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Modeling of a domestic frost-free refrigerator

J.K. Gupta, M. Ram Gopal, S. Chakraborty*

Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

Received 14 October 2005; received in revised form 27 April 2006; accepted 29 June 2006

Available online 14 September 2006

Abstract

In the present study, a comprehensive thermo-fluidic model is developed for a domestic frost-free refrigerator. The governingequations, coupled with pertinent boundary conditions, are solved by employing a conservative control volume formulation, in

the environment of a three-dimensional unstructured mesh. Experiments are also conducted to validate the results predicted by

the present computational model. It is found that the computational and experimental results qualitatively agree with each other,

although certain discrepancies can be observed in terms of the exact numerical values obtained. For the freezer compartment, the

computationally predicted temperatures are somewhat higher than the experimental ones, whereas for the refrigerating compart-

ment, the computed temperatures are lower than the corresponding experimental observations. The difference between exper-

imental and computational results may be attributed to the lack of precise data on the airflow rates and the unaccounted heat

transfer rates through the door gaskets and the compressor. From the heat transfer and fluid flow analysis, certain modifications

in the design are also suggested, so as to improve the performance of the refrigerator.

Ó 2006 Elsevier Ltd and IIR. All rights reserved.

Keywords: Refrigerator; Modelling; Simulation; Performance; Comparison; Result; Experiment

Modelisation d’un refrigerateur domestiquefonctionnant sans formation de givre

Mots cles : Refrigerateur ; Modelisation ; Simulation ; Performance ; Comparaison ; Resultat ; Experimentation

1. Introduction

Thebasic function of a domestic refrigerator is to preserve

the quality of perishable food products. Several studies have

shown that the quality of food products directly depends on

temperature and air distribution inside the storage chambers.

Hence, unsuitable temperatures and air velocities may cause

food to undergo a premature deterioration. Even if the aver-

age temperature inside the refrigerator cabinet is adequate,

uncontrolled rise or fall in local temperatures may affect the

quality of food products. In many cases, the air temperature

may even turn out to be somewhat higher than the maximum

permissible values specified in the standards, in practice [1].

Although the problem associated with off-design

thermo-fluidic conditions prevailing in a refrigerator appears

to be very common, it has not been extensively studied. Only

a few theoretical and experimental studies in this regard

have been carried out on conventional, natural convection

* Corresponding author. Tel.: þ91 32 22282990; fax: þ91 32

22282278.

E-mail address: [email protected] (S. Chakraborty).

0140-7007/$35.00 Ó 2006 Elsevier Ltd and IIR. All rights reserved.

doi:10.1016/j.ijrefrig.2006.06.006

International Journal of Refrigeration 30 (2007) 311e322

www.elsevier.com/locate/ijrefrig

mailto:[email protected]


http://www.elsevier.com/locate/ijrefrig





driven, manual defrost refrigerators [1e4]. However, the

more commonly used modern-day frost-free domestic re-

frigerators have rarely been analyzed. Recently, Laguerre

and Flick [2] have presented an analysis on heat transfer

by natural convection in domestic unventilated refrigerators.

They have carried out an approximate analysis on conven-

tional refrigerators, by employing a two-dimensional analy-

sis, under isothermal wall conditions. A major conclusion

from their study is that in these refrigerators, the air is prac-

tically stagnant in the core region of the compartment,

which does not ensure adequate rate of convective heat

transfer between the air and refrigerated items. Although

the above simplified analysis gives an approximate feel of

the physical situation, impractical boundary conditions

and two-dimensional approximations detract the case far

away from the reality. Ding et al. [3], in a more recent study,

have explored various means for improving thermal homo-

geneity inside a refrigerator, using CFD modeling, and

have compared their numerical results with experiments.

They have studied the unventilated refrigerators, in which

the heat transfer takes place because of natural convectiononly. They have pointed out that the gap between the shelves

and the walls (including the door) plays a major role in

maintaining a uniform thermal state inside the system. As

an improvement, they have suggested a new system, which

includes an air duct and a blower. However, mathematical

details of the model and effects of operating conditions on

the refrigerator performance have not been discussed in their

study. A similar study, based on conventional refrigerators

has been carried out by Fukuyo et al. [4]. While similar

modeling efforts have been only a few, those have only

been restricted to idealized boundary conditions, without

considering intricate aspects of a frost-free refrigerating

system. In fact, no single study addressing a detailed

thermo-fluidic analysis of frost-free domestic refrigerators

has been reported in the literature. This may be attributed

to the fluid-dynamically complex and product-specific na-

ture of frost-free domestic refrigerators. Transport phenom-

ena in the refrigerant compartment of such refrigerators are

essentially of mixed convection type, while those in the

freezer are usually forced convection driven. The problem

is inherently transient and three-dimensional in nature. Toavoid the associated complexities, a certain degree of empir-

icism is always present in engineering design of such refrig-

erating systems. In this context, a comprehensive numerical

model may turn out to be extremely useful in designing such

types of refrigerators, for an optimal performance.

