ORIGINAL

Laser consecutive pulse heating in relationto melting: influence of duty cycle on melting

S. Z. Shuja Æ B. S. Yilbas Æ Shafique M. A. Khan

Received: 28 June 2008 / Accepted: 5 January 2009 / Published online: 20 January 2009

� Springer-Verlag 2009

Abstract Laser consecutive pulse heating of steel and

titanium is considered and the influence of consecutive

pulse duty cycle on the melting process is examined.

A model study is introduced to accommodate the phase

change process while an experiment is carried out to

measure the size of the melting region along the irradiated

surface. The simulations are repeated for three duty cycles.

It is found that the sizes of melt and mushy zones are

influenced by the duty cycle; in which case, radial distri-

bution of temperature is modified significantly for low duty

cycle as compared to for high duty cycle.

List of symbols

a Gaussian parameter (m)

Amush Mushy zone constant

cp Specific heat capacity J/kg Kð ÞH Total enthalpy J/Kð Þh Enthalpy J/kg Kð Þhref Reference enthalpy J/kg Kð Þht Heat transfer coefficient W/m2 K

� �

I0 Laser peak power intensity W/m2� �

k Thermal conductivity W/m Kð ÞT Temperature (�C)

Tliquidus Liquid temperature (�C)

Tsolidus Solid temperature (�C)

tc End of cooling period (s)

tf Beginning of falling period of the consecutive

pulse(s)

tp Pulse length of the consecutive pulse (s)

tr End of rise period of the consecutive pulse (s)

r Radial distance (m)

rf Reflection coefficient

S Momentum sink per unit mass flow rate ðm/sÞS0 Source term (W/m3)

T0 Initial temperature (�C)

t Time (s)

v Velocity m/sð Þz Axial distance (m)

Greek symbols

b The liquid fraction

e Porosity

q Density kg/m3� �

a ¼ k=qCpsð Þ Thermal diffusivity ðm2=sÞd Absorption depth (m–1)

1 Introduction

High power laser heating results in a phase change process

in the surface region of the irradiated material. In this

case, material undergoes a solid heating, melting, and

consequent evaporation. However, in some industrial

applications, such as heat treatment and surface modifica-

tion through controlled melting, the heating situation is

limited to a melting process. Although the depth of the

liquid layer is related with the focus setting of the focusing

lens and thermophysical properties of the substrate mate-

rial, the layer thickness can also be controlled by altering

the duty cycle of the laser pulses. This requires changing

the laser energy while keeping the pulse repetition rate

constant during the processing. Consequently, the heating

and cooling cycles change with during the pulsed heating

S. Z. Shuja � B. S. Yilbas (&) � S. M. A. Khan

Mechanical Engineering Department, KFUPM,

Box 1913, Dhahran 31261, Saudi Arabia

e-mail: bsyilbas@kfupm.edu.sa

123

Heat Mass Transfer (2009) 45:793–803

DOI 10.1007/s00231-009-0477-x

while altering the duty cycle and keeping the laser peak

power intensity the same. Moreover, the model studies

provide useful information on the physical processes taking

place during the laser heating process and facilitate the

relation between the laser parameters and resulting melt

geometry, which reduce the experimental cost and the time.

Consequently, investigation into the effect of the laser duty

cycle on the melting process becomes essential.

Considerable research studies were carried out to

examine the laser melting process. Kim and Sim [1]

investigated laser heating and subsequent melting process.

They indicated that the convection heat transfer in the

melting zone contributes to the size of the mushy zone.

Laser heating and temperature distribution in laser pro-

duced melt pool were studied by Rostami and Raisi [2].

