morad2016 (2).pdf

Experimental and numerical study on heat transfer characteristics for
methane/air flame impinging on a flat surface
M.R. Morad a, *
, A. Momeni b
, E. Ebrahimi Fordoei a
, M. Ashjaee b
a
Aerospace Engineering Department, Sharif University of Technology, Tehran, Iran
b
School of Mechanical Engineering, University of Tehran, Tehran, Iran
a r t i c l e i n f o
Article history:
Received 21 December 2015
Received in revised form
29 June 2016
Accepted 13 July 2016
Keywords:
Impinging flame
Mach-Zehnder interferometer
Premixed combustion
a b s t r a c t
Heat flux from a premixed methane/air slot laminar flame jet impinging upward to a horizontal target
plate is studied experimentally and numerically. Mach-Zehnder interferometer is used to obtain the
overall temperature field. The flame jet is produced by a slot nozzle with length of L ¼ 25 mm and width
of W ¼ 3 mm. The slot nozzle is parallel to the target plate which has the dimensions of
250 130 10 mm. The experimentally obtained heat flux distributions were compared for different
firing rates and nozzle to plate spacing. A second peak in heat flux to the target surface (an off-center
peak with respect to the axis of the nozzle) was observed for the shortest spacing and highest firing
rate in the present study. The heat flux distribution and the second peak in it could be successfully
simulated using numerical computations. With the help of numerical results and analyzing the velocity
components, it was found that the position of the second peak along the plate is in accordance with a
second stagnation point caused by the present configuration of the confined flame between the two
parallel plates, namely the target plate and the base plate of the two-dimensional nozzle. The results
show that the onset of the presence of the second stagnation point could be controlled by the spacing
and firing rate.
© 2016 Published by Elsevier Masson SAS.
1. Introduction
Impinging flame jets are widely used in heating, cooking, dry-
ing, power generation, metal annealing, and glass production in-
dustries. They are efficient due to their high ability to increase the
rate of heat and mass transfer [6]. Heat release characteristics from
a flame jet is strongly dependent to the temperature distribution
around the receiving medium. Comparisons between impinging
flame jets and isothermal gas jets have shown that Nusselt number
distribution is similar at same Reynolds numbers for circular noz-
zles [18,30]. For flame jets, many studies have been conducted to
investigate the effect of operating conditions on heat transfer
characteristics including Reynolds number, equivalence ratio and
plate to nozzle spacing. Part of these studies have used Butane/air
as the fuel and oxidizer to characterize the effects of flame spacing
[11], Nusslet number [20], local heat flux [10], the material of the
plate [36], and flow parameters such as Reynolds number and
equivalence ratio [23]. Most of the studies have investigated point
heating rather than line spread heating [33], and limited studies
have also considered the effect of non-circular slot using butane
[24].
A number of investigations have been focused on using methane
with circular burner. It is reported that the local heat flux corre-
sponding to the stagnation point increases with the Reynolds
number when the jet-to-plate distance is larger than the length of
the inner reaction zone [8]. For triangular configuration of three
interacting methane/air flame jets, the local heat flux distribution
became more non-uniform when inner jet spacing is increased
considerably [7,22] performed experiments to investigate heat
transfer features of methane-diffusion and premixed methane-air
flame impinged on a cold steel plate. They observed eddies in the
wall-jet region for diffusion flame. Comparative study is performed
on heat transfer distribution between impinging flame jet and
impinging air jet at different Reynolds numbers as well as non-
dimensional nozzle to plate spacing, reporting that there is a
good agreement between the Nusselt numbers for higher spacing
near stagnation region [16]. Nusselt number is also computed for
methane circular impinging flame based on an estimation of the
adiabatic wall temperature through theoretical description and
* Corresponding author.
E-mail address: morad@sharif.edu (M.R. Morad).
Contents lists available at ScienceDirect
International Journal of Thermal Sciences
journal homepage: www.elsevier.com/locate/ijts
http://dx.doi.org/10.1016/j.ijthermalsci.2016.07.005
1290-0729/© 2016 Published by Elsevier Masson SAS.
International Journal of Thermal Sciences 110 (2016) 229e240

