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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Numerical study on the effect of different hole locations in the fan case onthe thermal performance inside a gas oven range

Seong Hyun Parka, Yang Ho Kimc, Young Soo Kimc, Yong Gap Parkb,⁎, Man Yeong Haa,⁎

a School of Mechanical Engineering, Pusan National University, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of Koreab Rolls-Royce and Pusan National University Technology Centre in Thermal Management, Jang Jeon 2-Dong, Geum Jeong Gu, Busan 609-735, Republic of KoreacHome Appliance and Air Solution Company, LG Electronics, Gaeumjeong-Dong, Seong San Gu, Changwon, Republic of Korea

H I G H L I G H T S

• A numerical study of a gas oven range was carried out using an actual 3D geometry and ANSYS FLUENT.

• A test geometry was developed by referencing a real product.

• The flow pattern and temperature distribution inside the oven cavity changed dramatically.

• Thermal performance was evaluated based on the average temperature and temperature uniformity.

A R T I C L E I N F O

Keywords:Computational Fluid Dynamics (CFD)Gas oven rangeThermal performance

A B S T R A C T

This paper discusses the effect of the hole location in the fan case on the thermal performance of a gas ovenrange. A computational fluid dynamics (CFD) study was carried out in ANSYS FLUENT. A DO model was used toinclude the effect of thermal radiation in the oven cavity. A test geometry was developed by referencing a realproduct, including the oven cavity, external walls, fan cases, fans, and burners. The simulation was validatedwith experimental data and showed that the maximum difference in temperature is 2.5%, while the difference inaverage temperature is 0.44%. A total of 15 cases were examined using different hole locations in the fan case.The direction of the velocity vector at the holes was changed by the different hole locations, and the flow patternand temperature distribution inside the oven cavity also changed dramatically as a result. The thermal perfor-mance was evaluated based on the average temperature and temperature uniformity inside the oven cavity.

1. Introduction

Domestic ovens use electrical coil heating and gaseous fuel to pro-vide thermal energy to an enclosed cavity [1]. Ovens heat food to cookit by conduction, convection, and radiation. These three heat transfermodes should be included when modeling the temperature and velocityfields in domestic ovens. Radiation is often predominant at low airspeeds, while convection is much more important at higher air speeds[2]. Computational fluid dynamics (CFD) is useful for predicting thetemperature and velocity fields in the oven cavity while considering allthree heat transfer modes. Many researchers have developed CFDmethods to analyze the flow patterns and temperature fields.

Earlier studies conducted 2D CFD simulations because 3D calcula-tion is very computationally expensive for calculating the temperatureand velocity fields in an oven [3–6]. Wong et al. [3] developed a 2DCFD modeling method for a continuous baking process using sliding

mesh techniques and a segregated unsteady state solver. They assumedthat the burners are circular object with a fixed wall temperature.Therdthai et al. [4] established a two-axis CFD model and varied sev-eral oven operating parameters, including the heat supply, fan volume,and heat distribution in the oven.

With rapid advances in parallel computing technologies, numerous3D CFD studies have been carried out [7–16]. Numerical simulationshave been conducted using commercial code and have considered ra-diation models involving both steady and unsteady calculation toevaluate and improve the thermal performance of commercial proto-types. Some studies have considered different geometries change toincrease the thermal performance of products.

Mistry et al. [7] developed a three-dimensional transient CFD modelto simulate natural convection heat transfer in an oven for two differentcooking cycles. Their model of an electric oven included a three-di-mensional, unsteady, natural convective flow-thermal field coupled

https://doi.org/10.1016/j.applthermaleng.2018.03.087Received 30 December 2016; Received in revised form 30 August 2017; Accepted 26 March 2018

⁎ Corresponding authors.E-mail addresses: pyg777@pusan.ac.kr (Y.G. Park), myha@pusan.ac.kr (M.Y. Ha).

Applied Thermal Engineering 137 (2018) 123–133

Available online 27 March 20181359-4311/ © 2018 Elsevier Ltd. All rights reserved.

