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Applied Thermal Engineering 31 (2011) 103e111
Contents lists available at ScienceDirect
Applied Thermal Engineering
journal homepage: www.elsevier.com/locate/apthermeng
A methodology to model flow-thermals inside a domestic gas oven
Hiteshkumar Mistry a, *, S. Ganapathisubbu a,1, Subhrajit Dey a, Peeush Bishnoi a,1, Jose Luis Castillo b
a
b
Energy and Propulsion Technologies, GE Global Research, 122, EPIP, Whitefield Road, Bangalore 560 066, Karnataka, India
Mabe Mexico S de RL de CV, Acceso B#406, Parque Industrial Jurica, Queretaro 76120, Qro., Mexico
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 9 March 2009
Accepted 21 August 2010
Available online 25 September 2010
In this paper, the authors describe development of a CFD based methodology to evaluate performance of
a domestic gas oven. This involves modeling three-dimensional, unsteady, forced convective flow field
coupled with radiative participating media. Various strategies for capturing transient heat transfer
coupled with mixed convection flow field are evaluated considering the trade-off between computational time and accuracy of predictions. A new technique of modeling gas oven that does not require
detailed modeling of flow-thermals through the burner is highlighted. Experiments carried out to
support this modeling development shows that heat transfer from burners can be represented as nondimensional false bottom temperature profiles. Transient validation of this model with experiments
show less than 6% discrepancy in thermal field during preheating of bake cycle of gas oven.
Ó 2010 Elsevier Ltd. All rights reserved.
Keywords:
CFD
Gas oven
Convection
Radiation
Bake cycle
Thermal load
1. Introduction
Domestic ovens either use electrical coil heating or gaseous fuel
burning as a means of providing thermal energy to an enclosed
cavity. These ovens heat the food being cooked inside primarily
through radiation and convection. Oven preheat time, cooking
uniformity and time for cooking are some of the metrics that an
oven designer needs to consider. Energy efficiency of these ovens is
also an important consideration as future ovens might have
labeling based on energy consumption [1]. From a designer’s point
of view, it is useful to have a predictive tool that can provide
information about the thermo-convective flow field inside the oven
cavity. Such a tool will also help understand contribution of various
sources (such as vent, front glass door) to energy loss mechanisms
and hence help to design energy efficient products.
Development of a numerical model to capture the physics inside
oven cavities involves modeling three-dimensional, unsteady,
forced/mixed convection flow coupled with radiative participating
media. The model should be able to account for heat losses through
the oven walls and the vent, characteristic features of the flow field
inside the oven cavity and the relative magnitudes of convective
and radiative heat transfer. An earlier work of the authors [2] and
* Corresponding author. Tel.: þ91 80 4088 2658; fax: þ91 80 28412111.
E-mail address: [email protected] (H. Mistry).
1
Currently affiliated with Siemens Corporate Technology, Bangalore, Karnataka,
India.
1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.applthermaleng.2010.08.022
an article published by Abraham and Sparrow [3] describe different
approach to model heat transfer in an electric oven.
Capturing energy transfer from the source (burners) to the
cavity in gas ovens provides additional complexity due to the
nature of heat release (combustion) and the associated flow field
development close to the burners. It is possible to simplify the
burner by assuming it as a heat source at a designated temperature.
Wong et al. [4] in their CFD model development for industrial gas
ovens assumed burners as a circular object with a fixed wall
temperature. Mirade et al. [5] modeled an industrial biscuit baking
oven that used 56 gas burners, unevenly distributed. To account for
this uneven temperature profile, they split the burner region into
various sections and provided varying temperature profiles for each
section based on limited measurements. However, the authors have
not come across any effort to model domestic gas ovens, in which
the bottom burners are generally concealed below a metal plate,
often referred to as “false bottom plate”.
2. Experimental details
A GE freestanding gas range was used for experiments, as shown
in Fig. 1. This range consists of an inner cavity (0.60 m 0.48 m 0.49 m) with insulated walls, two burners: a top burner
(broil) and a bottom burner (bake). The ratings of broil burner and
bake burner are 3.96 kW and 4.69 kW respectively.