experimental data [14]. Recently, an investigation is performed on a
dual impinging flame of natural gas on a flat plate using circular
nozzles [27].
Although circular nozzle has been used extensively in many
industrial as well as academic applications, however, there are a
number of challenges in using circular nozzles that have made re-
searches study the effect of nozzle geometry. For impinging jets, it
is found that the heat flux to the target plate becomes uniform
when a slot nozzle is used instead of a circular nozzle [32]. This is
reported to be a result of greater impingement zone when using a
slot nozzle [6,9]. Improvement of the heat flux due to switching to
slot nozzles has been measured to be up to 25% [19]. General heat
transfer characteristics made by a slot nozzle have been observed to
be improved even compared to circular multiple jets. For instance,
in cooling of a multichip module, circular multiple jets generated a
blockage in vicinity of the jets leading to a complicate fluid distri-
bution downstream of the impinging location [34]. A comparison
between circular, square, and rectangular nozzles have also shown
that the Nusselt Number for rectangular nozzles in various Rey-
nolds numbers and spacings is 10e20% more than that of circular
and square nozzles [12]. Therefore, it is known that the advantages
of having an impinging flame jet are to improve the heat transfer
significantly, to lower the fuel consumption, and to increase the
productivity. Most of the previous studies on slot nozzle belong to
non-reacting jets and limited studies have been conducted on
impinging flames through slot nozzles.
The present study is different from all the others since it char-
acterizes the heat transfer as a result of a two-dimensional
methane/air premixed impinging flame from a slot burner to a
flat plate. The configuration is also unique since there are two
parallel walls that partially confine a two-dimensional flame
presently. The present configuration leads to different heat flux
characteristics comparing to heat flux due to circular flame
impingement which is already reported. A second peak in heat flux
is obtained experimentally along the target plate. The temperature
of the flat plate is not kept constant and Non-intrusive interfer-
ometry is used to experimentally visualize the impinging flame at
different flow conditions, which is already employed for flames of
methane and LNG in two-dimensional and axi-symmetric non-
impinging burners [2,3,15]. The isotherms are presented in the vi-
cinity of the slot and the plate and heat transfer coefficient is ob-
tained along the plate. A numerical simulation is finally presented
for the same configuration and flow conditions for an equivalence
ratio of 1. The numerical simulation can predict a second peak in
heat flux along the target plate successfully.
2. Material and methods
2.1. Experimental facility
Fig. 1 shows the schematic representation of the experimental
setup. Metered methane and air are fully mixed in a brass cylinder
before entering to a plenum chamber. After mixing of air and
methane, the mixture enters from the bottom side of a cubic
chamber of 220 mm each side with 6 mm thickness. The top surface
is covered by a square plate of 240 mm with 7 mm thickness. The
top plate is screwed to the chamber. The plenum chamber is half
filled with very small stainless steel beads (4 mm in diameter) in
order to produce uniform flow. A honeycomb structure is also
installed to dissipate possible eddies of the flow. The remaining
vacant height is sufficiently enough to eliminate small eddies. The
screwed top plate of the chamber is where the slot nozzle has been
machined with dimensions of 25 mm long and 3 mm wide. The
target plate holder is fixed to a 3D-positioner used to adjust the
distance between the target plate and the slot nozzle. The copper
target plate has the dimensions of 250 mm long, 130 mm wide and
10 mm thick and is horizontally held parallel to the slot nozzle. Ten
calibrated K-type thermocouples with 6 mm spacing from the
stagnation point extending to the wall jet region are utilized to
measure the copper plate temperature (see Fig. 2). Thermocouples
Nomenclature
C Goldstone-Dale equation constant
D diameter (m)
L target surface length (m)
M molecular weight (g/mol)
Nf fringe number
Nu Nusselt number
Pw wetted perimeter (m)
P pressure (pa)
R constant gases (J/K)
Re Reynolds number
T temperature (K)
u velocity (m/s)
Y mole fraction
c Speed of light (m/s)
h heat transfer coefficient (W/m2
K)
k thermal conductivity (W/mK)
n refractive index
q heat flux (W/m2
)
FR firing rate (kW)
A sectional area (m2
)
F fuel rate
Lo Loschmidt number
N number density
Greek symbols
ε fringes displacement (m)
f equivalence ratio
4 phase displacement
l wavelength (m)
m dynamic viscosity (N.s/m2
)
q phase difference
r density (kg/m3
)
t time (s)
y kinematic viscosity (m2
/s)
h effectiveness
Subscripts/Superscripts
act actual
ad adiabatic temperature
f flame
h hydraulic
mix mixture
ref reference
sto stoichiometric
∞ ambient
m molecules
e electron
w wall
M.R. Morad et al. / International Journal of Thermal Sciences 110 (2016) 229e240
230