T

with radiative heat transfer. They applied a suction pressure at the topvent to obtain a physically reasonable flow pattern through the ventopenings. The results showed good agreement with the experimentalresults. They also presented a comparative analysis of the thermal fieldsinside the oven for bake and broil cycles. Boulet et al. [8] developed a3D CFD model to describe the transient heat transfer in a pilot plantoven with radiation coupled with a mixed convection regime. The ra-diation model was simulated by a surface to surface (S2S) model,whereas a k-e realizable model was used for turbulence. The CFD modelwas validated with experimental data for transient temperature.

Chhanwal et al. [9] conducted a CFD calculation that consideredthree different radiation models: the discrete transfer radiation model(DTRM), discrete ordinates (DO) model, and S2S model. The simulationresults showed good agreement with the experimental results. Theysimulated a bread-baking process with bread in the center of the ovento investigate the profiles of temperature and starch gelatinization ofthe crust and crumb of the product. The bread temperature was vali-dated with experimental measurements. Rek et al. [10] numericallysimulated the heat transfer in a new generation of ovens by changingthe heater shape, fan cover shape, heater temperature, and ventilationsystem flow rate. They carried out steady-state 3D CFD calculation witha DO model for radiation. They determined the influence of changes inthe geometry and boundary conditions on the velocity and temperaturedistribution inside the oven cavity.

Smolka et al. [11,12] experimentally validated a 3D CFD analysis ofthermal and flow fields in a laboratory drying oven with varying ro-tational speed of the device fan, the effectiveness of the distributiongaps, and the rate of heat generated in the oven. The temperatureuniformity was improved by adjusting the device configurations. Anexperiment was carried out to look at the thermal performance of theimproved design, which showed good agreement with the CFD results.They concluded that the proposed CFD methodology can be applied todesigning an oven.

Many researchers have conducted CFD studies with various para-meters, including oven geometries, operating conditions, and boundaryconditions. However, there are few studies on the effect of the locationof holes in the fan case, which could influence the temperature valueand temperature uniformity of air inside the oven cavity. Therefore, aCFD study was conducted with different locations of four holes on sidesof the fan case to quantitatively estimate the effect on the thermalperformance. The calculations were conducted with full factorial de-sign. The thermal performance was evaluated based on the averagetemperature and temperature uniformity. The simulations were solvedusing the commercial code ANSYS FLUENT 13.0, and the numericalresults were validated with experimental results.

2. Numerical methodology

A three-dimensional geometry was created, including the ovencavity, fan case, and burner. The volume mesh was generated usingANSYS workbench 13.0. The structured cut-cell mesh was distributed inthe computational domain to generate a fine mesh around the small

holes. The total number of mesh faces was 18,174,889 with 5,950,913cells. A segregated steady state solver was used to solve the governingequations of momentum, mass, energy conservation, and the turbulencekinetic energy equation. For the turbulent flow, a k-ε model was usedwith the standard wall function near the wall boundaries. The radiationheat transfer was taken into account using the DO model in FLUENT,which solves the radiative transfer equation for a finite number ofdiscrete solid angles, each associated with a vector direction. All of thegoverning equations solved in the current study are shown below:

Continuity equation

∂

∂+ ∇

→=

ρt

ρ v·( ) 0 (1)

Momentum conservation equation

∂

∂

→+ ∇

→→= −∇ + ∇ +

→

tρ v ρ v v p τ ρg( ) ·( ) ·( ) (2)

= ∇→

+ ∇→

− ∇→τ μ v v v I[( ) 2

3· ]T

(3)

Energy equation

∂

∂+ ∇

→+ = ∇

tρE v ρE p kT( ) ·( ( )) · (4)

= − +E hpρ

v2

2

(5)

Radiation model equation (DO)

∫

∇→ → →

+ +→ →

=

+→ →′ → →′ ′

I r s s a σ I r s an σTπ

σπ

I r s s s d

·( ( , ) ) ( ) ( , )

4( , )Φ( , ) Ω

s

s π

24

0

4

(6)

where ρ is the density, →v is the velocity vector, μ is the viscosity, τ isthe stress tensor, E is the energy, p is the pressure, h is the enthalpy,

→ →I r s( , ) is the radiation intensity, a is the absorption coefficient, →r isthe position vector, →s is the direction vector, →′s is the scattering di-rection vector, and → →r sΦ( , ) is the phase function. Because the airtemperature inside the oven cavity varies widely, variation of thethermophysical properties of air such as density, viscosity, thermalconductivity, and specific heat were considered as polynomial functionsof temperature. To create the polynomial functions, the data were ex-tracted with reference to the NIST database [17]. All data were fittedwith a polynomial equation. The oven walls were made from stainlesssteel, and the external walls were made from wool. The emissivity ofstainless steel and wool were supplied by the manufacturers. Table 1presents the thermophysical properties used, including the emissivity ofeach solid.