They indicated that the melt pool size was influenced by

the laser output power and the material properties. The

numerical procedure for obtaining the interfaces during

laser heating process was introduced by Ganesh and Faghri

[3]. They presented a procedure for the liquid–solid and

vapor–liquid interfaces in the irradiated region of the

substrate material. Yilbas and Naqvi [4] studied the laser

heating and the phase change process, which took place in

the irradiated region. They formulated the phase change

process after accommodating the mushy zone consider-

ation. Laser induced heating and melting was modeled

analytically by Shen et al. [5]. They obtained the depth

profile and time evolution of temperature before and after

the melting process. The influence of laser beam geome-

tries on the laser heating and melting processes was

investigated by Safdar et al. [6]. They indicated that beam

geometry had significant influence on the melt size for

metals with low thermal conductivity. The laser heating

and phase changes in the irradiated region was examined

by Zhou et al. [7]. They showed that the recoil pressure was

the main driving force for the keyhole formation and the

melt flow in the molten layer produced complex flow

structure in this region. Laser heating and formulation of

melt pool was studied by Fathi et al. [8]. They indicated

that the closed form solution for temperature distribution

for a point heat source model was capable of capturing the

melting process. A microscale heat and mass transfer and

non-equilibrium phase change during the rapid solidifica-

tion process was examined by Wang and Prasad [9]. They

indicated that for fast moving solid–liquid interface, non-

equilibrium model should be accommodated to account for

heat and mass transfer. Heat and mass transfer modeling in

relation to laser melting was carried out by Raj et al. [10].

They indicated that by employing a particle-tracking

algorithm and simultaneous particle-melting consideration,

the species source term was estimated by the amount of

fusion of a spherical particle as it passed through a par-

ticular control element.

In the early studies [11–13], the phase change process

was formulated and predicted for laser pulses within the

range of nanoseconds. However, in most of the practical

applications, the laser pulse lengths are in the order of

milliseconds. In this case, a model study covering the laser

pulses with millisecond durations becomes necessary. In

the present study, laser heating and melting processes are

considered and influence of laser pulse duty cycle on the

melting process is examined. The consecutive pulses with

identical pulse lengths and intensities are used in the

analysis. A control volume approach is introduced for

numerical simulation of the governing equations. An

experiment is conducted for the laser parameters, which are

used in the simulations. The melt size at the irradiated

surface was predicted and compared with the experimental

results.

2 Experimental

The laser used in the experiment is a CO2 laser (LC-aIII-

Amada) and delivering nominal output power of 2000 W at

the pulse mode with adjustable frequencies. Nitrogen

emerging from a conical nozzle and co-axially with the

laser beam is used. 127 mm focal lens is used to focus the

laser beam. The laser heating parameters are given in

Table 1.

An optical microscopy is carried out to photograph the

laser melted surfaces.

3 Mathematical modeling

Laser heating situation is shown in Fig. 1. An enthalpy-

porosity technique is used to model the melting/solidifi-

cation process. In this case, the melt interface is not tracked

explicitly. Instead, a quantity called the liquid fraction,

Table 1 Laser heating parameters

Duty cycle Power (W) Period between

pulses (ms) (Hz)

Pulse length

(ms)

Nozzle gap

(mm)

Nozzle diameter

(mm)

Focus diameter

(mm)

N2 pressure

(kPa)

0.4 2,000 0.06 0.04 1.5 1.5 0.8 400

0.6 2,000 0.04 0.06 1.5 1.5 0.8 400

794 Heat Mass Transfer (2009) 45:793–803

123

which indicates the fraction of the cell volume that is in

liquid form, is associated with each cell in the domain. The

liquid fraction is computed at each iteration, based on an

enthalpy balance. The mushy zone is a region in which the

liquid fraction lies between 0 and 1. The mushy zone is

modeled as a ‘‘pseudo’’ porous medium in which the

porosity decreases from 1 to 0 as the material solidifies.

When the material has fully solidified in a cell, the porosity

becomes zero and hence the velocities also drop to zero

[14].

3.1 Energy equation

The enthalpy of the material is computed as the sum of the

sensible enthalpy, h, and the latent heat, DH:

H ¼ hþ DH ð1Þ

where

h ¼ href þZT

Tref

cpdT ð2Þ

and href is the reference enthalpy, Tref is the reference

temperature, cp is the specific heat at constant pressure.

The liquid fraction, b, can be defined as:

b ¼ 0 if T\Tsolidus

b ¼ 1 if T [ Tliquidus

b ¼ T � Tsolidus

Tliquidus � Tsolidus

if Tsolidus\T\Tliquidus ð3Þ

Equation 3 is referred to as the lever rule [14].

The latent heat content can now be written in terms of

the latent heat of the material, L:

DH ¼ bL ð4Þ

The latent heat content can vary between zero (for a

solid) and L (for a liquid).

For solidification/melting problems, the energy equation

is written as:

o

otqHð Þ þ r � ðqv

*HÞ ¼ r � krTð Þ þ S0 ð5Þ

where H is the enthalpy, q is the density, v*

is the fluid

velocity, S0 is the source term.