are embedded in 2.5 mm diameter holes with 9 mm depth in the
backside of the target plate. In order to ensure sufficient contact
between the thermocouple junctions and the target plate, the holes
are filled with copper powder. For each experiment, temperatures
are monitored by a temperature recorder (Lutron BTM-4208SD),
while the ambient pressure and relative humidity are recorded
simultaneously by a pressure sensor (Testo 511) and a humidity
sensor (Samwon SU503B), respectively. A 30 mW HeliumNeon laser
beam with wavelength of ¼ 632.8 nm and optical plates (mirrors
and beam splitters) with diameter of 10 cm are parts of the optical
arrangement. All the interferograms are digitized with a CCD
camera (Artcam-320P) connected to a video recorder through a PC.
Heat generation and absorption systems, including the slot nozzle
chamber and the target plate, are covered up with a transparent
Plexiglas box, with 360 mm long, 250 mm wide and 900 mm height
to avoid air entrainment and disturbances from the laboratory
environment during each experiment.
2.2. Data reduction
The phase information of the laser beam through the flame is a
function of flame refractive index [31]:
4ðx; yÞ
2p
¼
1
l
ZL
0
ðn∞ nðx; y; zÞÞdz (1)
where N¼4/2p denotes the fringe number, n(x,y,z) is the local
refractive index along the light beam path through the flame and
n∞ is the ambient refractive index. Since refractive index along the
light beam path is considered constant for a two dimensional case,
equation (1) can be rewritten as follows:
4ðx; yÞ
2p
¼ ðn∞ nðx; yÞÞ
L
l
: (2)
The local refractive index can then be expressed as:
Fig. 1. Experimental setup. The test chamber is transparent and Mach-Zehnder interferometer is used to visualize the gradient formed in the vicinity of the slot and the target plate
shown in the figure.
Fig. 2. The orientation of the target plate made of copper with respect to the slot
burner. The first thermocouple is installed right above the slot and measures the
temperature of the stagnation point.
M.R. Morad et al. / International Journal of Thermal Sciences 110 (2016) 229e240 231

nðx; yÞ ¼ n∞
Nl
L
; (3)
The corresponding temperature of each fringe can be deter-
mined by applying Gladstone-Dale equation when the local
refractive index is determined [5]:
Tðx; yÞ ¼

n∞ 1
nðx; yÞ 1

T∞; (4)
Based on equation (4), local temperature can be calculated for
any fringe map. The common procedure for data reduction is to
consider line sections on the fringe map and to calculate n(x,y) and
T(x,y) using equations (3) and (4). It is sufficient to calculate
refractive indices and temperatures of all fringes using equations
(3) and (4). Most of the previous studies used molar refractivity of
air in cases of combustion [25,29]. However, an extension of the
Gladstone-Dale equation is employed in this study [35]:
n 1 ¼
1
Lo