Fig. 2 is a schematic of the expected flow fields in the burner
zone. The natural gas fuel enters the burner through an orifice that
entrains primary air from the surroundings. This lean mixture (A/F
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
Fig. 1. Gas Oven.
ratio w 8.5) comes out through the burner ports and mixes with the
secondary air available. NortonÔ surface igniters (made of SiC) are
used to initiate combustion and are located at the rear end of the
burner. Once combustion starts, high temperature blue colored
conical flames appear at burner ports which is characteristic of
premixed combustion. To ensure safety of operation, a dual bimetallic valve opens gas flow into burners only when the surface
igniter is ON. This enables immediate combustion of the gas as they
exit through burner ports. Bake burner is generally concealed
below a metal plate (known as false bottom) with a radiation
deflector plate below it (Fig. 2). The provision of a deflector plate
over gas burner helps to heat up the false bottom wall uniformly.
There are also openings in the false bottom through which hot gas
enters into the cavity.
Normal operation of oven involves heating the cavity until it
reaches a set point temperature and cyclic switching (ON/OFF) of
burners that is controlled with a thermostat. While conducting
experiments, this thermostat was by-passed and the glow bar was
powered independently. To facilitate steady state operation and
better monitoring of burner heat input, the experimental set-up
included a volume flow meter (Rota meter) for measuring gas flow
into burners and a pressure sensor to monitor the pressure.
For oven surface temperature measurements and cavity gas
temperature measurements, J (IroneConstantan) type thermocouples (2.54e-04 m) with SS sheathing were used. These thermocouples were calibrated within 1% of a reference thermometer
traceable to ITS-90 in liquid bath. It is well known that thermocouple measurements are prone to offset due to heat transfer in the
Fig. 2. Schematic of flow inside the burner zone for a gas oven.
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
105
Fig. 3. Temperature measurement location.
exposed ambient. This is due to the fact that temperature of the
junction, which is the equilibrium temperature, is not the
temperature of the medium. Energy balance performed on a thermocouple junction at temperature Tc exposed to a gas at temperature Tg yields the following relationship:
It can be seen that the difference between the gas temperature
and the thermocouple reading is due to transient response of the
thermocouple (first term on the right side of equation), conduction
heat transfer through the thermocouple (second term), radiation
heat transfer with surroundings (third term). A thermocouple
located at center of the oven to measure air temperature participates in radiation with heater elements and the wall. These errors
were minimized by providing radiation shields and avoiding direct
viewing of thermocouple tip with heater surfaces. Highly polished
aluminum foils were used as radiation shields. Thermocouple wires
of 10e15 D length were kept inside the oven to minimize conduction error.
Maximum uncertainty in temperature measurements was
arrived as 9%, inclusive of all error/uncertainty components. This
includes less than 2% variation observed during repeatability trials;
for thermocouples distributed inside the oven cavity, a variation of
2% of temperature data was observed when thermocouple location
was varied within 0.05 m in space. The remaining 5% attributed to
thermocouple participating in heat transfer. As indicated by the
transient term of Eq. (1), it will require small diameter bare wire
thermocouples to exactly track the transient slope. In order to
overcome the sluggish response of thermocouples and to minimize
radiation losses, thermocouples were buried inside an aluminum
Fig. 4. TC location @ nine points inside the oven cavity.
Fig. 5. IR snapshot of false bottom of oven.
Tg Tc ¼
rc Cpc d vTc
4h
vt
þ
kc d v2 Tc
4
4
s3
T
þ
T
c
h;w
4h vx2c
(1)
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
Fig. 6. Schematic of Gas oven.
Fig. 8. Bake burner.
rod and heating of the aluminum rod was tracked. This also
simulates a thermal load used in oven experiments. A rod of
(1 inch 1 inch 20 inch) size was used for these trials.
Temperature measurements were carried out using thermocouples (TC) at various locations within the cavity for the purpose
of validation (Figs. 3 and 4). Fig. 4 shows the location of thermocouples within the cavity (at corners of cuboid). A naming
convention was used to compare these data with CFD model
results. For example, thermocouple at Top Left corner towards the
Back wall of oven cavity was named TLB. Thus BRF locates the
thermocouple positioned at bottom right corner of cuboid towards
the front door. Surface thermocouples pasted to the false bottom
were used for obtaining temperature profile of the false bottom
plate (discussion about the need for measuring false bottom is
postponed till next section). Since TCs provide point measurements, to obtain a temperature profile of the false bottom would
need many TCs to satisfy reasonable resolution in measurements.
