Applied Thermal Engineering 26 (2006) 2448–2456
www.elsevier.com/locate/apthermeng
Modeling of transient natural convection heat transfer in electric ovens
Hitesh Mistry
a
a,*
, Ganapathi-subbu a, Subhrajit Dey a, Peeush Bishnoi a, Jose Luis Castillo
b
General Electric ACFD Lab, GE Global Research Centre, 122, EPIP, Whitefield Road, Bangalore 560 066, Karnataka, India
b
Mabe Mexico S de RL de CV, Acceso B #406, Parque Industrial Jurica, Queretaro 76120, Qro., Mexico
Received 22 December 2005; accepted 10 February 2006
Abstract
Prediction of transient natural convection heat transfer in vented enclosures has multiple applications such as understanding of cooking environment in ovens and heat sink performance in electronic packaging industry. The thermal field within an oven has significant
impact on quality of cooked food and reliable predictions are important for robust design and performance evaluation of an oven. The
CFD modeling of electric oven involves three-dimensional, unsteady, natural convective flow-thermal field coupled with radiative heat
transfer. However, numerical solution of natural convection in enclosures with openings at top and bottom (ovens) can often lead to
non-physical solutions such as reverse flow at the top vent, partly a function of initialization and sometimes dependent on boundary
conditions. In this paper, development of a physics based robust CFD methodology is discussed. This model has been developed with
rigorous experimental support and transient validation of this model with experiments show less than 3% discrepancy for a bake cycle.
There is greater challenge in simulating a broil cycle, where the fluid inside the cavity is stably stratified and is also highlighted. A comparative analyses of bake and broil cycle thermal fields inside the oven are also presented.
2006 Elsevier Ltd. All rights reserved.
Keywords: CFD; Natural convection; Radiation; Electric oven; Cooking; Thermal load
1. Introduction
Domestic ovens, both gas and electric ranges are common appliances used for cooking. The thermal field within
an oven has significant impact on quality of cooked food
and reliable predictions are important for robust design
and performance evaluation of an oven. The present study
covers detailed approach of constructing numerical model
of electric oven. While extensive experimental work goes
into helping build a robust CFD model, the final outcome
is a flexible, predictive tool based on CFD methodologies.
Food is cooked in oven by radiative heating, convective
heating or a combination of both. Cooking cycle with heat
generated only from top heater is known as broil cycle and
cooking mainly through the bottom heater is known as
bake cycle. The typical bake cycles involve top heater
cycling at less than half load to enhance heat transfer.
*
Corresponding author. Tel.: +91 80 250 32658.
E-mail address: [email protected] (H. Mistry).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.applthermaleng.2006.02.007
Broiling utilizes advantage of the radiation from the heater
to rapidly heat the top of the food, which promotes browning and suppresses the natural convection current since the
hot air is blocked by the ceiling of the oven. In bake cycle,
heating primarily takes place because of buoyancy driven
hot air flow. Nature of heat transfer mechanism plays a
critical role in quality of food. For example, natural convection fluid flow is important in maintaining the quality
of delicate food products that require a dry atmosphere
(e.g. cream puffs, pastry shells).
The CFD modeling of electric oven involves threedimensional, unsteady, natural convective flow field coupled with radiative heat transfer. A series of papers
published by Abraham and Sparrow [1–6] consider heat
transfer in vented enclosures involving radiation when bottom heater is operating. These set of papers involving
experimental and numerical studies discuss the importance
of modeling buoyancy forces directly rather than using
pseudo-density difference in the model, sensitivity studies
of thermal load and measurement probe with respect to
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
2449
Nomenclature
3
Rayleigh number bgDTL
am
temperature (K)
wattage (W)
heat transfer coefficient (W m2 K1)
thermal conductivity (W m1 K1)
specific heat (J kg1 K1)
thermocouple tip diameter (m)
density (kg m3)
Stefan Boltzmann constant (W m2 K4)
emissivity
velocity of air (m s1)
pressure (Pa)
length of thermocouple (m)
centre oven temperature
their radiative properties. Though heat transfer in enclosures with bottom heating has been studied [1–7], researchers have not attempted thermal field prediction for broil
cycle. In this paper, CFD modeling of an electric oven cavity to simulate bake and broil cycles has been discussed;
stably stratified flow being a characteristic of the latter.