The 3D CFD geometry was developed with reference to a real pro-duct geometry taken from the manufacturer. This gas oven consists ofan oven cavity, outer wall, fan case, fan, insulation wall, and burner, asshown in Fig. 1. The oven cavity includes a glass wall, inner stainlesswall, fan case, and burner. The thermal and flow fields were calculatedfor an oven cavity by varying the fan geometry.

Nomenclature

ρ air density (kg/m3)→v velocity vector (m/s)p pressure (Pa)→g gravitational acceleration (m/s2)μ dynamic viscosity (kg/m s)τ stress tensor (Pa)E energy (J/kg)k thermal conductivity (W/mK)h sensible enthalpy (J/kg)

σ Stefan–Boltzmann constant (W/m2 K4)a absorption coefficientT temperatureTreference reference temperatureθ dimensionless temperatureθcal calculated dimensionless temperatureθexp measured dimensionless temperature

θΔ dimensionless temperature discrepancyθvol avg, volume-averaged temperature inside the oven cavityVchamber volume of oven cavityRMSvol temperature uniformity inside the oven cavity

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The temperature and heat transfer coefficient of ambient air wereset to be the same as those of the experiment. To consider the radiationheat transfer, mixed convective and radiative boundary conditions wereused at the external wall to introduce heat transfer with the sur-rounding ambient air. The glass wall was located on the front side of thegas oven, which also had mixed convective and radiative boundaryconditions. The fan case was located on the opposite side of the glassinside the oven cavity. The four fan holes supply hot gas injected fromthe burner holes to the oven cavity, as shown in Fig. 2. A ventilationduct is located on top of the oven cavity. Pressure outlet boundaryconditions were used for this boundary with the static pressure set toatmospheric pressure.

Fig. 3 shows a schematic of the calculation and the mass flow rateconditions in each hole. To simulate the hot air flow injected from theburner to the oven cavity, mass flow conditions were used at each of the143 burner holes. To reduce the computational time, the mass flow ratewas calculated for each hole using the burner geometry. The calculatedmass flow rate conditions were applied to calculate the temperature and

flow fields in the oven cavity. Constant temperature conditions wereapplied to each hole. The temperature conditions were the same at allburner holes.

3. Results and discussion

3.1. Validation test

A validation test was carried out by measuring the temperatureinside the oven cavity of the actual product. For the measurement, aframe was manufactured to fix thermocouples in the measuring loca-tions. Fig. 4 shows the positions of the measuring probes of temperatureinside the oven cavity. The spatial temperature was measured using 100thermocouples in the oven cavity. Fig. 5 shows a qualitative comparisonof the experimentally measured and numerically calculated tempera-tures at selected positions. The average temperatures inside the ovencavity matched very well. The following dimensionless temperatureand temperature discrepancy were defined for the comparison:

=θ TTreference (7)

=−

×θθ θ

θΔ

| |100(%)cal exp

exp (8)

where θ is the dimensionless temperature, T is the temperature, Treferenceis the reference temperature, θcal is the calculated dimensionless tem-perature, θexp is the measured dimensionless temperature and θΔ is thedimensionless temperature discrepancy. The simulation results showedgood agreement with the measured data. The maximum difference

Table 1Thermophysical properties used.

Material Properties

ρ (kg/m3) Cp (J/kg K) k (W/mK) μ (kg/m s) ε

Air (Fluid) f(T) f(T) f(T) f(T) –Wool (Solid) 160.0 1088.568 0.1163 – –Glass (Solid) 2225.0 835.000 1.4000 – 0.90Stainless (Solid) 8238.0 468.000 13.4000 – 0.85

Fig. 1. Computational domain and boundary conditions for CFD simulation.

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Fig. 2. Schematic diagram of fan case geometry.

