Numerical Simulation of Air Flow and Heat Transfer in Domesticrefrigerators

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Journal of Food Engineering 81 (2007) 144–156

Numerical simulation of air flow and heat transfer indomestic refrigerators

O. Laguerre a,*, S. Ben Amara a, J. Moureh a, D. Flick b

a UMR Genie Industriel Alimentaire INRA-INAPG-Cemagref-ENSIA, BP. 44, 92163 Antony Cedex, Franceb UMR Genie Industriel Alimentaire INRA-INAPG-Cemagref-ENSIA, 16 rue Claude Bernard, 75231 Paris, France

Received 24 February 2006; received in revised form 17 October 2006; accepted 21 October 2006Available online 15 December 2006

Abstract

This work was carried out in order to study heat transfer by natural convection in domestic refrigerators without ventilation. Only therefrigerating compartment was studied for three configurations: empty refrigerator, refrigerator equipped with glass shelves and refrig-erator loaded by product. Both experimental and numerical approaches were used.

The simulations were carried out using CFD (computational fluid dynamic) software by taking into account or by neglecting radi-ation heat transfer. The following conditions were assumed: constant evaporator temperature, three-directional laminar air flow. Numer-ical results show temperature stratification in the refrigerating compartment (warm zone at the top and cold zone on the bottom) for allconfigurations. A comparison of the calculated air temperature and the experimental values shows good agreement when radiation istaken into account.� 2006 Elsevier Ltd. All rights reserved.

Keywords: CFD; Simulation; Closed cavity; Refrigeration; Domestic refrigerator

1. Introduction

Domestic refrigerators are widely used in industrializedcountries. There are approximately 1 billion domesticrefrigerators worldwide (IIR, 2002). In France, there are1.7 refrigerators per household (AFF, 2001). In developingcountries, the production is rising steadily: total productionrose 30% in 2000 (Billiard, 2005). Some indications showthat food is often stored in domestic refrigerators at tem-peratures that are too high. In refrigerators without venti-lation, strong temperature heterogeneity is often observed,with warm zones (sanitary risk) and cold zones (freezingrisk) due to very low air circulation. For this type of refrig-erator, widely used in Europe and in developing countries,heat transfer occurs principally by natural convection.Knowledge of air temperature and velocity profiles in a

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doi:10.1016/j.jfoodeng.2006.10.029

* Corresponding author. Tel.: +33 140 966 121; fax: +33 140 966 075.E-mail address: [email protected] (O. Laguerre).

refrigerator is important for food quality control. Indeed,if the consumer knows the position of warm and cold zonesin the refrigerator, products can be placed correctly.

This work was carried out in order to gain a betterinsight into air flow and heat transfer inside a refrigerator.Three configurations were studied: an empty refrigeratorwith and without shelves, and a loaded refrigerator. Theobjective was to quantify the air temperature and velocitydistribution in the refrigerating compartment in the pres-ence of obstacles (shelves and product) and to comparethe results with those obtained using an empty compart-ment. The influence of heat exchange through natural con-vection (between the air and the walls) and by radiation(between the internal walls) was studied. Both experimentaland numerical (CFD software) approaches were used.

The practical objective of this study is to predict thewarm and cold zones in a domestic refrigerator. This objec-tive can be reached by the characterisation of air flow andheat transfer in the appliance.

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Nomenclature

I intensity of radiation, W m�2 per unit solid an-gle

L characteristic length, m~n normal vectorg acceleration due to gravity (9.81 m s�2)Nu Nusselt numberQ heating power, WR radius, mRa Rayleigh numberNRC radiation–convection interaction parameterT air temperature, �C or KTamb ambient temperature, �C or KTevap evaporator temperature, �C or KTh warm wall temperature, �C or K

Tc cold-wall temperature, �C or KTs surface temperature, �C or KDT temperature difference between cold and warm

walls, �C or K

Greek symbols

a air thermal diffusivity, m2 s�1

b thermal expansion coefficient, K�1

e emissivity of the wallq air density, kg m�3

k air thermal conductivity, W m�1 K�1

t air kinematic viscosity, m2 s�1

X solid angleU radiative flux, W m�2

Fig. 1. Air flow in a closed cavity (Tian & Karayiannis, 2000).