A þ
B
l2

Nm 4:46 1014
l2
Ne; (5)
Where Lo is Loschmidt number, A and B are constants relevant to
molecules or atoms, Nm is the number density of molecules and Ne
is the electron number density [1]. Radiation heat flux is generally
neglected because of a very low emissivity in premixed flames [4].
Jet hydraulic diameter, Dh ¼ 4A/Pw, is used as the characteristics
length of the slot nozzle, where A and Pw are the cross sectional area
and the wetted perimeter of the cross-section, respectively. The
corresponding Reynolds number is expressed as:
Re ¼
uexitDhrmix
mmix
; (6)
where mmix can be calculated by applying the following averaging:
mmix ¼
P
miYi
ffiffiffiffiffiffi
Mi
p
P
Yi
ffiffiffiffiffiffi
Mi
p : (7)
Furthermore the equivalence ratio is defined as:
f ¼
ðF=AÞact
ðF=AÞstoic
; (8)
The local convective heat transfer coefficient is computed using
hx ¼ kx;mix w
1
Tfilm Tw

vT
vy

w
; (9)
where ðkx;mixÞw is the conductive heat transfer coefficient of the
fluid impinging to the surface at the surface temperature. This co-
efficient is obtained based on the assumption of binary mixture of
methane and air [21] as
kx;mix ¼
X
n
i¼1
Yiki
Pn
j¼1 Yjjij
; (10)
in which jij is
0:37653

1 þ

mi
.
mj
0:5
Mj Mi
0:25
2
1 þ Mi Mj
0:5
when i s j and is 1 if i ¼ j. The temperature of the flame jet at the
film of the fluid formed near the wall is Tfilm [37], which could be
determined since the temperature field is obtainable in the present
method throughout the vicinity between the target plate and the
slot burner. Nusselt number at any position along the wall could be
expressed as
Nux ¼
hxDh
kx;mix
; (11)
with Dh being the hydraulic diameter of the nozzle. The average
conductive heat transfer coefficient is
kx;mix ¼
1
Tfilm Tw
Z
Tfilm
Tw
kðTÞdT: (12)
Finally, the heat flux could be computed from the relation
q
00
¼h(Tref Tw). Here, Tref is flame temperature. In the present study,
since the temperature field is experimentally obtained for the
whole space between the two plates, the maximum temperature at
each case is chosen as Tref.
2.3. Validation and uncertainty analysis
Uncertainties of measuring devices including rotameters,
manometer and digital thermometer are evaluated by the calibra-
tion of instruments. The maximum flow uncertainties are 7% and
3.5% for the equivalence ratio and Reynolds number, respectively.
The refractive index of the combustion products is computed from
refractive indexes of the mixture of a complete combustion (CO2,
H2O, and N2) taken from Ref. [1] which increases degree of precision
compared to using the refractive index of air. The uncertainty due to
considering constant air and fuel properties is less than 3% [3].
Temperature field in non-impinging flame jets are already vali-
dated using the same interferometry setup (see Figs. 4 and 5 [3]. For
the present impinging flames, the temperature obtained from the
optical method is compared to that of thermocouples installed
along the target wall. The comparison of the two experimental
methods could be seen in Fig. 3a showing about 2% difference at the
impinging point (x ¼ 0 mm), while the difference reduces along the
plate farther from the impinging point. Nusselt number is also
compared between the present optical method and the semi-
empirical relation proposed by Ref. [26] showing a good agree-
ment at Reynolds numbers depicted in Fig. 3b. Based on the method
presented by Ref. [17] the average uncertainties in measuring
Nusselt numbers and heat fluxes are 4.2 ± 2.1% and 3.7 ± 1.9%,
respectively.
3. Experimental observations
Experiments are conducted at three different nozzle to plate
spacing of H ¼ 45.6, 35.3, and 26.3 mm. At each spacing, the
interferometry is performed and isotherms are obtained in the vi-
cinity of the nozzle and the plate. Heat flux could then be calculated
from the temperature data at different firing rates. Details of
different operating conditions is given in Table 1. Here, firing rate is
defined as mass flow of methane times the lower heating value
methane equal to 50 MJ/kg at room temperature.
3.1. Flame isotherms
The effect of the spacing between the nozzle and the flat plate is
illustrated as fringe lines in Fig. 4 for firing rates of 0.05 kW,
0.09 kW, and 0.14 kW. When the flame jet impinges to the flat plate,
the hot combustion products spread out from the stagnation point
to the wall jet region and a boundary layer develops simultaneously
232