2. Experimental details
A typical freestanding electric range was used for experiments as shown in Fig. 1 with the Cartesian co-ordinate
system. This range consists of an inner cavity with insulated walls and hinged front door, and two heating
elements—a top-heating element (broil) and a bottomheating element (bake). The cross section of the heater consists of Ni–Cr wire placed within MgO filled Incoloy
sheath. The cavity has a vent located on the rear side of
the top wall of the cavity for continuous removal of hot
and humid air. There is a deliberate leakage path known
as gasket opening at the front door, which entrains fresh
air. Heating of the cavity (oven set point) is controlled by
a thermostat, which keeps the heating elements ON/OFF
according to the pre-determined set point. Fig. 2 shows
operating condition during broil cycle, where the oven set
Fig. 1. Electric oven.
TC
a
m
g
b
L
thermocouple
thermal diffusivity (m2/s)
kinematic viscosity (m2/s)
gravitational acceleration (m/s2)
coefficient of thermal expansion (1/K)
height of cavity (m)
Subscripts
H
heater
c
thermocouple
w
oven wall
g
gas or air inside the oven
s
suction
Broil Cycle : COT
540
Temperature (K)
Ra
T
W
h
k
Cp
d
q
r
e
v
P
x
COT
Oven Set Point Temperature
490
440
390
340
290
0:00:00
0:07:12
0:14:24
0:21:36
0:28:48
0:36:00
0:43:12
Time (hr:min:s)
Fig. 2. A typical broil cycle.
point is reached in 15 min after which the heater element
starts cycling. The initial transient before heater starts
cycling is known as preheating. The front doors have a
double glazed window, which helps the operator to monitor the cooking without opening the door. Tin oxide coating is provided on inner glass walls to ensure low
transmissivity for reduced radiation losses. Convection
fans are normally provided at the rear wall of the cavity
to enable faster cooking.
A series of steady state experiments were carried out to
understand the contribution of various heat loss mechanisms in the oven such as loss through the walls, heat loss
through vent opening and glass viewing window of front
door. To facilitate steady state operation, the control circuit for heating elements was bypassed and the heater
was maintained at the required wattage. Heater power rating was set according to center oven temperature (COT).
Thermal field inside the cavity was tracked through thermocouples distributed inside the cavity. For oven surface
temperature measurements and cavity air temperature
measurements, J (Iron-Constantan) type thermocouples
(0.0100 ) with SS sheathing were used. These thermocouples
were calibrated within 1% of a reference thermometer
traceable to ITS-90 in liquid bath. For heater temperature
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H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
measurements, K (chromul–alumel) type thermocouples
were used. To facilitate easy location of thermocouples
and ensure repeatability, thermocouples were mounted at
eight corners of an open cuboid and at the center. It is well
known that thermocouple measurements are prone to offset due to heat transfer in the 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:
Tg Tc ¼
qc Cpc d oT c k c d o2 T c
þ
þ reðT 4H; w T 4c Þ.
4h
4h ox2c
ot
ð1Þ
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 along 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 10–15 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
5 cm 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 rod and heating of the aluminum rod was tracked. This also simulates a thermal load
used in oven experiments. A rod of 1 in. · 1 in. · 20 in. size
was used for these trials.