O. Laguerre et al. / Journal of Food Engineering 81 (2007) 144–156 145

2. Literature review

To demonstrate the air flow and heat transfer in a refrig-erator, literature on free convection phenomena in a closedcavity will be presented, then studies applied to domesticrefrigerators will be mentioned.

2.1. Air flow and heat transfer in an empty cavity

Air flow by natural convection in an empty cavity isrelated to the difference in wall temperatures. Only conven-tional convection (one vertical cold wall and one verticalwarm wall) is presented in this article. This configurationis often observed in domestic refrigerators where an evap-orator is embedded in the vertical back wall and the doorlocated opposite this wall is warm. The air density varia-tion due to the temperature gradient (perpendicular tothe gravitational direction) contributes to air circulation,hot air being lighter than cold air.

The flow regime in natural convection is characterisedby the Rayleigh number (Ra) defined as

Ra ¼ gbDTL3

amð1Þ

In general, the critical Rayleigh number, which distin-guishes the transition from laminar to turbulent flows, isapproximately 109 (depending on the geometry and bound-ary conditions, Incropera & Dewitt, 1996).

Several experimental studies have been carried out tomeasure air temperature and/or velocity in closed cavities(Ampofo & Karayiannis, 2003; Armaly, Li, & Nie, 2003;Betts & Bokhari, 2000; Mergui & Penot, 1996; Tian &Karayiannis, 2000).

Tian and Karayiannis (2000) used a Doppler laseranemometer to measure the air velocity in a rectangularcavity (height � width � depth = 75 � 75 � 150 cm, Ra =1.58 � 109) (Fig. 1). They observed two types of air cir-culation. The first one is the principal air recirculation

loop near to walls where the air temperature and velocityvary rapidly. The second one consists of small recircula-tion loops located between the boundary layers (nearwalls) and the centre of the cavity.

Eckert and Carlson (1961) carried out an experimentalstudy and they observed that outside the boundary layers,the temperature is homogeneous at a given height and thistemperature increases in the vertical direction. They alsoproposed a correlation between Nusselt (Nu) and Rayleigh(Ra) numbers. No velocity measurements were undertakenin this study.

Ostrach (1988), Catton (1978) and Yang (1987) carriedout a literature review on this subject, which presents theexperimental and modelling results (2-D and 3-D). Theseauthors emphasise the importance of the aspect ratio ofthe cavity and the temperature difference between wallson the flow regime.

Heat exchange by radiation between the internal wallsof the cavity is as important as that achieved by naturalconvection and this should be taken into account. Sev-

Fig. 2. Various heat exchange modes and air flow inside a domesticrefrigerator (source: Laguerre and Flick, 2004).

146 O. Laguerre et al. / Journal of Food Engineering 81 (2007) 144–156

eral authors (Balaji & Venkateshan, 1994; Ramesh &Venkateshan, 1999; Velusamy, Sundarajan, & Seethar-amu, 2001; Li & Li, 2002) showed by experimental andnumerical approaches that these two heat transfer modesoccur simultaneously. Ramesh and Venkateshan (1999)showed experimentally that for a square enclosure (verti-cal walls maintained at 35 and 65 �C, adiabatic horizon-tal walls, Ra = 5 � 105), the heat transfer by convectionand radiation between high emissive vertical walls(e = 0.85) is twice that between polished ones (e = 0.05).The result of this study is relatively different from thecase of a domestic refrigerator since the wall temperaturedifference between the evaporator and the other walls ison average 15 K. The effect of radiation is, therefore, lesssignificant. Balaji and Venkateshan (1994) proposed cor-relations (established from numerical simulations) toexpress the convection and radiation in a square cavityin function of e, Ra, Tc/Th and a radiation–convection

interaction parameter NRC ¼rT 4

hL

kðT h�T cÞ

� �.

