275 23.14 22.23 20.94 22.10 25.44 23.24 22.11 23.60

300 19.86 17.93 18.34 18.71 20.26 21.96 19.98 20.73

325 17.3 16.82 15.91 16.68 17.31 18.46 16.13 17.30

350 13.21 13.59 14.99 13.93 14.17 15.93 16.12 15.41

375 10.13 11.13 12.92 11.39 13.16 12.16 11.49 12.27

95

Table B.12 Evaporation time of Methanol on Copper Surface



60 5.47 4.83 5.29 5.19 8.35 7.91 7.61 7.96

70 4.91 3.98 4.01 4.30 5.11 5.49 4.89 5.16

80 1.61 1.79 1.93 1.78 2.32 2.14 2.93 2.46

90 0.41 0.31 0.48 0.40 0.62 0.71 0.98 0.77

100 0.54 0.47 0.63 0.55 0.74 0.89 0.63 0.75

125 1.01 1.12 0.95 1.03 1.32 1.49 1.53 1.45

150 8.45 8.93 7.96 8.45 9.55 10.11 11.21 10.29

175 31.13 33.56 34.92 33.20 35.78 39.24 40.21 38.41

200 29.85 28.76 29.31 29.31 30.15 31.26 32.46 31.29

225 26.26 27.36 24.35 25.99 27.12 28.24 25.93 27.10

250 24.31 23.23 21.15 22.90 24.39 23.26 25.53 24.39

275 20.14 19.27 19.97 19.79 21.23 20.23 23.21 21.56

300 18.16 17.26 17.99 17.80 19.39 18.98 17.93 18.77

325 16.46 15.31 14.36 15.38 17.52 16.81 18.33 17.55

350 13.18 12.96 12.32 12.82 14.34 14.54 15.1 14.66

375 10.16 9.87 11.34 10.46 11.82 10.92 12.25 11.66

Table B.13 Evaporation time of Distilled water on Mild Steel Surface



70 70.12 69.86 68.98 69.65 74.53 76.55 73.82 74.97

80 50.22 54.11 53.21 52.51 54.53 55.61 58.79 56.31

90 20.12 23.46 22.42 22.00 26.98 25.45 26.01 26.15

100 2.23 2.19 2.35 2.26 4.88 4.79 4.99 4.89

125 1.15 1.11 1.32 1.19 2.21 2.31 2.49 2.34

150 4.14 4.35 4.49 4.33 5.15 5.32 5.31 5.26

175 8.15 8.85 7.92 8.31 9.35 9.23 9.56 9.38

200 11.13 11.63 10.56 11.11 13.27 13.22 13.59 13.36

225 14.35 15.15 14.35 14.62 17.44 17.21 17.56 17.40

250 49.89 49.32 50.01 49.74 55.17 55.39 56.32 55.63

275 44.23 45.15 44.21 44.53 49.18 50.23 50.62 50.01

300 39.24 40.23 42.21 40.56 41.25 41.33 41.93 41.50

325 34.17 33.96 34.52 34.22 36.26 36.56 35.91 36.24

350 29.33 29.63 29.12 29.36 30.16 30.58 31.23 30.65

375 22.15 22.65 21.38 22.06 25.14 26.36 25.39 25.63

96

Table B.14 Evaporation time of NaCl Solution on Mild Steel Surface



70 63.11 64.23 62.1 63.15 65.42 66.46 66.11 65.99

80 41.23 42.22 40.19 41.21 49.12 48.25 47.12 48.16

90 16.12 14.99 15.21 15.44 22.99 23.56 23.01 23.19

100 1.66 1.69 1.81 1.72 3.88 3.79 3.98 3.88

125 0.37 0.32 0.41 0.37 0.59 0.62 0.55 0.59

150 0.79 0.89 0.65 0.78 0.99 1.25 1.05 1.10

175 1.81 1.32 1.66 1.60 2.53 2.45 2.96 2.65

200 8.52 7.95 7.88 8.12 10.11 9.86 9.72 9.90

225 12.11 13.01 12.56 12.56 13.98 13.52 14.02 13.84

250 19.25 19.23 19.54 19.34 22.21 22.58 22.69 22.49

275 40.1 40.55 41.23 40.63 45.32 45.62 45.98 45.64

300 37.83 37.62 37.12 37.52 39.27 39.37 39.03 39.22

325 32.54 32.56 32.33 32.48 36.34 36.54 36.51 36.46

350 27.15 27.89 27.48 27.51 29.95 29.33 29.3 29.53

Table B.15 Evaporation time of Ethanol on Mild Steel Surface



70 2.56 2.46 2.72 2.58 3.77 3.95 3.99 3.90

80 1.45 1.61 1.31 1.46 2.36 2.29 2.59 2.41

90 0.38 0.42 0.32 0.37 0.46 0.48 0.38 0.44