3. Numerical modeling
Due to complex geometry, the internal volume of the
oven cavity was meshed with tetrahedral element. The grid
size of the oven cavity was largely decided by the mesh resolution near the heaters, gasket opening and the vent outlet. The surface mesh was generated using GAMBIT and
volume mesh in TGrid. The difference in steady state thermal field predicted by grid size with 0.97 million cells and
1.5 million cells was of the order of 0.5%, much within
the required accuracy of prediction for oven thermal performance. So, the grid with 0.97 million cells was chosen
for all future numerical studies, steady state and transient,
presented in this paper. The commercially available solver
FLUENT 6.1 was used for current studies.
3.1. Material properties
The thermal properties of air were evaluated considering
water vapor content in it. An ideal incompressible formulation for density has been used to capture natural convection heat transfer. The multi layered oven sidewalls,
heater and door were modeled using effective conductive
resistance through a lumped thickness. Literature review
[2,3] revealed that radiation heat transfer inside the oven
cavity is the most dominant mode of heat transfer. Higher
dependence on radiative mode of heat transfer made it
essential to pay due attention to radiative model and the
radiative properties. Sensitivity studies of heater and oven
sidewall emissivity ascertained unknown emissivity values
for these surfaces and to understand their importance in
heat transfer participation. With 30% reduction in heater
emissivity, temperature at oven wall reduced by 10% but
for reduction of 20% in wall emissivity, temperature at
oven wall reduced by 0.2%. This observation indicates that
thermal field inside the oven is more dependent on heater
emissivity compared to sidewall emissivity. Finally, the
emissivity values for heater and sidewall were chosen as
0.85 and 0.9, respectively, which were subsequently substantiated by IR camera measurements.
3.2. Boundary conditions
The heaters have been modeled as volumetric heat
source to capture the effect of heat capacity of the heater
materials during the transient simulations. The outside surfaces of the oven wall and the glass door were modeled as a
combination of convective and radiative heat transfer with
the ambient. The gasket opening and vent outlet were specified as pressure boundary conditions. The inlet air temperature at gasket opening was considered to be at ambient
temperature 296 K.
3.3. Radiation model
For radiation models, discrete ordinate (DO) and surface-to-surface (S2S) were short-listed based on the applicability and accuracy required for the current study. The
DO model takes into account media participation in addition to the surface-to-surface radiation effects. However,
the S2S radiation model considers the latter only. The difference of temperature prediction at the center of the oven
and oven walls by the DO and S2S models for a simplified
but similar geometry were of the order of 0.2%. While, the
comparison of the thermal field was similar, the computational time for S2S model was almost half of the DO model
for an identical grid. Moreover, air in the current operating
temperature range can be considered as non-participating
media in radiation [8]. Considering all of the above, S2S
seemed a suitable choice for the electric oven modeling.
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
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3.4. Laminar vs turbulent
In a natural convective field, the order of Rayleigh number gives an indication of whether the flow field is laminar
or turbulent. Calculations of Rayleigh number based on
vertical height of cavity and temperature difference across
the cavity show Ra O (108). Transient nature of thermal
field indicates a variable Rayleigh number. Under such
conditions, it is difficult to numerically predict the flow
field, particularly during transition regime, due to nonavailability of a suitable modeling approach. Hence, it
was decided to compare thermal fields in both laminar
and turbulent regimes. A comparison of thermal field for
assumption of completely laminar flow and completely turbulent flow at thermocouple locations inside the cavity
showed a maximum of 3% difference in the temperature
data. It has been observed that the thermal field is similar
for both cases and henceforth a laminar approach should
be able to predict the thermal performance with reasonable
accuracy. It is important to note that the computational
time involved in solving a laminar flow field is less compared to the turbulent approach. Abraham and Sparrow
[6] have also made similar observations while studying
steady state thermal-flow field of an electric oven when bottom heater is ON and thus carried out their numerical solution with laminar assumption.
4. Results and discussion
Steady state solution takes less computational time
than the full transient oven cycle. It is practical to do
validation and accounts of heat losses initially on steady
state cases. Moreover, steady state solution would give
an opportunity to check on ‘‘effective’’ thermal conductivities of the composite wall material before going on to
transient calculations, which involve effect of specific heat
as well.