These correlations show that the radiation effectincreases when the wall emissivity and/or wall tempera-tures increase. Moreover, Li and Li (2002) reported thatthe radiation increases in comparison with convection asthe size of the enclosure increases. Colomer, Costa, Con-sul, and Oliva (2004) reported that in a transparent med-ium, radiation significantly increases the heat flux. Theseauthors also reported that for a given Planck number,and constant reference temperature ratio, the contribu-tion of radiation remains almost constant for a rangeof Rayleigh number. An estimation of convection andradiation heat transfer in a refrigerator was carried outin our previous study (Laguerre & Flick, 2004). Theequivalent radiative heat transfer coefficient betweentwo parallel plates was evaluated to represent the radia-tive exchange between the evaporator wall and the door.It was found that, the radiative heat transfer coefficient isthe same order of magnitude as the convective heattransfer coefficient. This confirms the importance ofradiation.

2.2. Air flow and heat transfer in a domestic refrigerator

In an empty refrigerator, cold air near the evaporatorflows downward and warm air near the door and the otherside walls flows upwards (Fig. 2). The heat exchanges insidethe cavity are related to natural convection between inter-nal walls and air, radiation between evaporator and theother walls and conduction within the walls (Laguerre &Flick, 2004). In the case of a refrigerator filled with prod-ucts, the products are cooled by natural convection, byradiation between the surface of the products and the inter-nal walls of the refrigerator, and through conduction andradiation between products.

Several studies have been carried out on the cold pro-duction system of domestic refrigerators (Alsaad & Ham-mad, 1998; Bansal, Wich, & Browne, 2001; Chen, Wu, &

Sun, 1996; Graviss & Zurada, 1998; Grazzini & Rinaldi,2001; Radermacher & Kim, 1996). The main objectiveof these studies is to optimize energy consumption. How-ever, fewer studies have been carried out on phenomenainside the refrigerating compartment. Among these stud-ies, those conducted by Masjuki et al. (2001) and Jamesand Evans (1992) were experimental studies on emptyand loaded refrigerators. The objective of these studieswas to analyze the effects of several parameters on thetemperature in the refrigerating compartment (thermostatsetting, frequency of door openings, filled volume, tem-perature and humidity of ambient air). It is difficult tounderstand the mechanism of heat transfer by naturalconvection from the results obtained by these studies,due to the complexity of the refrigerator operation (com-pressor ‘‘on” and ‘‘off” cycles, different degrees of insula-tion in walls, heat loss through gaps, etc.). Measurementof air flow in a freezer compartment under real operatingconditions was carried out by Lacerda, Melo, Barbosa,and Duarte (2005) using PIV (particle image velocimetry).It was observed that the flow field was strongly influenceby the temperature variations due to the ‘‘on” and ‘‘off”

operation cycles of compressor. This behavior was attrib-uted to natural convection and the physical properties(viscosity) of air, which strongly depend on the tempera-ture. Another study on air flow in a ventilated domesticfreezing compartment was carried out by Lee, Baek,Chung, and Rhee (1999). In this study, comparison ofthe velocity field obtained by CFD simulation and byexperiment (PIV measurement) was undertaken. Theseauthors observed that the flow was very complex: jet-likeflow around entrance ports, impinging and stagnationflow on the walls and large recirculation flow in thecavity.

Several numerical studies have been carried out on heattransfer in empty domestic refrigerators (Deschamps,Prata, Lopes, & Schmid, 1999; Pereira & Nieckele, 1997;Silva & Melo, 1998). However, few studies have been car-ried out on loaded refrigerators. The numerical studies

Table 1Characteristics of the refrigerator

External dimensions (height � width � depth) 149 cm � 60 cm � 59 cmInternal dimensions (height � width � depth) 136 cm � 52 cm � 44 cmDimensions of the evaporator 90 cm � 48 cmThermostat setting +5 �CNumber of shelves 4


mentioned previously provide knowledge on the tempera-ture and velocity heterogeneity under determined condi-tions. However, radiation was not taken intoconsideration in spite of the fact that this heat transfermode is of the same order of magnitude as that of convec-tion. In our study, both empty and loaded refrigeratorswere studied and both natural convection and radiationwere taken into account in the simulation.