The aim of the present work is to develop a Computa-

tional Fluid Dynamics (CFD) model for domestic frost-

free refrigerators, for prediction of temperature and velocity

fields in the freezer and refrigerating compartments. Using

this model, effects of various operating and design parame-

ters on the refrigerator performance can be studied, leading

to an optimal design and performance estimation of therefrigerator. Experiments are also performed to obtain the

temperature variations inside the compartments, and the

numerical results are subsequently compared with experi-

mental findings, in order to quantitatively assess various fea-

tures of the numerical model adopted.

2. Mathematical modeling

2.1. The physical model

The main objective of a refrigerator is to keep the stored

food items at low temperatures to arrest their rate of

Nomenclature

Ec Eckert Number

g Acceleration due to gravity (m sÀ2)

h Heat transfer coefficient (W mÀ2 K À1)

k Thermal conductivity (W m

À1

K

À1

) p Pressure (Pa)

Pr Prandtl Number

Ra Rayleigh Number

Ri Richardson Number

T Temperature (K)

t Thickness (m)

u X -component of velocity (m sÀ1)

v Y -component of velocity (m sÀ1)

V Velocity vector

w Z -component of velocity (m sÀ1)

x , y, z Co-ordinates

Greek symbolsa Thermal diffusivity (m2 sÀ1)

b Coefficient of thermal expansion (K À1)

h Similarity variable

f General scalar variable

n Kinematic viscosity (m2 sÀ1)

rDensity (kg m

À3

)Subscripts

a Surroundings

0 Reference state

N Ambient

nb Neighbour

P Grid point central to each computational cell

r Radiative

w Wall

o Overall

312 J.K. Gupta et al. / International Journal of Refrigeration 30 (2007) 311e 322




deterioration with time. To achieve this purpose, the refrig-

erated space is kept at a temperature lower than that of

its surroundings. Hence, there would always be a heat trans-

fer from the surroundings to the inner compartments and

from the refrigerated items (which actually act as heat

source).

The refrigerator considered here is a frost-free refrigera-tor, in which the evaporator is not directly exposed to the re-

frigerating compartments. Rather, air is first made to flow

over the evaporator, so that it can be simultaneously cooled

and dehumidified. The cold and dry air is then blown into the

compartments. The air mass takes heat and moisture from

the products being refrigerated and surroundings, and be-

comes relatively warm and humid in this process. This

warm and humid air stream is again made to flow over the

evaporator coils, where it again becomes cold and dry by re-

jecting sensible and latent heat to the refrigerant flowing

through the evaporator. This cycle keeps on repeating over

the entire regime of operation.The side view of a typical frost-free refrigerator (includ-

ing the airflow path), mentioned as above, is schematically

shown in Fig. 1. As shown in the figure, the cold air first

flows inside the refrigerating (fresh food) and freezer cham-

bers, and extracts heat from the refrigerated items kept at

those locations. Exit air streams from these chambers even-

tually mix just beneath the evaporator. The air stream then

flows over the evaporator (placed at the back of the freezer),

where it is cooled and dehumidified. Subsequently, the fan

blows the cold air into the freezer inlet, from which a portion

flows into the freezer, while the rest enters the refrigerating

compartment. A defrost heater is placed just below the evap-

orator which removes periodically the frost formed on the

evaporator coils. In convectional refrigerators, defrosting is

doneby manually switching offthe refrigerator, and allowing

the frozen layer to melt on account of heat transfer from the

surroundings. In frost-free refrigerators, however, this is

done automatically by a combination of defrost heatere

timerethermostat control.

From the above discussions, it is apparent that modelingof a domestic frost-free refrigerator essentially requires ap-

propriate representations of the freezer compartment (which

is normally maintained at a temperature of around À18 C or

less) and the refrigerating compartment (which is main-

tained at an average temperature of about 5 C). In most

of the domestic refrigerators, the refrigerating compartment

has the following three parts:

1. Chiller compartment : it is maintained at an average

temperature of around 0e4 C and is used to store

food products such as milk, fish, meat that are most

susceptible to thermal degradation.2. Vegetable compartment : it is used to store vegetables,

and is maintained at temperatures of around 5e13 C.