4.1. Steady state validation—vent suction pressure
Fig. 3 shows velocity vectors on the oven mid-plane (Y–Z)
with atmospheric pressure boundary condition set at the
vent outlet. It indicates reversed flow at vent outlet and
front door gasket opening leading to numerical oscillations. This reversed flow is contradictory to experimental
observations. The reason for having reversed flow at
vent outlet is due to the ‘‘ambient’’ boundary condition
that was employed at the vent outlet and front door gasket
opening in the numerical model. In reality, there is a local
low pressure region that will be created at the vent outlet
that causes the flow to move out of the vent from the top
of the oven.
This low pressure region is a combined effect of hydrostatic pressure difference due to density difference along
the cavity height and the pressure drop when air enters
the oven vent (from the cavity) due to the sudden change
Fig. 3. Velocity vectors at oven mid-plane (Y–Z) with atmospheric
pressure BC at vent outlet.
in area. This pressure drop will be the proportional to
1
qv2 , the density being mean density of air at temperature
2
corresponding to air temperature at vent entry. Temperature of air at vent entry is guided by heater temperature
and position of the heater. However, it is difficult to
calculate pressure drop in oven vent without knowing
air temperature at the oven vent entry apriori. Moreover,
the natural convection velocity magnitude also depends
upon the heater rating and the heating cycle being
used.
The boundary condition set at vent outlet should take
into account this pressure drop. This was simulated by
applying a ‘‘numerical’’ suction pressure at the vent outlet.
A detailed exercise was carried out to arrive at the right
magnitude of this suction pressure through a series of
steady state experiments combined with numerical analysis
to establish the suction pressure dependence on cavity temperature and the cycle.
Fig. 4. Velocity vectors at oven mid-plane (Y–Z) with suction pressure
(2 Pa) at vent outlet.
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H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
Table 1
Vent sensitivity studies for broil cycle
Suction pressure: 0.5 Pa
Suction pressure: 1 Pa
Suction pressure: 2 Pa
Heater
Inside left wall
Outside left wall
Inside glass wall
Outside glass wall
% Discrepancy
% Discrepancy
% Discrepancy
+14.7
+21.6
+4.9
+26.4
+6.8
+11.4
+10.5
+3.3
+13.9
+3.9
+8.4
+0.5
+1.9
+1.2
+0.3
Fig. 4 shows velocity vectors on the oven mid-plane (Y–Z)
with suction pressure of 2 Pa set at vent outlet. It shows
air movement in the expected direction. This flow field
matches qualitatively with experimental observation.
The procedure used to identify the correct suction pressure value for given operating conditions would now be
described. Thermal field data inside the cavity and cavity
walls (total 12 points) obtained through experiments at different heater wattages for both bake and broil cycles were
compared with the numerical model results at the same
conditions. Since suction pressure has to be applied in
the numerical model to simulate physical flow conditions,
this suction pressure value was varied to keep the discrepancy between measured temperature and the numerical
prediction within 10%. The suction pressure that provides
thermal field closely matching with experimental data has
been chosen as the suction pressure for that operating condition. Though it is possible to obtain an accurate value of
suction pressure by keeping the discrepancy within 5%,
from modeling point of view, 10% accuracy was deemed
reasonable. Table 1 shows an example of this comparison
matrix for broil cycle operating at 1200 W steady state that
fixes the suction pressure as 2 Pa.
The synergy between experimental and numerical studies at different wattages helped to build a transfer function
between the heater temperature and vent suction pressure.
These functions (Fig. 5) are as follows:
Transfer function for broil cycle
P s ¼ ð4:1e06 T 2H Þ þ ð0:0011T H Þ þ 0:26.