Fig. 3. Burner boundary conditions used.

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between the calculated and measured temperatures is 2.5%, while thedifference in average temperature is 0.44%.

3.2. Grid dependency test

A grid dependency test was conducted with varying number of cellsin computational domain. Numbers of the cells considered were about4,400,000, 5,500,000 and 8,100,000. The differences in the volume-averaged temperature in the cavity obtained using coarse and fine gridswere less than 0.4%, as shown in Table 2. Thus, the number of the gridpoints used in this computation was 5,500,000.

3.3. Test cases

Table 3 shows the test conditions. “Open” means that the face isunder interior conditions and the flow passes through this boundary,and “closed” means that the wall boundary condition is applied. Otherboundary conditions and material properties were the same in all cases.A total 15 cases were examined.

3.4. Flow pattern near the fan case

The flow direction at the holes in the fan case was changed withdifferent hole locations. The flow direction changes because of the ro-tating flow pattern generated from the fan and the change in flow re-sistance according to the area of the holes in the fan case. The change inthe flow direction at the top right hole was large when we close thebottom right hole. However, the change in the flow direction was verysmall when we close other holes. The angle between the velocity vectorand coordinate axes was defined to indicate the direction of the hot airflow. The air inside the oven cavity and at the bottom inlet of the ovenrange is drawn in by a fan and heated by the burner, and then it flowsback to the oven cavity.

Fig. 6 shows a schematic of the velocity vector at the four holes inthe fan cases and the angle between the velocity vector and coordinateaxes. If the angle is larger than 90◦, the hot air flows in the reversedirection of the coordinate axis. Fig. 7 shows the angle between thevelocity vector and coordinate axis at the four holes. The holes were allopened in case 01, whereas the bottom right hole was treated as a wallboundary in case 02. At the top right hole, ω and ϕ were similar valuesfor case 01 and case 02. However, φ was larger than 90◦ in case 01 andsmaller than 90◦ in case 02. Therefore, hot air flows in the downwarddirection in case 01 and in the upward direction in case 02.

Fig. 8 shows the cross-sectional temperature fields and tangentialvelocity vector at the center of the fan case. Since the fan rotates in theclockwise direction in case 01, hot air also flows in the clockwise di-rection. In case 02, closing bottom right hole results in increased flowresistance on the right side of the fan case, and the hot air tends to flowmainly to the left side of the case. At the bottom right side of the innerfan case, hot air travels along the fan case walls and turns back towardsthe fan. The flow is then directed to the oven cavity through the topright hole because the flow resistance of the top right side hole issmaller than that of the fan side. There is a recirculating region at thebottom right side of the inner fan case. The hot air flows to both thebottom and middle right sides of the oven cavity and the top and middle

Fig. 4. Locations to measure air temperatures.

Fig. 5. Comparison of temperature of numerical results with those of experi-ment.

Table 2Grid dependency test results.

Grid number Volume averaged temperature [K] Difference (%)

4,440,000 454.7 0.355,500,000 453.1 –8,100,000 453.05 0.01

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left sides in case 01. However, in case 02, hot air flows to the top rightside of the oven cavity and top and middle left sides. The change in thedirection of hot air at the top right hole changed the temperature dis-tribution in the oven cavity.

In case 01, a high-temperature region was observed at the right sideof the fan case, and there was a relatively low temperature region onthe left side, as shown in Fig. 8(a). Closing the bottom right hole resultsin increased air temperature on the left side of the oven cavity becausethe flow rate increases with increasing the flow resistance on the rightside of the cavity, as shown in Fig. 8(b).

3.5. Temperature distribution in the oven cavity

For comparison of the thermal performance, the average tempera-ture and temperature uniformity inside the oven cavity were defined asfollows:

∫=θV

θdV1vol avg

chamber V, (9)

∫= −RMSV

θ θ dV1 ( )volchamber V vol avg,

2

(10)

where θvol avg, is the volume-averaged temperature inside the ovencavity, Vchamber is the volume of oven cavity and RMSvol is the tem-perature uniformity inside the oven cavity. High average temperatureand low temperature uniformity are needed for good cooking perfor-mance.

Fig. 9 shows the volume-averaged temperature and temperature

Table 3Tested conditions considered in this study.