The volumetric heat source can be arranged to resemble

the laser repetitive pulses, i.e.,

S0 ¼ I0d 1� rfð Þ exp �dzð Þ exp � r

a

� �2� �

f ðtÞ

where I0, d, rf, a, f(t) are the laser peak power intensity,

absorption coefficient, reflectivity, the Gaussian parameter,

and the temporal distribution of laser pulse intensity,

respectively. Temporal variation of laser pulse intensity is

considered to be in trapezium shape in time domain. The

temporal variation of the laser pulse shape is resembles

almost the actual laser pulse shape used in the industry

(Amada BP 41040, 95912 Roissy Aeroport Cedex, France).

The laser pulse parameters used in the simulations are

given in Table 2 while Fig. 2 shows the temporal variation

of consecutive laser pulses. The time function (f(t))

representing the consecutive pulses is:

f tð Þ ¼

0; t ¼ 0

1; tr� t� tf

0; t ¼ tp

0; tp� t� tc

8>><

>>:

9>>=

>>;ð6Þ

Table 2 Laser pulse parameters used in the simulations

Duty cycle

(%)

Laser pulse

length, tp (ms)

Cooling period,

tc (ms)

Pulse rise time,

tr (ms)

Pulse fall time,

tf (ms)

Pulse intensity

(W/m2) 9 109Guassian parameter,

a (m) 9 10-4

40 0.04 0.06 0.0052 0.0026 1 2.997

60 0.06 0.04 0.0078 0.0039 1 2.997

Fig. 1 A schematic view of laser heating situation and a coordinate

system

Heat Mass Transfer (2009) 45:793–803 795

123

where tr is the pulse rise time, tf is the pulse fall time, tp is

the pulse length, tc is the end of cooling period. f(t) repeats

when the second consecutive pulse begins, provided that

time t = tf ? tc corresponds to the starting time of the

second pulse. The same mathematical arguments can apply

for the other consecutive pulses after the second pulse.

The solution for temperature is essentially an iteration

between the energy equation (Eq. 5) and the liquid fraction

equation (Eq. 3). Directly using Eq. 3 to update the liquid

fraction usually results in poor convergence of the energy

equation. However, the method suggested by Voller and

Prakash [15] is used to update the liquid fraction based on

the specific heat.

Since the heating problem is transient, the initial con-

dition should be defined. In this case, initially it is assumed

that the slab is at a uniform enthalpy, which can be spec-

ified as:

At t ¼ 0 : T ¼ T0

In order to solve Eq. 5, two boundary conditions for

each principal axis should be specified. Due to the short

duration of the laser pulse, an insulated boundary is

assumed at the surface, and at a distance considerably away

from the surface (at infinity) it is assumed that the heating

has no effect on the temperature of the slab; consequently,

at a depth of infinity, the temperature is assumed to be

constant and equal to the initial temperature of the slab. In

this case, the problem deals with the semi infinite-body and

this assumption simplifies the solution of the problem. The

boundary conditions, therefore, are:

z at infinity ) z ¼ 1 : T r;1; tð Þ ¼ T0 specifiedð Þr at infinity ) r ¼ 1 : T 1; z; tð Þ ¼ T0 specifiedð Þ

At symmetry axis ) r ¼ 0 :oT 0; z; tð Þ

or¼ 0

At symmetry surface ) z ¼ 0 : koT r; 0; tð Þ

oz

¼ ht Ts � T1ð Þ

where h is the heat transfer coefficient t at the free surface.

The heat transfer coefficient predicted earlier [16] is used

in the present simulations (ht = 104 W/m2 K).

3.2 Momentum equations

The enthalpy-porosity technique treats the mushy region

(partially solidified region) as a porous medium. The

porosity in each cell is set equal to the liquid fraction in

that cell. In fully solidified regions, the porosity is equal to

zero, which extinguishes the velocities in these regions.

The momentum sink due to the reduced porosity in the

mushy zone takes the following form:

S ¼ 1� bð Þ2

b3 þ e� �Amush v

*� �

ð7Þ

where b is the liquid volume fraction, e is a small number

(0.001) to prevent division by zero, Amush is the mushy

zone constant. The mushy zone constant measures the

amplitude of the damping; the higher this value, the steeper

the transition of the velocity of the material to zero as it

solidifies. The liquid velocity can be found from the

average velocity is determined from:

v*

liq ¼v*

bð8Þ

4 Numerical solution

To discretise the governing equation, a control volume

approach is introduced. The details of the numerical

scheme are given in [17]. The calculation domain is divi-

ded into grids and a grid independence test is performed for

different grid sizes and orientation. A non-uniform grid

with 350 9 400 mesh points along z and r axes, respec-

tively, is employed after securing the grid independence.