100 0.37 0.34 0.31 0.34 0.41 0.45 0.49 0.45

125 0.44 0.41 0.39 0.41 0.55 0.62 0.67 0.61

150 18.47 18.52 18.69 18.56 19.9 19.36 19.81 19.69

175 26.12 25.86 26.02 26.00 29.86 30.12 29.54 29.84

200 23.54 24.11 22.86 23.50 24.12 23.89 24.51 24.17

225 18.19 18.69 18.42 18.43 18.93 18.51 17.65 18.36

250 15.76 15.45 15.78 15.66 17.37 17.52 16.89 17.26

275 13.73 13.58 13.69 13.66 15.25 15.69 15.98 15.64

300 11.58 11.23 11.53 11.45 12.43 12.89 11.99 12.44

325 10.12 10.23 10.69 10.35 11.99 11.56 11.59 11.71

350 9.73 9.36 9.56 9.55 10.25 10.21 10.39 10.28

97

Table B.16 Evaporation time of Methanol on Mild Steel Surface



60 2.85 2.77 2.62 2.75 4.91 5.02 7.61 5.85

70 1.16 1.10 1.29 1.18 2.52 2.43 4.89 3.28

80 0.87 0.81 0.78 0.82 1.09 1.32 2.93 1.78

90 0.27 0.21 0.32 0.27 0.31 0.49 0.98 0.59

100 0.33 0.31 0.28 0.31 0.37 0.39 0.63 0.46

125 2.52 2.62 2.39 2.51 2.20 2.12 1.75 2.02

150 13.21 12.86 12.54 12.87 14.12 14.86 14.34 14.44

175 20.12 19.87 20.45 20.15 20.98 21.01 21.14 21.04

200 22.98 22.86 23.01 22.95 23.56 23.84 23.42 23.61

225 17.13 17.32 17.83 17.43 16.15 16.01 17.21 16.46

250 13.25 13.78 13.23 13.42 15.58 15.39 15.01 15.33

275 11.13 11.24 11.85 11.41 13.27 13.87 12.87 13.34

300 9.83 9.37 9.85 9.68 10.19 10.25 10.20 10.21

325 8.12 8.31 8.29 8.24 9.63 9.99 9.12 9.58

350 7.67 7.63 8.31 7.87 8.11 8.01 8.36 8.16

98

APPENDIX

SUMMARY OF THEORETICAL

AND EXPERIMENTAL RESULT C

C.1 Comparison of Theoretical and Experimental Result for small diameter liquid droplet

Leidenfrost time(sec)

Liquids Experimental

Al Brass Cu MS

Water 56.29 108.89 70.95 49.74

NaCl solution 47.48 61.15 59.58 40.63

Methanol 21.48 39.28 33.20 22.95

Ethanol 24.84 43.19 35.64 26.00


Liquids Theoretical (from correlation)

Al Brass Cu MS

Water 67.95 96.99 83.50 44.45

NaCl solution - - - -

Methanol 24.42 45.08 40.07 29.42

Ethanol 24.22 39.64 34.70 32.22

99

C.2 Comparison of Theoretical and Experimental Result for large diameter liquid droplet



Al Brass Cu MS

Water 67.54 118.45 81.29 55.63

NaCl solution 54.66 68.50 64.62 45.64

Methanol 25.39 44.99 38.41 23.61

Ethanol 28.69 46.68 40.60 29.84


Liquids Theoretical (from correlation)

Al Brass Cu MS

Water 72.99 94.43 93.10 43.61

NaCl solution - - - -

Methanol 26.86 43.28 44.07 25.26

Ethanol 26.05 37.99 38.08 25.47

100

C.3 Comparison of Leidenfrost point temperature for different liquid droplets (small and

large diameter)

Leidenfrost temperature(˚C)


Al Brass Cu MS

Water 200 175 200 250

NaCl solution 225 200 200 275

Methanol 225 150 175 200

Ethanol 200 150 175 175

101

APPENDIX

PROGRAM CODE D

C.1 Estimation of theoretical time

clear all;

close all;

clc

%Constants

sigma=5.669e-8;

g=9.81;

pi=3.1416;

Ru=8.3145;

%Temperature and pressure

Tp_dummy=(150+273.15); %Metal surface temperature

for i=19

Tp(i)=Tp_dummy+25;%Tp(1)=125 deg centigrade,....Tp(12)=400 deg centigrade.