3. Shelves: these are kept at 4e7 C (approximately), typ-

ically for the purpose of storing fresh food, cooked/

processed food items and beverages.

In the present analysis, the freezer and the refrigerating

compartments are considered as separate units. The mathe-

matical model is developed for the inner compartments

only. For a more detailed understanding of the geometric

features of the flow domain under concern, details of the

freezer and refrigerator control volumes are described, as

follows.

Fig. 1. Heat transfer and airflow in a refrigerator.




Fig. 2 shows an explored schematic diagram of freezer

compartment. The cold air first enters into the inner inlet

and then enters into the compartment through inner inlet

ports. A part of the air, which comes out of inner inlet ports,

goes into the portion above the shelf, and the remaining air

enters directly into the area below the shelf, through the gap

between the back wall and shelf. The air which is above the

shelf then descends through the door shelf, exits through the

Fig. 3. Refrigerating compartment e control volume.

Fig. 2. Freezer-control volume.




inner outlet port, and finally from the outlet. Similarly, the

air stream flowing below the shelf circulates in that region

and exits through the outlet.

Fig. 3 shows a schematic diagram of refrigerating com-

partment. Here, both the inlets and outlets are located at

the top of the compartment. The cold air, after getting out

of the front inlet, flows downwards, confronts the chillerwall, and eventually re-circulates inside the compartment.

This air, after coming back from the chiller, mixes with

the air blown through the back inlet ports. The mixed air de-

scends due to buoyancy, circulates through the shelves, and

finally exits through the door shelves (just above which the

outlet ports are located).

2.2. Major assumptions, governing equations

and boundary conditions

For mathematical analysis, the following simplifying

assumptions are made:

1. Fluid flow is taken to be incompressible. This is justi-

fied by very low Mach numbers ð Max10À3Þ, typical

to the present system.

2. Viscous dissipation terms in the energy equation are

neglected, which is justified due to low values of the

product of Eckert number and Prandtl number

ð Ec Â Pr w10À4 or lessÞ.

3. A steady state case is being analyzed. In reality there is

a continuous on and off cycling for compressor, which

brings transient nature to the problem. A steady state

or lowest attainable temperature state can be achieved

by cutting off the thermostat and letting the compres-sor work continuously.

4. The refrigerator is analyzed in an unloaded condition,

and effects of air leakage or frosting and the associated

mass transfer mechanisms are not considered. This is

a simplifying assumption.

5. Boussinesq assumption is employed for flow modeling

inside the refrigerating compartment, which is governed

by mixed convection ðRichardson numberð RiÞ ¼ðGr = Re2Þw1Þ, whereas buoyancy effects are neglected

for the freezer component, because of strong inertial

effects ð Riw0:05Þ. Variations of all thermo-physical

properties are assumed to be small, over the range of operating temperatures.

6. Radiation heat transfer within the refrigerator is not

considered. In the refrigerating compartment, none of

the walls are in direct contact with evaporator, and

the temperature difference between the surfaces facing

each other (shelves, side walls) is quite small (2e4 C).

Thus, the radiation heat exchanges between these sur-

faces can be neglected. Analogous considerations can

be made for the freezer compartment as well.

7. The flow is assumed to be laminar in both the compart-

ments. In the refrigerating compartment, this can be

justified by virtue of the Rayleigh numberð Raw108

or lessÞ being well below the transitional regime for

onset of turbulence. The above Rayleigh number esti-

mation is based on a characteristic length scale that is

either the height or the width of the heat transfer sur-

face under concern (depending on whichever is larger)

and the maximum temperature difference prevailing

within the walls. Such length scales and temperaturescales are adopted so as to obtain an estimation of

the highest possible Rayleigh number, corresponding

to the prevailing free convective heat transfer condi-

tions. Estimation of this upper limit, in turn, ensures

whether one is safely within the regime of laminar

transport or not. The Reynolds number corresponding

to the forced flow conditions over the solid boundaries

is estimated to be of the order of 104, based on the

maximum flow velocities entering the respective com-

partment and the maximum length in that direction (for

freezer it is the maximum length in z direction, for re-

frigerating compartment it is the height of the compart-ment) of flow. The above is also one order less than the

transitional Reynolds number for the onset of turbu-

lence. At the inlet ports, the Reynolds number is to

the tune of 103, which again explains the laminar na-

ture of flow. Here, the Reynolds number is based on

average velocity and hydraulic diameter of ports, in ac-

cordance with the convention for internal flows.