on the target plate. The embowed fringes near the plate are clarified
by movement of the decelerated jet flow close to the target. The
isotherms, associated with the raw experimental images shown in
Fig. 4, are obtained from data reduction and are depicted in Fig. 5.
As can be seen, a decrease in nozzle to plate spacing leads to
broader flames and higher temperatures towards the wall. A thicker
region of the temperature gradient normal to the plate is evident at
the maximum present firing rate and minimum spacing
(FR ¼ 0.14 kW and H ¼ 26.3 mm). When the firing rate is increased
and the spacing is decreased, the embowed fringes are shifted
along the target plate outwards. It could be noted that, at the
maximum present firing rate and minimum spacing, the embowed
fringes appear along the half of the plate as complete ellipses as
shown in Fig. 4. This behavior suggests the existence of a turn in
temperature gradient along and close to the surface because the
isotherms are ellipse and there could be two points located hori-
zontally on a single elliptical isotherm with equal temperatures. In
the next section, the heat flux and Nusseld number along the target
plate is extracted from the experimental data to investigate more
details of variations along the half plate.
3.2. Heat transfer characteristics
Heat flux and Nusselt number distribution is extracted from the
isotherm patterns for each experiment along the width of the plate
from the stagnation point (x ¼ 0) outwards (upto x ¼ 35 mm), and
the results are shown in Fig. 6. For the present maximum distance
between nozzle and the plate (H ¼ 45.6 mm), the heat flux is higher
at higher firing rate FR ¼ 0.14 kW and reduces almost linearly when
moving away from the stagnation point. At the stagnation point
however, the heat flux is higher for firing rate equal to 0.09 kW
which is, in the present experiments, corresponding to the
maximum equivalence ratio above the stoichiometric condition
(see Table 1). Although firing rate always increases the heat flux as
it is directly proportional to amount of heat release in the flame, but
the equivalence ratio becomes also influential around the stagna-
tion zone. In fact, it is observed that the higher the equivalence ratio
above the stoichiometry, the taller the height of the flame surface
with the maximum temperature zone. In other words, the inner
zone of unburned gas stretches as the flame speed changes, and the
maximum flame temperature area is enhanced. Therefore, at f¼1.6
the flame is more stretched and the high temperature area is closer
to the plate which increases the heat flux. This effect could be also
seen in the Nusselt number at the stagnation point.
At H ¼ 35.3 mm, the effect of maximum equivalence ratio is not
dominant at the stagnation point because the distance to the plate
is decreased. It is less than the threshold extent at which the rise of
the flame surface due to the equivalence ratio causes more heat flux
to the impinging zone. The heat flux for all firing rates decreases
and converges to an identical value at the middle point (x ¼ 18 mm)
after which, for the two lower firing rates, the heat fluxes remain
converged while decreasing. However, the heat flux distribution at
FR ¼ 0.14 kW does not follow the former trend and becomes almost
unchanged after the middle point. This can be interpreted as the
onset of a phenomenon named as the ”second peak” in heat flux
which is evident in Fig. 6 for the higher firing rate (FR ¼ 0.14 kW)
when the nozzle is close enough to the plate (H ¼ 26.3 mm).
The first peak occurs in the stagnation zone while the second
peak is at x¼ 24 mm which is at 67% of the whole width. The heat
flux at the second peak becomes 85% of the first peak as shown in
Fig. 6. The formation and growth of the second peak could be more
clearly seen in Fig. 7, corresponding to the firing rates FR ¼ 0.1 kW
Fig. 3. (a) Wall temperature comparison between the two experimental methods for Re ¼ 430, f ¼ 1, and H ¼ 35.3 mm. (b) Nusselt number obtained by the present optical method,
compared to semi-empirical relation proposed by Ref. [26].