Fig. 3. Domestic refrigerator geometry: (a) empty refrigerator; (b) refrigerato

3. Materials and methods

3.1. Refrigerator

A static cold refrigerator (without ventilation) was usedin this work. It was a single-door appliance with only arefrigerating compartment (without a freezer). The generalcharacteristics are shown in Table 1.

Three cases were studied (Fig. 3): an empty refrigeratorwithout shelves, empty refrigerator fitted with glass shelves(5 mm thickness, thermal conductivity of glass0.75 W m�1 K�1) and a refrigerator equipped with glassshelves and loaded with a ‘‘test product”. This product ismade of methylcellulose (thermal conductivity0.5 W m�1 K�1) and the dimensions of one package are10 � 10 � 5 cm (length � width � depth). The arrange-

r fitted with glass shelves; (c) refrigerator with glass shelves and products.

Table 2Resolution parameters used in simulation

Relaxation factor Type of discretization

Pressure 0.8 PrestoDensity 1 –Gravity forces 1 –Momentum 0.2 Second order upwindEnergy 1 Second order upwindRadiation 1 –Pressure–velocity – Simple

Table 3Number of cells used for the simulations

Mesh number Height(136 cm)

Half width(26 cm)

Depth(44 cm)

Total

Empty refrigerator 138 28 66 255024Refrigerator with

shelves222 28 66 410256

Refrigerator withshelves and products

240 62 74 1101120


ment of the packages is shown in Fig. 3c. All experimentswere carried out in a temperature-controlled room(20 ± 0.2 �C). As shown in Fig. 3, the evaporator is locatedin the upper part of the cabinet. The indentation observedin the lower right area of the figures represents the com-pressor placement. To avoid a too complex geometry, thecontainers for butter, eggs and bottles usually attached tothe door were removed during our experiments. This facil-itates the meshing of the refrigerator and the resultinterpretation.

3.2. Measurement of the thermal resistance of refrigerator

insulation

Measurement of the thermal resistance of refrigeratorinsulation was carried out in a temperature-controlledroom (6 �C). A heating coil was placed inside the ‘‘switchoff” refrigerator. The heat supplied to the coil is equal tothe heat loss to external air through the walls. The heatingpower was adjusted in such a manner as to maintain theaverage internal air temperature at 30 �C. In this manner,the average temperature of the insulating walls is almostthe same as under real operating conditions. To ensure ahomogeneous air temperature inside the refrigerator, asmall fan was installed near the heating coil. The internalair temperature (Tint controlled at 30 �C), external air tem-perature (Text controlled at 6 �C), power supplied to theheating coil (Q1) and fan (Q2) were recorded when thesteady state was attained (after 12 h) and the average val-ues were calculated over 3 h. Thus, the thermal resistance

Fig. 4. Air (average value on the symmetry plan), side wall (average valuetemperature changes in the empty refrigerator without shelves (thermostat set

of the refrigerator insulation can be calculated knowingQ1 + Q2 and Tint � Text.

The measurement was used afterwards for the bound-ary conditions in the CFD simulation. In fact, this exper-imental thermal resistance takes into account the thermalresistance between external air and internal walls. There-fore, a correction was undertaken on the measured valueby subtracting the thermal resistance between internal air

of three measurements: top, middle and bottom levels) and evaporatorting at 5 �C).


and walls. The internal convective heat transfer coeffi-cient was assumed to be about 10 W m�2 K�1. This cor-rection is weak because the thermal resistance betweenair and internal wall represents only around 7% of theoverall thermal resistance (between external and internalair).

3.3. Temperature measurement

Air and product temperatures were measured experi-mentally using calibrated thermocouples (Type T) placedin different positions of the symmetry plane of the refriger-ator and on the plane situated at 8 cm from side wall(Fig. 3). On each plane, the air temperature was measuredat five height levels (31.0, 61.0, 94.0, 114.5, 134.5 cm) andfor each height, five air temperature measurements wererecorded (1, 2, 21.5, 42, 43 cm from the evaporator).Firstly, the refrigerator operated over 24 h to ensure stabil-ization conditions, then the temperatures were recordedevery 2 min for 24 h and the average value was calculatedat each measurement point. An example of temperatureevolution inside the refrigerator is shown in Fig. 4. It canbe seen that the evaporator temperature varies from�16 �C to +7 �C, due to the thermal inertia, the air temper-ature varies less, from +3.5 �C to +7 �C, and the wall tem-perature varies from 4 �C to 9 �C.