The finer grids are located near the irradiated spot center in

the vicinity of the surface and grids become courser as the

distance increases towards the bulk of substrate material.

The central difference scheme is adopted for the diffusion

terms. The convergence criterion for the residuals is set as

wk � wk�1�� ��� 10�6 to terminate the simulations. Table 3

gives the thermal properties of material used in the

simulations.

Duty Cycle = 0.4

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20 0.25

TIME (ms)

YTIS

NET

NIE

VITAL

ER

tB = Begining of Heating CycletE = Ending of Heating Cycle

tB tE

tr tf

tp

tc

Two consecutive pulses for duty cycle 0.4.

Duty Cycle = 0.6

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20 0.25

TIME (ms)

TIS

NE

TNI

EVI

TA

LE

RY

Two consecutive pulses for duty cycle 0.6.

Fig. 2 Two consecutive pulses for two different duty cycles

796 Heat Mass Transfer (2009) 45:793–803

123

5 Results and discussion

Laser melting of steel and titanium is considered and

influence of laser duty cycle on the melt formation is

examined. The simulations are repeated for steel and tita-

nium for comparison reason. The size of the melted surface

after laser irradiation was measured and compared with the

predictions.

Figure 3a and b show temperature contours inside steel

substrate for two duty cycles. It should be noted that

beginning and ending of the pulses are shown for the

comparison reasons. The end of heating represents the end

Table 3 Material properties

used in the simulations [18, 19]Temp (K) 300 400 600 800 1,000 1,200 1,500

Steel Cp J/kg K 477 515 557 582 611 640 682

K W/m K 14.9 16.6 19.8 22.6 25.4 28 31.7

q kg/m3 8,018 7,968 7,868 7,769 7,668 7,568 7,418

Titanium Cp J/kg K 522 551 591 633 675 620 686

K W/m K 21.9 20.4 19.4 19.7 20.7 22 24.5

q kg/m3 4,540 4,525 4,495 4,465 4,435 4,405 4,360

Fig. 3 Temperature contours inside steel for duty cycle a 40%, b 60%

Heat Mass Transfer (2009) 45:793–803 797

123

of heating cycle while beginning of heating corresponds

to beginning of the heating cycle (Fig. 2), i.e. the time

difference corresponds to the pulse length of the laser

consecutive pulses. In the simulations, 50 consecutive

pulses are used. Melting initiates at the end of 20th pulses,

which can also be seen from Fig. 4a and b, in which

the liquid and mushy zones are shown. The depth and the

diameter of the melt pool increases with increasing the

pulse repetitions. In addition, the depth of mushy zone

decreases significantly at the initiation of 30th, 40th, and

50th pulses. Although the pulse length is in the order of

0.1 ms, which is short, its influence on the melt formation

in the substrate material is significant. In this case, the

irradiated laser energy absorbed in the surface region

increases the internal energy gain of the substrate material.

The internal energy gain of the substrate material must be

large enough for the phase change process to take place,

since the latent heat of fusion is large (Table 3). It should

be noted that temperature of the substrate material at solid

phase is at the melting temperature before the 30th pulse

was initiated. Consequently, during the heating cycle, the

pulse energy absorbed by the substrate material is con-

sumed via latent heat of fusion. Moreover, in the region of

the melt zone vicinity, a mushy zone is developed. In this

region, material is in semi-molten state. After the 40th and

50th pulses, the liquid depth layer increases beyond the

absorption depth of the substrate material and energy

transfer to the mushy zone from the liquid region is gov-

erned by the conduction process; in which case, absorption

of energy from the irradiated field in the mushy zone

becomes negligible. Moreover, the size of mushy zone is

larger in the radial direction than in the axial direction. This

is because of the irradiated spot radius at the surface and

the laser power intensity distribution in the radial direction,

which is Gaussian. Consequently, power intensity reduces

significantly towards the edge of the irradiated spot, which

in turn lowers the energy absorbed in this region. Hence,

the complete melting replaces with the mushy zone along

the radial direction in this region. The effect of the pulse

length on the size of the mushy zone is evident when

comparing the mushy size before and after heating periods.

In this case, radial expression of mushy zone is evident for

Fig. 4 Melting and mushy zone contours inside steel for duty cycle a 40%, b 60%

798 Heat Mass Transfer (2009) 45:793–803

123

the end of the heating situation. This argument is also true

for the melting zone, particularly for high duty cycle (duty

cycle = 0.80%).