8. The condenser and evaporator coils are considered as

isothermal walls, because of the nearly isothermal

phase change processes associated with these compo-

nents. These are incorporated as boundary conditions

in the domain with finite conductive resistances.

9. Heat transfer between freezer and fresh food compart-

ments is neglected.

10. Uniform velocity and temperature profiles are assumed

at the inlet.

Based on the above assumptions, the heat transfer and

fluid flow equations can be described as follows:

Continuity

vu

v x þ vv

v yþ vw

vz¼ 0 ð1Þ

X-momentum conservation

uvu

v x þ v

vu

v yþ w

vu

vz¼ À 1

r0

v p

v x þ nV2u ð2Þ

Y-momentum conservation

uvv

v x þ v

vv

v yþ w

vv

vz¼ À 1

r0

v p

v yþ nV2v þ gbðT À T 0Þ ð3Þ

Z-momentum conservation

uvw

v x þ v

vw

v yþ w

vw

vz¼ À 1

r0

v p

vzþ nV2w ð4Þ




Energy conservation

uvT

v x þ v

vT

v yþ w

vT

vz

¼ aV2T ð5Þ

Boundary conditions appropriate to the above system of equations are summarized in Tables 1 and 2, for the freezer

and refrigerator compartments, respectively. The values of

overall heat transfer coefficients are estimated; based on

the thermal resistances offered by various heat transfer

paths, as follows:

1

ho

¼ 1

ha þ hr

þ t w

k w

where ha is the ambient heat transfer coefficient, hr is an

equivalent heat transfer coefficient to account for the radia-

tion effects, t w is the wall insulation thickness and k w is the

thermal conductivity of the wall. Heat transfer within theshelves is not modeled in detail. Rather, the shelves are mod-

eled as geometrical obstacles to the flow, with a finite con-

duction heat transfer resistance.

2.3. Numerical implementation

The computational domains, as depicted in Figs. 2 and 3,

are discretized using a mesh generating software, GAMBIT.

Adequate care is taken to capture the steep gradients of the

field variables near the solid boundaries. In order to achievethis purpose, both hydrodynamic and thermal boundary layer

thicknesses are estimated and 10e15 computational cells

havebeen designed to lie within the same, so as to obtain suf-

ficient resolutions close to the fluidesolid interfaces. A com-

prehensive mesh-sensitivity study has also been undertaken,

and it has been revealed that a further refinement in the grid

resolution does not alter the numerical solutions appreciably.

The above choice of mesh distribution, therefore, happens to

be an optimized compromise between the requirements of

numerical accuracy and computational economy.

The mesh generated as above is subsequently exported

to a commercial CFD software, FLUENT. The governingequations mentioned as above are discretized using a finite

volume method, where the overall computational domain

is divided into finite-sized elemental control volumes.

Table 1

Boundary conditions for the freezer compartment

Boundary Temperature Velocity

Inlet Uniform temperature profile, T N¼ 251.7 K Velocity inlet with uniform profile

VN ¼ 0:5ð0i þ 0 j þ 1k Þ m sÀ1

Outlet Zero normal gradient Zero normal gradient

Top wall Convective, T N¼ 302 K, ho ¼ 0.27 W mÀ

2 K À1 No slip

Left side wall Convective, T N¼ 302 K, ho ¼ 0.37 W mÀ2 K À1 No slip

Right side wall Convective, T N¼ 302 K, ho ¼ 0.37 W mÀ2 K À1 No slip

Bottom Adiabatic No slip

Back wall Convective, T N¼ 251 K, ho ¼ 11.11 W mÀ2 K À1 No slip

Front wall Convective, T N¼ 302 K, ho ¼ 0.59 W mÀ2 K À1 No slip

Table 2

Boundary conditions for refrigerating compartment

Boundary Temperature Velocity

Inlet

Front Uniform temperature profile, T N¼ 253 K Velocity inlet with uniform profile