Tp_dummy=Tp(i);

end

for i=19

%Rest temperature and pressure

Ts=(78.3+273.15); %Liquid saturation temperature

Tv=(Tp(i)+Ts)/2; %Average vapor temperature

Ps=101.3e3; %Partial pressure of diffusing vapor

M=46e-3; %Molecular weight of water

%Radius

ro=1.23e-3; %Initial droplet radius

rp=.0889; %Metal surface radius

%Area

Ap=pi*rp^2;%Metal surface area

Alb=pi*ro^2;%Flat liquid droplet bottom surface area

Ap_ring=pi*(rp^2-ro^2);%Ring shaped metal surface area

Als=2.67*pi*ro*ro;%Cylindrical liquid droplet side surface area

%Volume

102

Vo=(4*pi*ro^3)/3;

%Emissivity

ep=.26; %Metal surface emissivity (of copper)

el=0.07;

%Properties at Ts (of water)

rhol=757;

kv_sat=19.9e-3;

rhov_sat=1.435;

hg=963e3;

cpv_sat=1.83e3;

muv_sat=10.4e-6;

D=.119e-4;

%Properties at Tv (of water)

kv=kv_sat*(Tv/2);

rhov=rhov_sat*(2/Tv);

cpv=cpv_sat*(Tv/2);

muv=muv_sat*(Tv/2);

%Vapor layer thickness

delta=1e-3; %let

%Iteration for delta

while 1

%Shape factor from metal surface to flat bottom of liquid droplet

Fbpl=Fb(ro,rp,delta);

%Shape factor from metal surface to cylindrical side surface of liquid droplet

Fspl=Fs(ro,rp,delta);

Qcbflux(i)=kv*((Tp(i)-Ts)/delta);%Conduction heat flux from metal surface to flat bottom of

liquid droplet

Qrbflux(i)=(sigma*(Tp(i)^4-Ts^4))/(((1-ep)/ep)*(Alb/Ap)+Alb/(Ap*Fbpl)+(1-

el)/el);%Raidation heat flux from metal surface to flat bottom of liquid droplet

Qbflux(i)=Qcbflux(i)+Qrbflux(i);%Total heat flux at the flat bottom of liquid droplet

v(i)=(Qbflux(i))/(rhov*(hg+.5*cpv*(Tp(i)-Ts)));%Vertical velocity at flat bottom of liquid

droplet

delta_new=((9*muv*v(i)*ro)/(8*rhol*g))^(1/3);

if abs(delta_new-delta)<1e-6

delta=delta_new;

break;

end

delta=delta_new;

103

end

delta_matrix(i)=delta;

Qcsflux=(kv*(Tp(i)-Ts))/delta;%(May be discarded)Conduction heat flux from metal surface to

cylindrical side of liquid droplet

Qrsflux(i)=(sigma*(Tp(i)^4-Ts^4))/(((1-ep)/ep)*(Als/Ap_ring)+Als/(Ap_ring*Fspl)+(1-

el)/el);%Radiation heat flux from metal surface to cylindrical side of liquid droplet

mpr_s(i)=(sqrt(2)*D*Als*Ps*M)/(Ru*Ts*ro);%Total mass flow rate from cylindrical droplet

side

mpr_b(i)=(Qbflux(i)*Alb+Qsflux(i)*Als-mpr_s(i)*hg)/(hg+.5*cpv*(Tp(i)-Ts));%Total mass

flow rate from flat droplet bottom

mpr(i)=mpr_b(i)+mpr_s(i);%Total mass flow rate from droplet

t(i)=(rhol*Vo)/mpr(i); %Total vaporization time

end

disp('Theoritical result for distilled water on copper surface');

final_value_table=[t'];

disp(' Tp t');

disp(final_value_table);

plot((Tp-273.15),t); %Tp has taken in degree by -273.15

xlabel('Temperature of metal surface(Degree centigrade)');

ylabel('Vaporization time, t');

C.2 Engineering Correlation of experimental data

% Code for correlation constants

clear all;

close all;

clc

y=[0.0209,0.0213,0.0231,0.0253,]; %observed value

x1=[0.7634,0.8489,0.9251,0.9940,]; %observed value,,

x2=1e-4.*[0.0180,0.0293,0.0448,0.0654,]; %observed value

p=(sum(x1.*x1));

q=(sum(x1.*x2));

r=(sum(x2.*x2));

A=[p q;q r];

C=[sum(x1.*y);sum(x2.*y)];

B=inv(A)*C; %constants

104

for i=1length(y);