Fig. 5. Mesh structure: (a) empty refrigerator; (b) refrigerator fitted w

4. Modelling

4.1. Main assumptions and boundary conditions

In the present study, the Rayleigh number (Ra) is about6 � 108 (estimation based on the height of the evaporatorand the temperature difference between the internal airand the cold-wall surface). Laminar flow assumption wasmade for the flow regime in our simulation sinceRa < 109. Furthermore, several numerical studies showedthat turbulence does not change the predicted air tempera-ture pattern (Deschamps et al., 1999; Kingston, Woolley, &Tridimas, 1994). Boussinesq approximation was used sincethe air temperature variation is small compared with themean absolute value.

The thermal boundary conditions are based on experi-mental data:

� Uniform global heat transfer coefficient between exter-nal air and internal wall (0.34 W m�2 K�1).� Constant external air temperature (20 �C).� Constant evaporator temperature (�0.5 �C) which is the

average value during ‘on’ and ‘off’ running cycles ofcompressor. This constant temperature is used in orderto avoid excessive complexity in the calculation and toreduce calculation time.

ith glass shelves; (c) refrigerator loaded with the ‘‘test product”.


The simulations were performed with the finite volumemethod using CFD software Fluent 6.1 with the resolutionparameters indicated in Table 2.

Fig. 6. Predicted temperature fields (�C): (a) on the symmetry plan of empty refthe symmetry plan of refrigerator loaded with products; (d) on the plan situa

Transient simulation was performed but only the resultsobtained after simulation convergence were used in thecomparison with the experimental values.

rigerator; (b) on the symmetry plan of refrigerator with glass shelves; (c) onted at 8 cm from the side wall of refrigerator loaded with products.


4.2. Mesh

Structured mesh was used to describe the geometry ofthe refrigerator. Finer meshes were used near walls, shelvesand products. The number of cells used in each case isshown in Table 3 and mesh structures are shown inFig. 5. To ensure that the results were not influenced bythe cell numbers, a sensitivity study was carried out before-hand. Only one half of the refrigerator was meshed becauseof the symmetry plane.

4.3. Discrete ordinate method (DO) for radiation

The discrete ordinate method (Chui & Raithby, 1993)was successfully used to simulate the coupling of convec-tion and radiation in closed cavity (Colomer et al., 2004;Sanchez & Smith, 1992).

This model can take into account the participating med-ium. However, in our case, air is considered as transparent(with neither absorption nor diffusion). The general equa-tion of heat transfer by radiation (in a given~s direction) is

~r � ðIð~r;~sÞ~sÞ ¼ 0 ð2ÞIð~r;~sÞ is radiative intensity in ~s direction (at ~r position)(W m�2 per unit solid angle).

For a gray surface of emissivity er, the net radiative fluxleaving the surface is

Urad out ¼ ð1� erÞZ~s�~n>0

I in~s �~n dX|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

incident flux

þerrT 4s ð3Þ

The walls are assumed as gray diffuse: Iout = /rad_out/p. Iin

is intensity of incident radiation in ~s direction (at ~r posi-tion); ~n is normal vector; Ts is surface temperature, K; Xis solid angle.

A sensitivity study of solid angle discretization was car-ried out beforehand in order to ensure that the simulationresults were not influenced by the number of solid anglesubdivisions.

5. Results and discussion

5.1. Numerical simulation (taking into account radiation)

The results presented in this paragraph concern simula-tion, which takes into account heat transfer by convection

Table 4Average and maximum air temperatures for the three simulations

Average temperature in the maincavity (�C)

Mca

Empty refrigerator 3.8 8.Refrigerator with glass shelves 4.0 9.Refrigerator with glass shelves and

products5.1 9.

between walls and air and by radiation between the internalwalls of the refrigerating compartment.