VN ¼ ð0:2= ffiffiffi

2p Þð0i À 1 j þ 1k Þ m sÀ1

Back Uniform temperature profile, T N¼ 253 K Velocity inlet with uniform profile

VN¼ ð

0:45= ffiffiffi2p Þð

0iÀ

1 j À

1k Þ

m sÀ1

Outlet Zero normal gradient Zero normal gradient

Top wall Adiabatic No slip

Left side wall

Left wall 1 Convective, T N¼ 327 K, ho ¼ 0.44 W mÀ2 K À1 No slip

Left door wall Convective, T N¼ 302 K, ho ¼ 0.40 W mÀ2 K À1 No slip

Right side wall

Right wall 1 Convective, T N¼ 327 K, ho ¼ 0.44 W mÀ2 K À1 No slip

Left door wall Convective, T N¼ 302 K, ho ¼ 0.40 W mÀ2 K À1 No slip

Bottom Convective, T N¼ 302 K, ho ¼ 0.27 W mÀ2 K À1 No slip

Back wall Convective, T N

¼ 327 K, ho ¼ 0.37 W mÀ2 K À1 No slip

Front wall Convective, T N¼ 302 K, ho ¼ 0.59 W mÀ2 K À1 No slip




Discretized equations for each variable are formulated by

integrating the corresponding governing equation over the

three-dimensional computational control volumes. An un-

structured grid system with hexahedral elements is used to

discretize the computational domain. A co-located scheme

is used, where both the scalar and vector quantities are

stored at the cell centers. The face values for the convectionterms are interpolated from the cell center values following

the power law scheme [5]. The values of pressure at the cell

faces are interpolated following the PRESTO scheme,

which uses the discrete continuity balance for a staggered

control volume centered around the cell face to compute

the staggered (i.e., face) pressure. The procedure is similar

in spirit to the staggered-grid schemes used with structured

meshes [5]. On simplification, the final discretized equations

for each of the conserved scalars take the following form:

a Pf P ¼X

nb

ðanbfnbÞ þ zU DV ð6Þ

where subscript P represents a given grid point, while sub-

script nb represents the neighbors of the given grid point P,

f is a general variable such as velocity or enthalpy, a is the co-

efficient calculated based on the power law scheme,DV is the

volumeof the controlvolume. The coefficienta P isdefinedas:

a P ¼X

nb

anb À z PDV ð7Þ

The terms zU and z P are used in the source term lineari-

zation as:

z

¼zU

þz Pf P

ð8

ÞA point implicit (GausseSeidel) linear equation solver is

used in conjunction with an algebraic multigrid (AMG)

method to solve the resultant scalar system of equations for

the dependent variable in each cell and the pressureevelocity

coupling is achieved by SIMPLE algorithm [5]. Exploiting

a vertical symmetry of the problem domain, one half of the

controlvolumes depicted in Figs. 2 and 3 is essentially solved.

3. Results and discussions

Results are obtained for frost-free refrigerator working

under steady state (with thermostat shorted) and under no-

load conditions. A summary of the important numerical pa-rameters, corresponding to the above-mentioned simulation,

is presented in Table 3. From the table, it is evident that the

present model satisfies overall mass and energy balance con-

ditions, within acceptable tolerances, both for the freezer as

well as the refrigerating compartment.

3.1. Airflow and temperature variations in

the freezer compartment

The numerical model employed for analyzing the freezer

compartment considers a three-dimensional, incompressible,

and laminar forced convection. Fig. 4(a) shows the velocity

vectors at the near side panel, while Fig. 4(b) shows the

temperature distribution at the same. It can be seen from

Fig. 4(a) that a large portion of air first flows over the top,

while a small portion comes down through the gap between

the main shelf and the back wall. Portion of air that is atthe top flows from back wall to the front wall, subsequently

comes down through the door shelves, and finally flows out

through the exit ports. Fig. 4(a) clearly shows that the model

takes into account all the shelves and even the slots in the

door shelves. It is also quite clear from Fig. 4(a) that the air

entering at the top can only come down either through the

gap between the back wall and the main shelf, or via the slots

at the door shelves, or via the gap between the door shelves

and main shelf. Portion of the air that flows down through

the gap between the back wall and main shelf also moves

from back to front, and finally exits through the outlet.

Regarding the temperature profile, it is clear from Fig. 4(b)

that though the temperature is almost uniform above andbelow the shelves, portion below the shelf is warmer due to

insufficient airflow in that region.