Variables

Top left hole Bottom left hole Top right hole Bottom right hole

Case 01 Open Open Open OpenCase 02 Open Open Open ClosedCase 03 Open Open Closed ClosedCase 04 Open Closed Closed ClosedCase 05 Open Closed Open ClosedCase 06 Open Closed Closed OpenCase 07 Open Closed Open OpenCase 08 Open Open Closed OpenCase 09 Closed Open Open OpenCase 10 Closed Closed Open OpenCase 11 Closed Closed Closed OpenCase 12 Closed Open Closed OpenCase 13 Closed Open Open ClosedCase 14 Closed Closed Open ClosedCase 15 Closed Open Closed Closed

Fig. 6. Schematic diagram of angle between velocity vector and coordinate axes.

(a) Case 01

(b) Case 02

Fig. 7. Angle between velocity vector and coordinate axes at fan case holes.

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uniformity in the oven cavity for different hole locations in the fan case.The results show complicated tendencies for different hole locations.The following three cases were selected for analysis:

Case 01: This baseline case represents a common commercial gasoven range. All holes in the fan case were opened.Case 06: This case shows the best thermal performance. The bottomleft hole and top right hole were closed, and hot air flowed throughthe bottom right hole and top left hole. The performance is betterbut the flow resistance is higher compared to case 01.Case 09: This case which shows worst thermal performance. The topleft hole was closed, and hot air flowed through the other holes. Theflow resistance is lower than that of case 06, and thermal perfor-mance is poorer.

The thermal performance was not increased by reducing the flowresistance in the fan case. The velocity field inside the fan case changedwith different hole positions in the fan case. Therefore, the recirculatingflow pattern in the oven cavity was dramatically changed by varyingthe boundary conditions in the fan case.

Fig. 10 shows the distribution of stream lines in the oven cavity, and

(a) Case 01

(b) Case 02Fig. 8. Distribution of temperature and velocity vector in the vertical plane at the center of fan cases.

Fig. 9. Volume-averaged temperature and RMS of temperature in the cavitywith different location of hole.

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the colors represent the temperatures of the working fluid. In case 01,the air flow on the right side of the oven cavity is much stronger thanthat on the left side, as shown in Fig. 10(a). Hot air injected from theright side of the fan case impacts the side wall of the oven and thenrecirculates in the oven cavity due to its high speed. Hot air injectedfrom the left side of the fan case impacts the left side wall of the ovenand is drawn in by the fan or leaves through the hood outlet because thevelocity is lower than that on the right side. Hence, the temperaturedistribution inside the oven cavity shows an imbalanced pattern.

In case 06, the hot air flow was stronger than that in case 01 at bothopened holes in the fan case, as shown in Fig. 10(b). Hot air injectedfrom the fan case impacts the oven side wall and then flows in theopposite direction of the side wall. Because the hot air flows on both

sides were stronger than in case 01, the impacting hot air recirculatesand mixes in the oven cavity. As a result of mixing flow, the tempera-ture distribution in the oven cavity is uniform, and the average tem-perature is higher than in case 01.

In case 09, closing the top left hole increases the velocity of the hotair on the right side of the oven cavity, and the velocity decreases on theleft side of the cavity, as shown in Fig. 10(c). At the bottom right side ofthe oven cavity, hot air impacts the side wall of the oven and travelstoward the top left side, similar to case 01. The hot air flow was muchstronger than in case 01 at the bottom right hole. On the left side of theoven cavity, the hot air stream from the fan case was drawn in by thefan and turns back to the inside of the fan case. Hot air could not flow inthe upward direction because the air was very slow on the left side ofthe oven cavity. Hence, the temperature on the top left side of the ovencavity was lower than in the other two cases.

For detailed observation of the temperature and velocity fields ineach case, the temperature fields and velocity vectors in six cross-sec-tions of the oven cavity are shown in Fig. 11. The six cross sections weretaken at constant x and z coordinates. Fig. 12 shows the temperaturedistribution of each case in a cross section of the oven cavity, which isnormal to the fan case and located in the x-direction. In case 01, thestrong hot air flow impacts the side wall of the oven. The hot tem-perature region is locally distributed, as shown in Fig. 12(b) and (c).The temperature on the right side of the oven cavity is higher than thaton the left side due to the higher velocity on the right side.