Hence Infrared Thermometry (IR) was used simultaneously to
identify the temperature hot spots on the false bottom. In order to
overcome the ambiguity related with emissivity settings, a black
body (emissivity ¼ 0.95) pasted on to the surface was used for
calibration and a TC was also pasted to verify the temperature
readings of IR camera. FLIRÔ IR results (Fig. 5) clearly reveal
a pattern with a symmetry existing in x direction. Based on the IR
inputs, few critical locations were chosen for the TC measurements.
3. Numerical modeling
accounting for the surface-to-surface radiation effects. The DO
model was selected based on the applicability and accuracy required
for the present objectives. The DO model solves the radiative transfer
equation for a finite number of discrete solid angles, each associated
with a vector direction fixed in the global Cartesian system can be
written as
dIð
Z4p
! !
sT 4
r; sÞ
! !
! ! ! ! Ið r ; s ÞF s ; s 0 dU0
þ ða þ ss ÞIð r ; s Þ ¼ an2
p
ds
0
(2)
The model solves for as many transport equations, as there are
directions. The implementation in FLUENT solver uses a conservative variant of the DO model called the finite-volume scheme [8],
and its extension to unstructured meshes [9]. The weighted-sumof-gray-gases model (WSGGM) was used for total emissivity
calculation of combustion products over the distance. The basic
assumption of WSGGM is that the total emissivity of “i” number of
gases over a distance “s” can be written as
3¼
I
X
i¼0
a3;i ðTÞ 1 eki ps
(3)
The FLUENT solver uses values of a3, i and ki obtained from [10].
These values depend on gas composition and temperature of the
gas. When the total pressure is not equal to 1 atmospheric pressure,
scaling rules for ki are used as described in [11].
3.1. Governing equations and radiation model
3.2. Modeling approach and computational domain
Among the combustion products, carbon dioxide and water vapor
act as primary participating media in radiation within the oven
cavity [7]. The radiation model used in current studies, Discrete
Ordinate (DO) model, solves for media participation in addition to
Fig. 6 shows a schematic of the gas oven and clearly indicates the
coupling of the oven cavity zone and burner zone through the false
bottom wall and the openings in it. Fig. 7(a) and (c) show various
Fig. 7. CFD modeling computational domains of gas oven.
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107
1
Analytical
CFD: Coarse Grid
CFD: Medium Coarse
0.9
CFD: Refined Grid
0.8
Vx/Ve
0.7
0.6
0.5
0.4
0.3
Fig. 9. Computational domain with single burner port for grid sensitivity studies.
0.2
0
2.5
5
7.5
10
12.5
15
x/D
Fig. 10. Comparison of centerline velocity decay with analytical calculation.
Considering the complexity of the geometry of the internal
volume of the oven cavity, it was decided to generate a tetrahedral
volume mesh. The grid size of the oven cavity was largely decided
by the mesh resolution near the false bottom openings, gasket
opening and the vent outlet. The surface mesh was generated using
GAMBIT 2.1.6 and volume mesh using T-Grid 3.6.8. The commercially available solver FLUENT 6.2.16 has been used for the current
studies.
3.3. Material properties
The combustion products comprise of predominantly carbon
dioxide, water vapor, nitrogen and carbon monoxide. An ideal
incompressible formulation for density, mixing law for specific
heat, mass weighted mixing law for thermal conductivity and mass
weighted mixing law for dynamic viscosity (as available in Fluent
version 6.2.16) have been used towards material properties of the
working fluid. The oven sidewalls, heater and door have been
modeled using effective conductive resistance instead of modeling
the detailed geometries of these features.