Fig. 5(a) shows that the variation of velocity magnitude

is from 0 to 0.33 m sÀ1 while Fig. 5(b) shows the variation

of temperature along the central vertical line, which varies

from 252.75 to 255.75 K. The velocities arefound to increase

as one moves away from the solid boundaries, and the peak

value occurs at a location of about 0.1 m down the top, within

the portion of the freezer compartment that is located above

the shelf. A lower value of peak velocity occurs in the region

below the shelf, just outside the thin hydrodynamic boundary

layer formed adjacent to the solid boundary at the bottom.Regarding the thermal field, from Fig. 5(b) it can be seen

that the top wall temperature is the highest. The temperature

suddenly drops outside the thermal boundary layer formed

in the vicinity. Within the rest of the freezer compartment lo-

cated above the shelf, the temperature is virtually uniform,

because of a strong dominance of forced convection mecha-

nisms. Thermal conditions in the region below the shelf are

warmer, due to lower rates of airflow in that region.

Fig. 6 shows the variation of temperature along the cen-

tral longitudinal axis, as one moves from one lateral side to

the other. From the figure, it is quite clear that the variations

along this direction are negligible (except near the wall), and

Table 3

Overall mass and energy balance

Quantity Freezer Refrigerating

compartment

Mass flow rate in (kg sÀ1) 0.005281034 0.0013260324

Mass flow rate out (kg sÀ1) 0.005281034 0.0013260324

Relative error in mass balance (%) 0 0

Cooling capacity (W) 9.197922 33.2058

Heat transfer from surrounding to

the inner compartment (W)

9.140672 33.0608

Relative error in energy

balance (%)

0.577 0.4366




the bulk temperature is quite uniform. The steep gradients at

the walls occur because of the formation of thin thermal

boundary layers in thevicinity, as a consequence of low ther-

mal diffusivity of air.

3.2. Airflow and temperature variations in

refrigerating compartment

The flow in refrigerating compartment is three-

dimensional, incompressible, and a combined consequence

of free and forced convections (i.e., mixed convection).

Fig. 7(a) shows the velocity vectors within the refrigerating

compartment, at the symmetry plane, while Fig. 7(b) shows

the corresponding temperature profile. It is seen from

Fig. 7(a) that the air from the front inlet first goes into the

chiller compartment. Since this air is cold, a gravitational

stability makes it to settle down on the chiller shelf itself.

However, as the air gains heat from the surroundings, it be-

comes lighter. Finally, the hot air flows back and mixes with

the cold air stream emanating from the inlets located at the

Fig. 4. (a) Velocity vectors at the near side panel ( x ¼ 0.1 m). (b) Temperature variation at the near side panel ( x ¼ 0.1 m).




back. The resultant mass of cold air flows down due to buoy-ancy effects. A part of this cold air stream enters the first

shelf, where again it first settles down on the shelf, subse-

quently gets re-circulated as it mixes with the inlet stream

of air flowing at the back, and the combined stream flows

down through the gap between the back wall and the main

shelf. This happens at each and every shelf, and eventually

the air reaches the lid of vegetable compartment. A warmer

air stream subsequently rises from the bottom part of the

door, mixes with the side air streams, and finally exits

through the outlet.

Fig. 5. (a) Velocity magnitude variation at the line of variation

( x ¼ 0.27 m, z ¼ 0.15 m). (b) Temperature variation at the line of

variation ( x ¼ 0.27 m, z ¼ 0.15 m).

Fig. 6. Temperature distributions on the center line of the shelf of

freezer ( x ¼

0.02 m, y¼

0.165 m).

Fig. 7. (a) Velocity vectors at the symmetry plane of refrigerating

compartment ( x ¼ 0.27 m). (b) Temperature distribution on the

symmetry plane of refrigerating compartment ( x ¼ 0.27 m).




The temperature profile in the refrigerating compartment

is shown Fig. 7(b). It can be seen from the figure that the

temperature in the chiller compartment is the lowest, and

the temperature increases as one moves along the downward

direction. Such a gradient of temperature is established on

account of the advective effects imposed by the cold air

stream that first enters into the chiller and subsequentlygoes into the shelves located below. So far as the portion ad-

jacent to the door is concerned, the temperature rises from

the bottom to the top, in accordance with the prevailing di-

rection of flow. Further, since a major portion of the cold

air stream descends through the gap between the back wall

and door shelves, this portion remains colder relative to its

surroundings.