and FR ¼ 0.16 kW. The equivalence ratio for the both firing rates are
equal to 1 (see Table 1). Therefore, each column of the figure in-
dicates the effect of the nozzle to plate distance on heat flux and
Nusselt number at constant firing rate and stoichiometric condi-
tion. At the lower firing rate, the second peak starts at the minimum
distance to nozzle (H ¼ 26.3 mm) and the heat flux crosses over the
distribution of larger distances before the middle of the plate. After
the middle point of the plate the heat flux reaches a maximum
value again. As the firing rate increases, the amount of the second
peak rises and a birth of a second peak for the medium distance
(H ¼ 35.3 mm) could also be noticed (see Fig. 7 for the medium H at
x ¼ 24 mm). The wall temperature along the plate is illustrated in
Fig. 8 for all firing rates as well as nozzle to plate distances. As it is
depicted, the wall temperature rises with firing rate but remains
almost constant along the wall till 36 mm. However, for the mini-
mum distance where there is a second peak in heat flux as well as
Nusselt number, there is also a peak at the same position in wall
temperature for firing rates greater than 0.09 kW. It is convenient to
define a combustion effectiveness for the present data. Here, the
effectiveness is considered as h¼(Tref T∞)/(Tf T∞), in which Tf is
the open flame temperature obtained experimentally. The open
flame temperature for the same configuration is measured for
equivalence ratios of 1 (Tf ¼ 1950 K) and 1.3 (Tf ¼ 2020 K) reported
in Ref. [3] which is consistent with the value of the flame temper-
ature obtained by thermocouple in Ref. [13] for equivalence ratio of
1. The effectiveness is plotted for different firing rates and spacing
shown in Fig. 9. In fact, here, the effectiveness shows the deviation
of impinging flame temperature with respect to the free flame
temperature. It could be seen that the effectiveness is more than
90% and is not variable considerably along the wall. The wall
temperature itself (see Fig. 8) is also not very variable along the
36 mm width particularly because the flame is two-dimensional
and there is also a flat plate parallel to the target plate at the
level of the slot burner. For all distances, the effectiveness is higher
for stoichiometirc mixture (FR ¼ 0.1 and 0.16). This is more evident
for H ¼ 45.6 mm where the flame has more time for heat transfer
Fig. 4. Experimental fringes from raw images captured by CCD camera at different operation conditions. The rows show three firing rates while the columns illustrate three nozzle
to plate spacing mentioned in the figure.
234

with the environment. For stoichiometric mixture, at the minimum
distance (H ¼ 26.3 mm) the effectiveness associated with firing rate
of 0.1 gives the maximum effectiveness. The temperature for this
particular firing rate and equivalence ratio is the nearest temper-
ature to the open flame temperature. This result is rational due to
the facts that the equivalence ratio is 1, the distance between the
burner and the plate is short with lesser heat loss, and the firing
rate is medium with less acceleration of gases. All these factors
together help to produce higher local temperature in the medium.
Fig. 5. Experimental isotherms at different operating conditions.
Table 1
Different operating conditions.
Firing rate (kW) Mixture flow rate (m3
/s) 105
Mixture velocity (m/s) f Re
0.05 1.69 0.74 0.9 214
0.09 1.80 0.80 1.6 227
0.1 3.39 1.51 1.0 431
0.14 3.51 1.56 1.3 443
0.16 5.10 2.26 1.0 647

4. Numerical simulation
In the present study, FLUENT was used to model the flow field
and heat transfer for the flame impinging on the target flat surface.
The general form of continuity, momentum, and energy equations
for two-dimensional laminar reacting flow can be written as:
V$ðr u
!
Þ ¼ 0
V$ðr u
!
u
!
Þ ¼ Vp þ V$ t
! þ r g
!
V$ð u
!
ðrE þ pÞÞ ¼ V$ kVT þ t
!$ u
!