1
Numerical: COT/Tmax
Experimental: COT/Tmax
0.975
Numerical: Tload/Tmax
0.95
Experimental: Tload/ Tmax
0.925
T/ T maximum
Location of temperature measurement
0.9
0.875
0.85
0.825
0.8
0.775
0.75
0
200
400
600
800
1000
Time (s)
a
1
Numerical: Tload/Tmax
Experimental: Tload/Tmax
Numerical: COT/ Tmax
Experimental: COT/Tmax
0.95
0.9
0.00
Broil
Bake
T/Tmax
Suction Pressure
-1.00
-2.00
-3.00
0.85
0.8
0.75
-4.00
0.7
-5.00
0.65
-6.00
300
0
600
900
1200
b
200
400
600
800
1000
Time (s)
TH (K)
Fig. 5. Transfer function between vent suction pressure and heater
temperature.
Fig. 6. Comparison of experimental COT and load temperature with
numerical prediction for preheating: (a) broil cycle (1200 W) and (b) bake
cycle (1200 W).
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
4.2. Transient validation: preheating cycle
Transfer function for bake cycle
P s ¼ ð3e
06
T 2H Þ
ð0:0011T H Þ þ 0:11.
Suction pressure dependence on the type of oven cycle and
the heater rating is clear in Fig. 5. Since bake cycle velocities are higher than broil cycle increased suction pressure is
attributed to increased pressure drop for flow through the
vent. It may be noted that these transfer functions are
applicable only for the range of wattages for which trials
have been carried out, that indeed covers the operating
range of oven.
1.00
10
Experimental: TLoad/ TMax
Numerical: TLoad/ TMax
Current
0.95
8
0.90
Current (ampere)
TLoad / TMax
2453
6
0.85
0.80
4
It is common practice to use a load in the oven to simulate the food being cooked for transient validation studies
[1–6]. Moreover, TC inserted inside the thermal load
avoids radiation and convection errors. A platform of
low conductivity material was used to restrict heat being
pumped out from thermal load through base of the oven.
Aluminum has been selected as a thermal load because of
its high thermal conductivity and also reasonably high
diffusivity.
Fig. 6a and b show comparison of experimentally measured COT and load temperature with numerical prediction for preheating broil (1200 W) and bake (1200 W)
cycles, respectively. The suction pressure BC at vent outlet
has been set as a function of heater temperature. The maximum discrepancy between experimental measurement and
numerical prediction with air temperature (COT) was 6%
with the broil cycle and 8.5% with the bake cycle. However,
with load temperature, discrepancies dropped to 2% and
2.5%, respectively. This confirms the surmise that transient
phenomenon is better captured with thermal load.
0.75
2
0.70
0.65
0
0
200
400
600
800 1000 1200 1400 1600
Time (s)
a
1.00
12
Experimental: TLoad/ TMax
Numerical: TLoad/TMax
Current
0.95
10
0.85
8
0.80
6
0.75
0.70
4
Current (ampere)
TLoad / TMax
0.90
0.65
2
0.60
0.55
0
0
b
250
500
750
1000
1250
Time (s)
Fig. 7. Comparison of experimental COT and load temperature with
numerical prediction for full cycle: (a) bake cycle (2300 W) and (b) broil
cycle (2900 W).
Fig. 8. Thermal field at oven mid-plane (Y–Z) for transient bake cycle
(1600 W): (a) time = 360 s and (b) time = 900 s.
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H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
4.3. Transient validation: full cycle
The cooking cycles of oven involve intermittent ON/
OFF operation of the heaters as has already been mentioned in an earlier section. It is important to validate the
CFD model with transient thermal response of load in
cooking cycles too. Fig. 7a and b shows comparison of
experimentally measured load temperature with numerical
prediction for bake (2300 W) and broil (2900 W), respectively through the ON–OFF cooking cycle. Heater ON–
OFF conditions are also plotted as heater current in these
figures. The maximum percentage discrepancy with bake
cycle was 2.7% and 10% with broil cycle. The relatively
higher percentage discrepancy with broil cycle is a common
observation and is a matter of further investigation.