Fig. 8(a) shows that the velocity magnitude variation is

from 0 to 0.19 m sÀ1 while Fig. 8(b) shows the temperature

variation, along the central vertical axis located on the plane

of symmetry and it varies from 265 to 277 K. The velocity

profile between any two adjacent solid surfaces (shelves orwalls) does not exhibit any regular pattern, by virtue of

a combined effect of the differing thermal fields and diverse

conditions of forced flow (a variable mixed convection pat-

tern, in totality). Maximum velocity is observed at the por-

tion between vegetable compartment lid and bottom shelf

just above the vegetable crisper lid. The vegetable crisper

lid acts as an obstacle and allows very little amount of air

to go down. It is actually the part of total cold air from the

inlet which could come through the gaps between the

shelves and back wall and the part which came back after

getting re-circulated within the cavity between the shelves.

This is much higher than the cold air part circulating within

all the enclosures between the two shelves. Hence a maxi-mum is observed at this location as the air is cold and will

try to settle on the lid.

Regarding the temperature variation, it can be seen from

Fig. 8(b) that temperatures at the lowest point of the troughs

correspond to a local minima. Since the cold air first settles

on the shelf and then rises, the bottom of each shelf corre-

sponds to the location of an associated cold spot. On an av-

erage, there is a trend of increasing cold spot temperature, as

one descends down the central vertical axis. This is because

of the fact that the cold air exchanges heat from its surround-

ings, as it moves down, and thereby becomes warmer.

Fig. 9 shows the temperature variation along the centralhorizontal axis, as one moves from the one side to the other.

It is clear from the figure that the temperature is almost

uniform in this direction. The chiller compartment is at the

lowest temperature, while the temperature increases as one

moves down from that zone. Because of the presence of

the inlet ports, temperature of the chiller is considerably

lower at the center, in comparison to the same at other

locations.

3.3. Comparison with experiments

Experiments are carried out to capture temperature vari-

ation in a 320 l frost-free refrigerator, in an unloaded and

thermostat-shorted condition, so that steady state (lowest

attainable temperature) conditions can be achieved. A data

acquisition system was used with K-type thermocouples to

keep track of temperature at walls and shelves for about

22 h at every 1 s interval. The uncertainty in temperature

measurement [6] is Æ1 C. When the thermostat is shorted,

the compressor and the fan are maintained in a running con-

dition. When the compressor is on, the air is cooled as it

Fig. 8. (a) Variation of velocity magnitude at the line of variation of

refrigerating compartment ( x ¼ 0.27 m, y ¼ 0.19 m). (b) Variation

of temperature at the line of variation of refrigerating compartment

( x ¼

0.27 m, z¼

0.19 m).

Fig. 9. Temperature distribution on the center line (z ¼ 0.19 m) of

chiller base ( y ¼ 0.9 m) and shelves (upper at y ¼ 0.5 m and lower

at y¼

0.3 m) for refrigerating compartment.




flows over the evaporator coil. The air, after passing over the

evaporator coils, enters into the compartment and gains heatfrom the walls, as well as from the air located within the

compartment itself. The hotter air stream again flows out

of the compartment, and subsequently over the evaporator

coils, as it gets cooled. This cycle continues. As the sur-

rounding temperature is constant, in principle, a point is

reached when the heat gain from surroundings becomes

equal to evaporator cooling capacity, i.e., a steady state is

attained, corresponding to the lowest possible temperatures

prevailing inside the compartments. Since the numerical

model computes for a steady state, the computational results

are validated against the ‘lowest attainable temperature test’,

mentioned as above.

Fig. 10 depicts the temperature variation, along the cen-

tral vertical axis on which the thermocouple points are lo-

cated, within the freezer compartment. It is clear from the

numerical results shown in Fig. 10 that while moving from

the top to the bottom, the temperature first drops drastically,

and then remains nearly a constant. Finally, the temperature

rises slowly, as one proceeds towards the bottom. The trend

shown by the experimental data is also the same. A compar-

ison between experimental and numerical predictions of

temperature, at chosen locations along the central vertical

axis, is summarized in Table 4. Differences between the

computed and measured values can be attributed to errors

in experimental measurements and also to insufficient infor-mation about the local airflow rates occurring in practice.

Fig. 11 shows the temperature variations along the cen-tral vertical axis, within the refrigerator compartment.

Here also, a similar trend in experimentally and numerically

obtained temperature profiles can be observed. The compu-

tationally obtained temperatures, however, are always found

to be on a lower side, which may be attributed to the unac-

countable heat leakage into the compartment from the

door gaskets (not considered in the numerical model). More-

over, in the numerical analysis the temperature of the back

wall is assumed to be a constant and same as the condenser

temperature (i.e., 327 K), which in reality might be an un-

derestimate, because of the presence of the compressor

and the de-superheating condenser coils. Table 5 depicts

a comparison between experimental and computational

values of temperature, at the shelf and the outlet. Both the

numerical and experimental results show that the tempera-

ture at the lower shelf is lower than that at the upper one, be-

cause of the fact that the flow in this region is directed from

the bottom to the top.