Y(i)=B(1)*x1(i)+B(2)*x2(i);

end

% Code for correlation graph

y1=y(1,18);y2=y(1,915);y3=y(1,1623);

Y1=Y(1,18);Y2=Y(1,915);Y3=Y(1,1623);

sumY=sum(Y);

sumy=sum(y);

m=sumY/sumy;

x11=1length(Y);

x11=x11*max(y)/length(Y);

y11=x11*m;

y12=x11*1;

figure (2);

axis tight

plot(y1,Y1,'ro')

hold all

plot(y2,Y2,'bs')

hold all

plot(y3,Y3,'mv')

hold all

plot(x11,y12,'g')

xlabel('Obseved value');

ylabel('Calculated value');

legend('water','methanol','ethanol','equation')

% Code for plotting heat flux graph

clear all;

close all;

clc

r=1.23e-3;

v=(4*pi*r^3)/3;

Ta=[70,80,90,100,125,150,175,200,225,250,275,300,325,350,375];

Tb=[70,80,90,100,125,150,175,200,225,250,275,300,325,350,375];

Tc=[70,80,90,100,125,150,175,200,225,250,275,300,325,350,375];

Ts=[70,80,90,100,125,150,175,200,225,250,275,300,325,350,375];

ta=[72.46333,68.55667,44.25667,17.16667,]; %Observed time

105

tb=[118.4533,78.53333,40.73667,4.893333,]; %Observed time

tc=[97.92,77.97333,56.58667,32.45667,]; %Observed time

ts=[69.65333,52.51333,22,2.256667,]; %Observed time

pl=1000;

hg=2256.7e3;

disp('HEAT FLUX OF WATER ON ALUMINUM')

qa=(4.921332e-3*pl*hg)./ta;

disp(qa)

plot(Ta,qa,'ko')

hold all;

xlabel('surface Temperature(degree C)');

ylabel('heat flux(Watt per meter square)');

disp('HEAT FLUX OF WATER BRASS')

qb=(4.921332e-3*pl*hg)./tb;

disp(qb)

plot(Tb,qb,'k*')

hold all;



disp('HEAT FLUX OF WATER ON COPPER')

qc=(4.921332e-3*pl*hg)./tc;

disp(qc)

plot(Tc,qc,'kv')

hold all;



disp('HEAT FLUX OF WATER ON MILD STEEL')

qs=(4.921332e-3*pl*hg)./ts;

disp(qs)

plot(Ts,qs,'k+')

hold all;



legend('Heat flux on AL','Heat flux on BR','Heat flux on Cu','Heat flux on MS');

plot(Ta,qa,'k',Tb,qb,'k',Tc,qc,'k',Ts,qs,'k')

106

%Code for comparison of theoretical (correlated) and experimental graph

clear all;

close all;

clc

r=1.23e-3;

ea=.05;eb=.09;ec=.045;es=.1;

pl=958.3 ;

pv=.597;

kv=25e-3;

Ts=100;

u=12.55e-6;

s=5.669e-8;

h=2256.7e3;

cp=2.03e3;

Tp=[150,175,200,225,250,275,300,325,350,375,400];

dT=Tp-Ts;

h1=h+0.5*cp.*dT;

disp('water-al')

x1a=sqrt((kv*g*pv*(pl-pv).*dT.*r)./(u*h1));

x2a=((s*ea*(Tp.^4-Ts^4))./h1);

xa=x1a.*0.0197+x2a.*1280.5;

ta=(pl.*r)./xa;

disp('correlated value of ta ')

disp(ta)

disp('water-br')

x1b=sqrt((kv*g*pv*(pl-pv).*dT.*r)./(u*h1));

x2b=((s*eb*(Tp.^4-Ts^4))./h1);

xb=x1b.*0.0169+x2b.*501.9980;

tb=(pl.*r)./xb;

disp('correlated value of tb ')

disp(tb)

disp('water-cu')

x1c=sqrt((kv*g*pv*(pl-pv).*dT.*r)./(u*h1));

x2c=((s*ec*(Tp.^4-Ts^4))./h1);

xc=x1c.*0.0160+x2c.*1171.9;

tc=(pl.*r)./xc;

disp('correlated value of tc')

disp(tc)

disp('water-st')

x1s=sqrt((kv*g*pv*(pl-pv).*dT.*r)./(u*h1));

x2s=((s*es*(Tp.^4-Ts^4))./h1);

107

xs=x1s.*0.0143+x2s.*1483.4;

ts=(pl.*r)./xs;

disp('correlated value of ts')

disp(ts)

Documents

Sessile Drop Evaporation in Relation to Leidenfrost Phenomenon (B.Sc. Thesis Report)