Figures 5a and b show temperature contours in the

irradiated region of titanium for two duty cycles, while

Figs. 6a and b show the melting and mushy zones corre-

sponding to two duties. Temperature contours behavior is

similar to its counterparts corresponding to steel, provided

that the sizes of molten and mushy zones are different. In

this case, relatively lower latent heat of melting and ther-

mal diffusivity are responsible for the larger depth of

melting and mushy zones for titanium. The energy diffu-

sion from the mushy zone to solid bulk is suppressed for

low diffusion coefficient of titanium. This lowers the

energy dissipation from the irradiated region to the solid

bulk via conduction. It should be noted that temperature

gradient across the melting and mushy zones are not

significant. This is particularly true for the melting zones

with large depths, where the melt zone size exceeds the

absorption depth. Therefore, energy transfer from the

melting zone to mushy zone is not considerable via diffu-

sion to extend the size of the mushy zone. As the pulse

repetition rate increases, the changes in the melting and

mushy zones become less during the pulse beginning and

ending. This is because of the absorption depth, which is

limited within the melting region and energy diffusion by

conduction towards the melt pool bottom is small during

the short pulse duration, i.e. energy transfer to the mushy

zone is not large enough to extend the molten material

towards this zone.

Figure 7 shows temporal variation of surface tempera-

ture for titanium and steel. The radial location is at the

irradiated spot center (laser beam axis). The oscillatory

behavior of temperature profiles is associated with the

pulse repetitions; in which case, temperature reduces in the

pulse beginning and increases during the pulse length until

the pulse ending. The rise of temperature in the early

heating period is high and as the time progresses, the rise

Fig. 5 Temperature contours inside titanium for duty cycle a 40%, b 60%

Heat Mass Transfer (2009) 45:793–803 799

123

becomes gradual. This is because of the internal energy

gain of the substrate from the irradiated field in the early

heating period. Since temperature gradient in the vicinity

of the surface is low in early heating period, conduction,

convection and radiation losses from the surface region

becomes less. Consequently, internal energy gain enhances

temperature rise at surface during this period. However, as

the heating progresses, temperature in the surface region

increases while the temperature gradient in the surface

vicinity becomes high. This, in turn, accelerates the con-

vection, radiation, and conduction energy transfer from the

surface region. Therefore, energy gain from the irradiation

field in this region is largely dissipated from the surface

region giving rise to gradual increase in surface tempera-

ture. Moreover, once the melting temperature is reached at

the surface, energy absorbed from the irradiated field is

consumed through the melting process. Temperature

oscillation becomes almost steady once the melting tem-

perature is reached. This situation can be clearly observed

for 0.4 duty cycle. It should be noted increasing duty cycle

results in increased energy in the pulse of consecutive

pulses. Therefore, temperature rises in the liquid layer as

pulses progresses beyond the melting temperature. This is

more pronounced for titanium, which is because of the low

thermal conductivity and thermal diffusion coefficient.

Consequently, super heating in the liquid phase occurs for

titanium at an earlier heating period than that of steel.

Figure 8 shows temperature variation inside the

substrate material along the symmetry axis for different

duty cycles at the beginning of the 50th consecutive

pulse. Temperature decay is gradual in the surface

vicinity and it becomes sharp in the region next to the

surface vicinity. The gradual decay of temperature in the

surface vicinity is associated with the absorption depth of

the substrate material; in which case, energy is absorbed

in the vicinity of the substrate material due to small

absorption depth. This gives rise to attainment of high

temperature in this region. It should be noted that laser

beam energy is absorbed in the substrate material

according to the Lambert’s law, i.e. laser power intensity

decreases exponentially with increasing depth from the

surface. Consequently, absorption almost ceases and

internal energy gain from the irradiated field reduces

significantly in the region next to the surface vicinity.

Fig. 6 Melting and mushy zone contours inside titanium for duty cycle a 40%, b 60%

800 Heat Mass Transfer (2009) 45:793–803

123

This results in sharp decay of temperature in this region.

Increasing duty cycle enhances temperature rise in the

surface region and the conduction energy loss from the

surface region to the solid bulk enhances due to high

temperature gradient. This increases temperature below

the surface. However, energy gain in the surface region is

significantly high for the high duty cycles. Therefore

temperature decays more sharply for high duty cycles

than that corresponding to the low duty cycle heating.