Table 6 shows a comparison between the experimentally

obtained and computationally obtained cooling capabilities,

as calculated from the inlet and outlet temperatures and the

pertinent airflow rates. It is quite clear that the values pre-

dicted by the model are on the lower side. This may be attrib-

uted to the small uncertainties regarding the actual air mass

flow rates and due to additional heat leakages into the com-partment through the gaskets and compressor.

Fig. 10. Comparison between experimental and computational re-

sults at the symmetry plane of freezer ( x ¼ 0.27 m, z ¼ 0.15 m).

Table 4

Comparison between experimental and computational temperatures

at outlet and shelves for freezer

Point Temperature (K)

Computational Experimental

Upper shelf 253.4 252.3 Æ 1

Lower shelf 253.5 252.9 Æ 1

Outlet 253.9 254.3 Æ 1

Fig. 11. Comparison between experimental and computational

results at the symmetry plane of refrigerating compartment

( x ¼ 0.27 m, z ¼ 0.19 m).

Table 5

Comparison between experimental and computational temperatures

at outlet and shelves for refrigerating compartment

Point Temperature (K)

Computational Experimental

Upper shelf 275.75 283.7 Æ 1

Lower shelf 273.4 282.1 Æ 1

Outlet 277.4 284.9 Æ 1




4. Conclusions

In the present study, a thermo-fluidic model for a domes-

tic frost-free refrigerator is developed, and is simulated by

employing a finite volume method, with an unstructured

meshing. Experiments on temperature measurement are

also conducted, in order to assess the pertinent predictions

from the numerical model. It is found that the trends in com-

putational and experimental results are qualitatively similar,

though there is a perceptible offset. For the freezer compart-

ment, the computationally predicted temperatures are mar-

ginally higher than the corresponding experimental values,

which may be attributed to the lack of exact data on airflow

rates. In case of the refrigerating compartment, the compu-

tationally predicted temperatures are lower than the experi-

mental ones. This may be attributed to the heat leakage

through the door gaskets, which is not considered in the

computational model. Also the temperature behind the

back wall is considered to be uniform, which in reality,

varies from de-superheating to sub-cooling temperatures.

On the basis of the results obtained, a few modifications

may be suggested to improve the performance of the refrig-erator. In case of the freezer compartment, the gap between

the back wall and main shelf may be increased, so as to en-

hance the airflow rates. In case of the refrigerating compart-

ment, the average temperature in the chiller zone happens to

be slightly higher than the desirable standards, which can be

lowered by increasing the mass flow rate of air from the front

inlet. However, at the same time the mass flow rate through

the back inlets needs to be reduced, so that the total massflow rate can be kept constant. Also, the door shelf should

be located such that it is sufficiently away from the plane

of the main shelf, so as to allow more air to flow down

and subsequently rise from the front portion of the main

shelf, thereby reducing the re-circulations, leading to the

utilization of the cold air in a more effective and energy-

efficient manner.

References

[1] O. Laguerre, E. Derens, B. Palagos, Study on domestic refrig-

erator temperature and analysis of factors affecting tempera-ture: a French survey, International Journal of Refrigeration

25 (2002) 653e659.

[2] O. Laguerre, D. Flick, Heat transfer by natural convection in

domestic refrigerators, Journal of Food Engineering 62

(2004) 79e88.

[3] G. Ding, H. Qiao, Z. Lu, Ways to improve thermal uniformity

inside a refrigerator, Applied Thermal Engineering 24 (2004)

1827e1840.

[4] K. Fukuyo, T. Tanammi, H. Ashida, Thermal uniformity and

rapid cooling inside refrigerators, International Journal of

Refrigeration 26 (2003) 249e255.

[5] S.V. Patankar, Numerical Heat Transfer and Fluid Flow,

Hemisphere/McGrawHill, 1980.

[6] S.J. Kline, F.A. McClintock, Describing uncertainties in single

sample experiments, Mechanical Engineering 75 (1953) 3e8.

Table 6

Comparison between experimental and computational cooling

capacities

Cooling capacity (W)

Experimental Computational

Freezer 13.5 Æ 1.35 9.198Refrigerating compartment 42.1Æ 4.21 33.2058


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