In case 06, the temperature is high near the holes in the fan cases, asshown in Fig. 12(e) and (f). The temperature in case 06 was generallyhigher than that in case 01 because of the effective mixing flow in theoven cavity. The temperature on the left side of the oven cavity waslower than in other locations in case 09, as shown in Fig. 12(h) and (i).Because the mixing flow in the oven cavity was very weak in case 09,the uniformity of the temperature at the cross sections was poor. At thecenter of the oven cavity, the temperature was highest in case 06 andlowest in case 09 among the three cases shown in Fig. 12(a), (d), and(e).

Fig. 13 shows the temperature fields in a cross section of the ovencavity that is normal to the fan case and located in the z-direction. Incase 01, the temperature on the right side is higher than that on the leftside at low height of the oven cavity, as shown in Fig. 13(a). At themiddle of the oven cavity, the temperature is lower than that at highheight of the oven cavity, as shown in Fig. 13(b). Due to the hot air flowon the top left side, the temperature on the left side is higher than thaton the right side, as shown in Fig. 13(c).

In case 06, although the bottom left hole was closed, the tempera-ture on the left side of the oven cavity is higher than that in case 01 dueto a strong recirculating flow from the top left hole, as shown inFig. 13(d). The recirculating flow from the top left hole and bottomright hole accelerate the mixing flow in the oven cavity, and the tem-perature in the oven cavity is higher than in case 01. These recirculatingregions also influence the uniformity of the temperature, which im-proved due to mixing flow by the two recirculating flows, as shown inFig. 13(e) and (f).

In case 09, temperature uniformity was very poor, as shown inFig. 13(g), (h), and (i). Because the flow on the left side of the ovencavity was very weak compared to the flow on the right side of the ovencavity, the temperature on the left side was lower than on the right side.Especially at high height of the oven cavity, the temperature was verylow on the left side of the oven cavity.

4. Conclusions

A numerical study of a gas oven range was carried out while con-sidering conduction, convection, and radiation. The simulation wassolved using an actual 3D geometry and ANSYS FLUENT. The ther-mophysical properties of air were varied as a function of air tempera-ture. To include the effect of thermal radiation, the emissivity of each

(a) Case 01

(b) Case 06

(c) Case 09Fig. 10. Streamlines in the oven cavity for the case 01, the case 06 and the case09.

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Fig. 11. Schematic diagram to represent the cross section location.

Fig. 12. Temperature distribution on the cross section at =x x0, x1 and x2 for the case 01, the case 06 and the case 09.

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material was defined.The simulation results showed good agreement with the measure-

ment data. The maximum difference between the simulation andmeasured temperature was 2.5%, and the difference in the averagetemperature was 0.44%. The direction of the velocity vector in each fancase hole was changed with the different hole locations. For quantita-tive comparison of the velocity direction, the angle between the velo-city vector and coordinate axes was defined. The direction of the ve-locity vector dramatically changed with the hole locations.

The thermal performance was evaluated by comparing the averagetemperature and temperature uniformity in the oven cavity. Thethermal performance was not increased by reducing the flow resistancein the fan case because of the rotating flow pattern induced by the fan.The velocity at the holes in the fan case changed with the different holelocations, and the recirculating flow pattern in the oven cavity changeddramatically as well. Due to the mixing flow, the thermal performancealso changed with the hole location.

Since hot air velocity increased with decreasing area of holes, themixing flow was accelerated in the cavity by closing hole in the fancase. However, when the holes were located only on one side of fancase, temperature uniformity was decreased because of an imbalancedflow pattern in the cavity. When the holes located at the top left sideand bottom right side of fan case or at the top right side and bottom leftside of fan case, temperature uniformity was improved and averagedtemperature was increased because of effective mixing flow in thecavity. In conclusion, location and area of holes in the fan case of gasoven range should be carefully designed with consideration of flow andtemperature uniformity in the cavity.

Acknowledgements

This research was supported by Basic Science Research Programthrough the National Research Foundation of Korea (NRF) funded bythe Ministry of Education, Science and Technology (NRF-2017R1C1B2007296 and NRF-2017R1A2B3004883).

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