Since the melting takes place rapidly for high duty cycles,

a constant temperature line representing the melting

process almost vanishes, i.e., this situation is more pro-

nounced as the duty cycle increases. As the duty cycle

reduces to 0.4, melting results in a constant temperature

line in the region close to the surface for steel. However,

this situation disappears for titanium because of low

thermal diffusivity and thermal conductivity.

Figure 9 shows temperature distribution at the surface

along the radial direction for different duty cycles. Tem-

perature decay is gradual in the region close to the

symmetry axis, which is true for both steel and titanium.

This occurs because of the melting takes place in this

region. In addition, laser power intensity distribution in the

radial direction is Gaussian. Temperature distribution

almost follows the laser power intensity distribution in the

radial direction, provided that the latent heat of fusion

modifies this situation during the melting process. This can

be observed for duty cycle 0.4. Consequently, energy

absorbed in the surface region of the substrate material is

consumed via melting process while temperature change is

small. Once the phase change completes in the surface

region, super heating of liquid takes place in this region.

Since the energy consumed for the phase change is large,

due to high latent of fusion, super heating of liquid is

suppressed by the progressing of the melting process. In the

case of duty cycle 0.4, a constant temperature line appears

towards the edge of super heated liquid. This corresponds

to the mushy zone in the region next to the melting zone,

where temperature remains at the melting temperature of

the substrate material.

Figure 10 shows optical micrograph of the top view of

the laser melted region of steel after 50th pulse ending. It is

evident that the melted section is rounded and clearly

visible from the solid phase. When comparing the size of

the melt diameter with the predictions as given in Table 4,

it is evident that the values in agreement for both duty

cycles. The small discrepancies are associated with the

experimental and measurement errors as well as the

Fig. 7 Temporal variation of surface temperature at the irradiated

spot center of steel and titanium for different duty cyclesFig. 8 Temperature variation along the symmetry axis inside steel

and titanium for different duty cycles at the end of 50th pulse

Heat Mass Transfer (2009) 45:793–803 801

123

assumptions made in the simulations such as homogenous

surface and material properties.

6 Conclusion

Laser consecutive pulse heating of solid substrate is con-

sidered and phase change during the pulse repetition is

examined. Temperature rise in the laser irradiated region is

computed for steel and titanium. An experiment is con-

ducted to validate the size of the melt zone in the radial

direction. In the experiments, the laser heating parameters

are kept identical to the simulation conditions. It is found

that temperature rises rapidly in the surface region in the

early heating period due to the internal energy gain of the

substrate material from the irradiated field. As the pulse

repetition progresses, temperature rise becomes gradual; in

which case conduction, convection and radiation losses

from the irradiated region suppress temperature rise. The

size of melting and mushy zones changes at the pulse

beginning and ending, which is more pronounced for the

pulse repetitions onset of the melting. This replaces with a

small change in mushy zone size for the late pulse

repetitions (50th pulses). The influence of duty cycle on the

melting process is significant. Increasing pulse duty cycle

results in deep and wide melting zones. In addition, tem-

perature at the surface increases substantially. The size of

mushy zone in the radial direction becomes larger for low

duty cycle (0.4) than high duty cycles (0.8). Temperature

distribution in the radial direction does not follow the laser

pulse intensity distribution in the same direction. This is

because of the latent heat of melting, which modifies

temperature distribution in this direction once the melting

temperature is reached. Titanium results in higher tem-

perature rise and larger melting and mushy zone sizes in

the irradiated region than steel, which is due to low thermal

diffusivity and thermal conductivity as well as latent heat

of fusion of titanium.

Acknowledgments The authors acknowledge the support of King

Fahd University of Petroleum and Minerals Dhahran Saudi Arabia.

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Fig. 9 Temperature variation along the radial direction at the surface

of steel and titanium for different duty cycles at the end of 50th pulse

200 µm 200 µm

Duty cycle 60% Duty cycle 40%

Fig. 10 Optical micrograph of melted surface after 50th pulse ending

for steel

Table 4 Predicted and measured melt diameters at the surface

Duty

cycle (%)

Steel Titanium

Experimental

(m)

Prediction

(m)

Experimental

(m)

Prediction

(m)

40 0.00017 0.00018 0.00021 0.0002

60 0.00026 0.00028 0.00032 0.0003

The tests were repeated five times and the standard deviation for steel

is 8 lm and it is 12 lm

802 Heat Mass Transfer (2009) 45:793–803

123

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