4.4. Comparison of bake and broil cycle heating
Figs. 8–11 show temperature profile (in K) at the midplanes (Y–Z and X–Y) for bake and broil cycles at two
Fig. 9. Thermal field at oven mid-plane (Y–Z) for transient broil cycle
(1600 W): (a) time = 360 s and (b) time = 900 s.
times (360 s and 900 s). Broil cycle shows higher temperatures close to the heater that indicates stably stratified fluid
inside the oven cavity. As a result of stable stratification
there is hardly any fluid movement inside the cavity leading
to non-uniform temperature distribution inside the cavity.
Thus the dominant mode of heat transfer in a broil cycle
would be through surface-to-surface radiation between
heater and oven walls and radiation between walls themselves. It is observed that bake cycle has more uniform temperature throughout the domain. This is mainly due to
convection currents formed at the bottom heater heating
the cavity volume before moving out through the top vent.
Thus dominant mode of heat transfer in bake cycle is radiation heat transfer between the heater and oven walls combined with convective heat transfer contributing to
temperature uniformity. There is more efficient heat transfer between oven walls and the adjacent fluid layers due to
higher flow velocities and more active boundary layer close
to oven wall for a bake cycle.
Fig. 12 shows temperature profile on the oven central–
vertical axis through its height for a broil and bake cycle.
It indicates a temperature gradient as a result of stable
stratification for a broil cycle and highly uniform temperature for a bake cycle because of efficient convective heat
transfer. The plot indicates there will be same broil
Fig. 10. Thermal field at oven mid-plane (X–Y) for transient bake cycle
(1600 W): (a) time = 360 s and (b) time = 900 s.
H. Mistry et al. / Applied Thermal Engineering 26 (2006) 2448–2456
2455
800
Broil
Bake
750
Temperature (K)
700
650
600
550
500
450
400
350
300
0.1
0.2
a
0.3
Y (m)
0.4
0.5
800
Broil
Bake
750
Temperature (K)
700
650
600
550
500
450
400
350
300
0.1
b
Fig. 11. Thermal field at oven mid-plane (X–Y) for transient broil cycle
(1600 W): (a) time = 360 s and (b) time = 900 s.
performance if the cooking load is kept within 5 cm from
the heater (essentially the top grid locater at ovens is at this
height). Beyond this there is a temperature gradient, which
will not contribute to efficient cooking for a broil cycle.
5. Conclusions
Development of a three-dimensional transient CFD
model has been described to simulate natural convection
heat transfer in ovens for two different cooking cycles.
In order to establish a physically reasonable flow pattern
through vent openings, a suction pressure was applied at
top vent. This suction pressure was found to depend on
the cavity heating pattern (bake, broil) and the heater temperature. In order to establish this relationship, steady
state experimental trials were carried out at different heater ratings. A transient validation of bake cycle showed
the model’s capability to simulate the thermal field and
the effect of cyclic heater ON–OFF conditions on a thermal load inside the oven within 4% accuracy. Broil cycle
heating, where the heater is close to top vent matched with
experimental data within 10%. A comparison of bake and
broil cycle heating pattern shows that the oven cavity is
more uniformly heated with a bake cycle due to convective heating.
0.2
0.3
Y (m)
0.4
0.5
Fig. 12. Temperature profile at oven central–vertical axis for broil and
bake cycle (1600 W): (a) time = 360 s and (b) time = 900 s.
Acknowledgements
We would like to thank Todd Graves, Business Program
Manager, GE Consumer and Industrial and Francisco
Anton, R&D manager, MABE for their support during
the course of this work. We would also like to thank Amol
Mulay, Sudeep Pradhan, Balaji Parthasarthy, Christopher
Omalley of GE Consumer and Industrial and Nath
Gopalaswamy for their participation and contributions in
various discussions on modeling approaches.
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