5.1.1. Temperature fields

The temperature fields obtained from simulations for thedifferent cases studied are shown in Fig. 6. Considering onlythe main cavity (excluding the vegetable box), for all cases,thermal stratification is observed with the cold zone at thebottom (�2 �C) of the refrigerating compartment and thewarm zone at the top (8–9 �C). In addition, a cold zone is alsoobserved along the back wall. This is related to cold air com-ing from the evaporator. When the refrigerator is loadedwith products, the temperature of the product located nearthe evaporator is lower than that located near the door. Inthe top half of the compartment, the temperature is relativelyhomogeneous at a given height (except in the boundary lay-ers near the walls). The temperature of the vegetable box isalmost constant for all cases studied (�8 �C).

The temperature field is slightly influenced by the pres-ence of obstacles: shelves and products. A slightly lowertemperature is observed at the bottom and a slightly higherone at the top compared with the empty refrigerator case.This is due to the fact that the shelves and/or the productsslowed down the air circulation in the central zone of therefrigerator. The presence of shelves and/or products alsoinfluenced the main air circulation in the boundary layerssituated along the evaporator and the side walls. However,this influence is weak because of the presence of air spacesbetween the shelves and the vertical walls (1.2 cm betweenthe back wall and the shelves), which facilitates the air flow.In our previous study, it was found that the thickness of theboundary layer was less than 2 cm (Laguerre, Ben Amara,& Flick, 2005).

In addition to the overall thermal stratification in thecavity, stratification is also observed in each gap betweentwo shelves or between a shelf and a product. It is to beemphasised that for the refrigerator loaded with the ‘‘testproduct”, the symmetry plane is located in the gap betweentwo piles. This explains why the packages are invisible onthis plane (Fig. 6c). On the plane situated at 8 cm from aside wall which cuts the product pile (Fig. 6d), a cold prod-uct zone near the evaporator can be clearly distinguished.This is related to the blockage of cold air by the product.

The average and maximum air temperatures in all casesare reported in Table 4. The air temperatures increase withincreasing numbers of obstacles.

aximum temperature in the mainvity (�C)

Average temperature in thevegetable box (�C)

2 7.40 8.21 8.0


5.1.2. Air velocity field

Fig. 7 presents the air velocity fields on the symmetryplane (Fig. 7a–c) and on the plane situated at 8 cm from

Fig. 7. Path lines: (a) on the symmetry plan of the empty refrigerator; (b) onsymmetry plan of the refrigerator loaded with products; (d) on the plan situa

the side wall (Fig. 7d) for the different cases studied. Con-sidering only the main cavity (excluding the vegetable box),for all cases, the main air circulation is observed near the

the symmetry plan of the refrigerator fitted with glass shelves; (c) on theted at 8 cm from the side wall of refrigerator loaded with products.


walls, and constitutes a recirculation loop. Air flows down-wards along the evaporator while its velocity increasesalong the course to attain a maximum value at the bottom

Fig. 8. Temperature field (radiation not taken into account): (a) on the symrefrigerator fitted with glass shelves; (c) on the symmetry plan of the refrigeratoside wall of the refrigerator loaded with products.

of the refrigerator (umax � 0.2 m s�1). Air then flowsupwards along the door and the side walls of the refriger-ator while its velocity decreases progressively and becomes

metry plan of the empty refrigerator; (b) on the symmetry plan of ther loaded with the ‘‘test product”; (d) on the plan situated at 8 cm from the


stagnant at the top of the refrigerator. This observation isin agreement with the air temperature field shown in Fig. 6,with cold air located at the bottom of the cavity and warmair at the top. It can also be observed that there is a weakhorizontal air flow from the door to the evaporator. How-ever, the air velocity at the centre of the cavity is very low(<0.04 m s�1). In the case of the refrigerator fitted with

Fig. 9. Comparison between experimental air temperatures and predictedrefrigerator; (b) refrigerator fitted with glass shelves; (c) refrigerator loaded w

glass shelves, in addition to the main air flow along thewalls as mentioned previously, there are also small airloops between the shelves. For the refrigerator loaded withproducts, air flows in the gaps between the shelves and theproducts (Fig. 7d).