P
i
hiJi
!
þ Sh
(13)
in which r is the density, u is the velocity vector, p is the static
Fig. 6. Heat flux and Nusselt number distribution for different firing rates at distances of (a) H ¼ 45.6 mm (b) H ¼ 35.3 mm, and (c) H ¼ 26.3 mm.
Fig. 7. Heat flux and Nusselt number distribution for different nozzle to plate distances for f¼1. Firing rates are (a) FR ¼ 0.1 kW and (b) FR ¼ 0.16 kW.
236

pressure, t is the stress tensor, T is the temperature, k is the thermal
conductivity, hi is the enthalpy of the species i, Sh is the heat of
chemical reaction, and E ¼ h p/r þ u2
/2 is the total energy. The
species transport equations are
V$ðr u
!
YiÞ ¼ V$ Ji
!
þ Ri þ Si
Ji
!
¼ rDi;mVYi DT;iVT=T
(14)
where Ji is diffusion flux of species i, Di,m is the mass diffusion
Fig. 8. Wall temperature at different firing rates and nozzle to plate distances of (a) H ¼ 26.3 mm, (b) H ¼ 35.3 mm, and (c) H ¼ 45.6 mm.
Fig. 9. Effectiveness at different firing rates and nozzle to plate distances of (a) H ¼ 26.3 mm, (b) H ¼ 35.3 mm, and (c) H ¼ 45.6 mm.

coefficient of species i, Di,m is the thermal diffusion coefficient of
species i, Yi is the mass fraction of species i, and Ri is the net rate of
production of species i by chemical reaction.
4.1. Computational domain
The modeling of the problem was done in Gambit 2.0, and the
schematic of this model along with the boundary conditions are
shown in Fig. 10. The impinging or target surface is shown by the
line CD, while the line AB is the base wall on which the two
dimensional inlet slot is constructed. The symmetry line shows the
axis of the slot. no-slip boundary condition was applied on the
target wall for both components of velocity. Since the target surface
temperature was variable along the surface, the experimentally
obtained data was imposed as plate temperature in the present
study. The atmospheric pressure boundary (pressure outlet) was
considered at a sufficiently large distance from the nozzle so that a
zero gauge pressure could be applicable. Methane and air (23% O2
and 77% N2) with an equivalence ratio of 1 is considered for the
inlet boundary condition. At the inlet fully developed parabolic
velocity profile was assumed as
u ¼ U 1

x
Dh=2
2
!
; (15)
where U is half of the maximum velocity, and Dh is the hydraulic
diameter. On the symmetry line of the burner the boundary con-
ditions were zero gradients of u with respect to both normal and
parallel directions.
4.2. Computational procedure
A fine non-uniform grid was used in the flame region and also in
the region near the target surface, while grid independency was
attained. Steady state physics is solved using a second order up-
wind scheme. A laminar combustion species transport model was
used with Arrhenius rate equation to determine the rate of for-
mation of the species, based on simplified one step global mecha-
nism. Constant initial velocity, temperature and mass fractions
were used over the entire computational domain. The flow field for
non-reacting case was calculated first, with 700e900 iterations.
Then the mixture was ignited by artificially assigning a temperature
of 1800 K at the nozzle exit. Solution converged in about 24,000 to
29,000 iterations. Discrete Ordinate method is used to simulate
radiation in the computational domain with coefficient and char-
acteristics of gray gases as proposed by Ref. [28].
4.3. Numerical results
Numerical simulation was carried out using commercial CFD
software (FLUENT) for the stoichiometric condition at FR ¼ 0.1 kW.
Fig. 10. Computational domain and boundary conditions.
Fig. 11. Heat flux distribution for FR ¼ 0.1 kW and f ¼ 1. The nozzle to plate distances are (a) H ¼ 45.6 mm, (b) H ¼ 35.3 mm, and (c) H ¼ 26.3 mm.
238