CFD_coarse
CFD_medium
CFD_Refined
Analytical
1.4
1.2
1
x/D
CFD modeling approaches possible for the gas oven. The approach
highlighted in Fig. 7(a) involves modeling of the full gas oven and
requires a very refined grid because of the extremely small length
scales in burner ports and relatively coarse grid within the oven
cavity region. Fig. 7(b) shows an approach of segregating the oven
cavity and burner region and modeling them separately. This
approach would give the temperature profile of false bottom and
the flow parameters of hot gas at false bottom openings from
burner zone that can then be used as inputs for modeling the oven
cavity interiors. Fig. 7(c) shows an approach of modeling the oven
cavity only. This modeling requires experimentally measured
temperatures on the false bottom and of the hot gas streams
through the false bottom openings. This approach is based on the
assumption that the physical phenomenon inside the oven cavity
can be captured if hot gas entry from false bottom openings and
heating of false bottom are modeled correctly. The first two
approaches require higher grid resolution compared to the last
approach. It is however necessary at this point to do a grid sensitivity study to quantify grid counts for burner modeling in the first
two approaches before adopting the final approach.
Fig. 8 shows bake burner below the false bottom of the oven
cavity. There are 53 burner ports with 0.075-inch diameter each on
each side of burner through which hot gas issue out. A judicious
choice led us to consider a computational domain with single
burner port and axial symmetry shown in Fig. 9 for quick assessment of grid resolution studies. Fig. 9 shows that x-direction and
r-direction have been considered as axial direction and radial
direction for flow, respectively. The three levels of grid: coarse,
medium and fine with 0.07 million cells, 0.08 million cells and 0.2
million cells, respectively, were considered to do a comparative
study for grid sensitivity. The numerical predictions of axial velocity
decay and half jet width from the above-described model were
compared against analytical calculations [6]. Figs. 10 and 11 show
the comparison between analytical results and numerical results for
axial centerline velocity decay and half jet width respectively. It is
clear that the best agreement was achieved with the finest grid so
far and still there was an indication of need for further refinement.
However, the effect of interaction of adjacent jets could be one more
reason for not having a very good agreement against the analytical
prediction, even with the fine grid. The requirement of more than
0.2 million cells for one array of burner port region translates in to
a huge grid count of approximately 22 million cells for the burner
zone, which makes the first two approaches prohibitive. The
thermal field prediction in oven cavity is most important for food
cooking from end-use point of view. The expected design changes in
the burner are minimal in the near future. Hence, it was decided to
do further studies with approach shown in Fig. 7(c).
0.8
0.6
0.4
0.2
0
5
7.5
10
12.5
15
17.5
Half Jet Width (r/D)
Fig. 11. Comparison of half jet width with analytical calculation.
20
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
Su c tio n P re ss ur e
(Pa)
0.00
-1.00
-2.00
-3.00
-4.00
-5.00
-6.00
300
450
600
750
900
1050
1200
TFalse Bottom (K)
Fig. 14. Suction pressure at vent outlet ¼ f (TFalse
The oven sidewalls were modeled using effective (conductive)
thermal resistance approach. The outside surfaces of the oven wall
and the glass door were modeled as a combination of convective
and radiative heat transfer interaction with the ambient. The gasket
opening and vent outlet were specified as pressure boundary
conditions. A numerical suction pressure was applied at the vent
outlet to avoid reversed flow, due to numerical instability during
iteration start up and it was found to be a function of the average
temperature of false bottom as indicated in Fig. 14. The relationships highlighted in an earlier work by Mistry et al. on electric oven
[2] for bake heater was found to be applicable in the current
studies, probably because of similar cavity dimensions and proximity of the bake heater with false bottom wall of the current oven.
The gasket opening has been modeled using pressure inlet BC with
atmospheric pressure.
Fig. 12. Schematic of false bottom wall.
Among the combustion product species, carbon dioxide and
water vapor act as the primary participating media in radiation. The
weighted-sum-of-gray-gases model [9] has been used to calculate
absorption coefficient of the mixture products. The emissivity
values for heater and sidewall were taken as 0.85 and 0.9, respectively, based on in-house IR camera measurements. The emissivities for the tin oxide coatings on the inner glass facing the oven
cavity (highly reflective) and outer glass facing ambient were taken
as 0.2 and 0.88, respectively.
3.4. Boundary conditions
Fig. 5 shows IR snapshot of the false bottom temperature profile.
This snapshot revealed a definite temperature profile on the false
bottom wall. It was further quantified by measuring temperatures
at various locations using K-type thermocouples (TC). Fig. 12 shows
a schematic of the false bottom wall in XeZ plane. For purpose of
generalizations, the temperature readings were normalized with
respect to the maximum temperature on the false bottom in both
the X and Z directions and it is presented in Fig. 13. Curve fitting to
the normalized temperature profiles help obtain a generalized rule
for the temperature boundary condition to be imposed on the false
bottom as a function of space and the maximum temperature,
which in turn would be related to the fuel flow rate.