It should be remembered that the containers attached tothe door were not represented in our study. In practice

values obtained by simulation with and without radiation: (a) emptyith products.


these containers are an obstacle to airflow along the doorand reduce the air velocity in this area.

Considering the vegetable box, one or two air recircula-tion loops were observed (Fig. 7). This is due to the pres-ence of the glass shelf (cold wall), which separates thevegetable box from the main cavity, and the five other wallswhich are warmer (heat loss through these walls).

5.2. Comparison with numerical simulation without radiation

Fig. 8 presents the air temperature field on the symmetryplane obtained by simulation without taking into consider-ation radiation (between internal walls of the refrigeratingcompartment, shelves and product surface). It wasobserved that overall the temperature field is similar to thatpresent when radiation is taken into account (a cold zoneat the bottom and a warm zone at the top). However, strat-ification is more pronounced without radiation, and thisleads to a higher temperature at the top of the cavity. Infact, for an empty refrigerator, the maximum temperaturerises from 8 �C (with radiation) to 15 �C (without radia-tion). This temperature increase can be explained by thefact that, without radiation, there is no heat exchangebetween the warm top wall and the other colder walls, par-ticularly the evaporator wall. This contributes to a high airtemperature at the top position. When radiation is takeninto account, the heat exchange between the top wall andthe other walls tends to reduce the top wall temperatureand consequently reduces air temperature near this wall.From a microbiological point of view, the growth rate ismuch higher at 15 �C than at 8 �C. It is therefore necessaryto take into consideration radiation in the simulation inorder to better describe the phenomena occurring indomestic refrigerators.

5.3. Comparison between the predicted air temperature and

experimental values

Fig. 9 presents a comparison between the experimentaland predicted air temperature results (with and withouttaking into account radiation). It can be seen that the sim-ulation results with radiation agreed with the experimentalvalues to a greater extent, while simulation without radia-tion over-estimated the air temperature, particularly atthe top of the refrigerator. The peaks observed on the tem-perature profile in the presence of shelves and/or productscan be explained by the higher conductivity of glass com-pared with air and by the cold air flow along the uppersides of the shelves.

The agreement between the experimental and simulationresults is relatively poor in the case of a loaded refrigerator,even though the radiative heat exchange between the prod-uct and the walls was taken into account. This may beexplained by the geometry complexity. Further refinementcould lead to a better agreement, but the computing time isalready very high (about 8 days using a cluster of four pro-cessors of 2Go of RAM).

6. Conclusions

Numerical simulation of air flow and heat transfer wascarried out within the refrigerating compartment of adomestic refrigerator without a fan. Three configurationswere studied: an empty refrigerator, an empty refrigeratorfitted with glass shelves and a refrigerator loaded withproducts. When radiation was taken into consideration insimulation, the predicted air temperatures were in goodagreement with the experimental values. However, whenradiation was not taken into account, the temperaturewas over-estimated, particularly at the top of the refrigera-tor. Radiation allows heat exchange, particularly betweenthe top wall and the cold wall (evaporator); consequently,it limits the stratification phenomena.

The obstacles (shelves and/or products) slow down theair circulation in the central zone of the refrigerator andmildly influence the main air circulation along the walls.This is confirmed by the maximum values of air tempera-ture: 8.2 �C for an empty refrigerator without shelves and9.1 �C for an empty refrigerator with shelves and refrigera-tor loaded with products.

Whatever the configuration studied (empty with/with-out shelves, loaded with products) for this type of refriger-ator, the air temperature at the top of the refrigerator isabout 5 �C higher than the average air temperature, andtherefore it is important to avoid placing sensitive productsin this position.

The CFD simulation developed by our work can befurther used as a tool to study the influence of operatingconditions on the temperature and velocity fields: theevaporator temperature (parameter related to the ther-mostat setting by the consumer), the dimensions of theevaporator (parameter related to design) and the percent-age of product-occupied volume in the refrigeratingcompartment.

Acknowledgement

The authors would like to thank to the French Ministryof Agriculture and the ‘‘Ile de France Regional Council”for their financial support.

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Numerical Simulation of Air Flow and Heat Transfer in Domesticrefrigerators

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