The results could be seen in Fig. 11 for the largest, the medium, and
the smallest spacing. As could be seen, both the heat flux variation
and the position of the peaks are captured in the simulation. The
second peak is also appeared for the shortest spacing in the nu-
merical results. The advantage of the simulation is that the flow
velocity could also be examined numerically since there is a lack of
experimental data of velocity field. The simulation slightly un-
derestimates the heat flux in most of the cases which could be due
to global reaction mechanisms as well as numerical uncertainties
[8]. We present the numerical results for both components of the
velocity field namely; normal and parallel to the target plate. Lets
focus on the shortest spacing since the second peak is only asso-
ciated with this spacing. The variation of normal velocity compo-
nent is shown in Fig. 12 at four different distances from the nozzle.
The distances are started from Z ¼ 15 mm to Z ¼ 26 mm which is
0.5 mm less than the distance of the target plate from the nozzle in
this case. It is evident that near the center of the nozzle (around
x ¼ 0), the normal velocity is positive due to air motion causing by
the flame. This component has the highest value at the center and
decreases by getting away from the nozzle horizontally. At a
particular width from the center the normal component becomes
zero and then negative meaning that the direction of the normal
velocity changes at the present configuration. The negative value of
the normal velocity reaches a minimum value (or maximum
downward velocity) and obviously tends to zero for further width
away from the flame. This maximum normal downward velocity
becomes off center as one moves towards the plate. At Z ¼ 26 mm,
the maximum normal downward velocity is located at x ¼ 25 mm
which is located exactly at the width where there is a second peak
of the heat flux in Fig. 11. It is useful to investigate the parallel ve-
locity simultaneously to get more information. The variation of the
parallel velocity is also plotted along the width of the target plate at
the same normal distances from Z ¼ 15 mm to Z ¼ 26 mm and could
be seen in Fig. 12.
It is obvious that the parallel velocity is zero at the center of the
flame up to the target plate and increases depending on the normal
position from the nozzle. This variation is associated with the
present configuration in which there are walls in the two extremes
of the normal position. At Z ¼ 25 and 26 mm, which are near the
plate, there is a peak in parallel velocity after which the velocity
decays. After the stagnation point where the flame impinges to the
plate at the center, the gas first accelerates parallel to the plate and
then decelerates due to the plate boundary layer. At Z ¼ 26 mm, the
deceleration brings the fluid adjacent to the plate to zero parallel
velocity at x ¼ 25 mm and then the parallel velocity becomes
negative for x 25 mm. This means that there exists a second
stagnation point at x ¼ 25 mm which explains why the heat flux has
a second peak (exactly at x ¼ 25 mm) at this spacing and firing rate.
5. Conclusion
Experimental and numerical examinations are performed on
laminar impinging methane/air premixed flame heat transfer to a
target flat plate using a two-dimensional slot nozzle. Three dis-
tances (H ¼ 45.6, 35.3, and 26.3 mm) between the nozzle and the
target plate was used with five different firing rates. The heat flux
was obtained along the plate and its maximum value was found to
be exactly above the nozzle which is the main stagnation point.
However, a second peak in the heat flux was recognized corre-
sponding to the minimum nozzle distance (26.3 mm) and higher
firing rates (more than 0.1 kW). Numerical investigation for firing
rate of 0.16 kW and equivalence ratio of f ¼ 1 revealed that there is
a stagnation point along the plate at x ¼ 25 mm which is exactly the
same point where the second peak in heat flux occurs.
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