Steady state validation of the gas oven was conducted before
going on to modeling the transient preheating cycle. The steady
state solution gives an opportunity to check the “effective” thermal
conductivities of the composite wall material. Figs. 3 and 4 show
temperature measurement locations for steady state validation
except the thermal load that was used for the transient cases. The
numerically predicted temperature of gas at nine locations inside
the cavity and temperature on the surface of the oven door and
both sides of the cavity walls were compared against experimentally measured temperature for the steady state validation.
1
0.9
T /T m a x
0.98
4. Results and discussion
T /T m a x
1.00
Bottom).
0.95
0.93
0.8
0.7
0.6
0.90
-0.2 -0.15 -0.1 -0.05 0
0.05
0.1
0.15
0.2
0.5
0
0.1
0.2
0.3
x (m)
z (m)
Along x-axis
Along z-axis
Fig. 13. Normalized temperature plots on false bottomwall.
0.4
0.5
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
109
Fig. 15. Grid sensitivity studies.
Fig. 17. Time step independence studies.
4.1. Steady state validation
The three levels of grid: coarse, medium and fine grid with
0.5 MM cells, 1 MM cells and 2 MM cells, respectively, were
considered to do grid sensitivity studies for thermal field prediction
with constant fuel flow rate to the burner. Fig. 15 shows difference in
thermal field prediction at nine locations within oven cavity from
medium to fine grid and coarse to fine grid. It is clear from the figure
that the difference in temperature prediction from medium to fine
grid and coarse to fine was of the order of 4 K (w0.5%) lesser than
uncertainty in TC measurement. So, it was decided that the coarse
grid with 0.5 MM cells was adequate for future studies with no
significant loss in accuracy and a permissible turn-around time.
As discussed in the previous section, normalized temperature
plots (XeZ plane) on false bottom wall were obtained based on
experimental data, as a function of the maximum temperature of
false bottom wall for different burner fuel flow rates. The steady
state temperature profile of false bottom wall for different fuel flow
rates were obtained by incorporating experimentally measured
maximum temperature of false bottom in the normalized equations
in both X and Z directions. Experimentally determined temperatures of the hot gas flowing in through the four openings on the false
bottom were also used as boundary conditions for the CFD model. As
for flow rates through these openings, equal mass split of the total
gas flow rate was assumed & implemented. Fig. 16 shows percentage
discrepancy between experimentally measured temperature and
numerical results at nine points within the cavity, oven walls and
glass door for 6.7e-05 m3/s, 1.0e-04 m3/s and 1.3e-04 m3/s fuel flow
rates in steady state condition. From the temperature uniformity
point of view, 10% discrepancy in prediction is reasonable. Fig. 16
shows that the discrepancy observed in all the present cases was
less than 30 K (w6%). These results validate the modeling
approach with false bottom temperature profile with respect to
computationally costlier options of full-scale burner & combustion
modeling to predict the right thermal field inside the cavity.
4.2. Transient validation
It is a common practice to use a load inside the oven to simulate
the food being cooked for transient validation studies. This has also
been demonstrated & validated in an earlier work [2]. The transient
studies of gas oven were done at design fuel flow rate in gas oven
during preheating. Time step independence studies were initially
carried out and it was identified that a time step size of 10 s would
be reasonable for carrying out reliable computations for the preheating cycle (typically of the order of 20 min). Fig. 17 shows
numerical prediction of the thermal load temperature for three
choices of time steps: 1 s, 5 s and 10 s at the design fuel flow rate
supplied to the oven. The difference in thermal load temperature
prediction was of the order of 1% when changing from 1 s to 10 s. It
is important to note that numerical solution with time step more
Fig. 16. Discrepancy in steady state thermal field prediction and experimental results for different fuel flow rates.
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
experimental measurement of these high temperature low velocity
flows through these openings is not an easy task. Standard hot wire
probes need calibration at these temperatures. Otherwise one has to
resort to non-intrusive optical techniques such as Particle Image
Velocimetry. Varying the mass flow rate through the openings by
20% (in all the openings and also uneven distribution between holes
closer to front end of cavity and rear end) did not alter the temperature predictions in the thermal load. It was thus concluded that use
of equal mass flow rate BC at false bottom openings in gas oven
modeling was reasonable enough. Moreover, the discrepancy
between experimental results and numerical prediction of thermal
load temperature was of the order of 6%, which was within the
acceptable limit. These results further validated the simplified
approach in transient studies.
Fig. 18 shows sensitivity study of transient thermal boundary
conditions at false bottom wall and its openings. Fig. 18(a) shows
comparison of numerical prediction against experimentally
measured temperature of thermal load when steady state false
bottom opening gas temperature was specified in model during
whole duration of bake preheating. It is interesting to note that the
same discrepancy (w6%) was observed between numerical prediction and experimental results when compared with transient
temperature variation of false bottom as input. Fig. 18(b) shows
comparison of experimentally measured temperature of thermal load
with numerical prediction when steady state false bottom temperature profile specified in model during whole duration of bake preheating. There was a significant change in numerical prediction when
compared with transient temperature profile of false bottom as input.
5. Conclusions
Fig. 18. Sensitivity studies of transient thermal boundary conditions at false bottom
wall and openings.
A CFD based methodology has been established for modeling
heat transfer and fluid flow inside a residential gas oven. In this
approach, heat transfer from oven burners have been represented as
wall temperature boundary conditions of false bottom plate that
conceals the burner. Experiments carried out with infrared thermography and thermocouples show that false bottom temperature
field can be represented in a non-dimensional form with reference to
its maximum temperature. It was also seen that false bottom plate
thermal profile was independent of gas flow rates. Transient thermal
field evolution during bake cycle showed no sensitivity (within 20%)
to gas flow rate variations through false bottom openings.
Steady state validation of thermal field at various locations
inside the oven cavity and transient validation with a thermal load
showed 6% discrepancy with experimental data. This tool can be
used to predict oven performance parameters such as preheating
time and thermal uniformity. This exercise also shows that thermal
field evolution in the cavity is highly sensitive to the thermal
transients of the false bottom.
Acknowledgements
than 10 s indicated divergence. Hence, it was decided to do further
studies with 10 s time step for quick turn-around time and no
significant loss in accuracy. However, initial part of the solution (up
to 30 s) was obtained with 0.5 s time step discretization because of
numerical stability.
The modeling approach with temperature profile BC at false
bottom wall requires amount of mass flow rate of hot gas at false
bottom openings as input. Fig. 12 shows schematic of false bottom
wall with four openings. Though it is logical to assume equal mass
flow rates through all the openings, presence of food load closer to
any of these openings may alter this distribution. Thus the authors
decided to do sensitivity studies of mass flow rate coming in to
the cavity through these openings. It may be noted here that
We would like to thank Francisco Anton, R & D Manager, MABE T
& P, Mexico, Todd Graves, Business Program Manager, GE Consumer
and Industrial for their valuable inputs and support without which
this work would not have been possible. We would also like to thank
Balaji Parthasarthy, Amol Mulay, Pravin Naphade and Christopher
Omalley of GE Consumer and Industrial for their participation and
contributions in various discussions on modeling approaches.
Nomenclature
B
BC
oven depth
boundary condition
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H. Mistry et al. / Applied Thermal Engineering 31 (2011) 103e111
CFD
COT
Cp
D
I
T
TC
W
a
d
h
k
m
n
p
!
r
s
!
s
!0
s
sec
3
k
r
V
U’
s
ss
computational fluid dynamics
centre oven temperature
specific heat
discrepancy
radiation intensity
temperature
thermocouple
oven width
absorption coefficient
thermocouple tip diameter
convection heat transfer coefficient
thermal conductivity
mass flow rate
refractive index
sum of the partial pressures of all absorbing gases
position vector
path length
direction vector
scattering direction vector
second
emissivity
absorption coefficient of gas
density
phase function
solid angle
stefan boltzmann’s constant
scattering coefficient
Subscripts
LB
lefteback
LF
leftefront
Max
maximum
RB
RF
a
c
f
h, w
mix
111
righteback
rightefront
air
thermocouple
fuel
heater or oven wall
mixture
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