2. evaluating the effect of the space surrounding the

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Evaluating the effect of the space surrounding thecondenser of a household refrigerator

Ramadan Bassiouny*

Dept. of Mech. Power Eng. and Energy, Faculty of Engineering, Minia University, Minia 61111, Egypt

a r t i c l e i n f o

Article history:Received 4 August 2008

Received in revised form

10 February 2009

Accepted 18 March 2009

Published online 2 April 2009

Keywords:

Domestic refrigerator

Modelling

Simulation

Convection

Air

Air condenser

a b s t r a c t

The paper presents an analytical and computational modeling of the effect of the spacesurrounding the condenser of a household refrigerator on the rejected heat. The driving

force for rejecting the heat carried by the refrigerant from the interior of a refrigerator is

the temperature difference between the condenser outer surface and surrounding air. The

variation of this difference, because of having an insufficient space, increasing the room air

temperature, or blocking this space, is of interest to quantify its effect

The results showed that having an enough surrounding space width (s > 200 mm) leads

to a decrease in the temperature of the air flowing vertically around the condenser coil.

Accordingly, this would significantly increase the amount of heat rejected. Moreover,

blocking this space retards the buoyant flow up the condenser surface, and hence increases

the air temperature around the condenser. This would also decrease the heat rejected from

the condenser. Predicted temperature contours are displayed to visualize the air plumes’

variation surrounding the condenser in all cases.

ª 2009 Elsevier Ltd and IIR. All rights reserved.

Impact de l’espace autour du condenseur d’un re frige rateurdomestique : e valuation

Mots cle s : Refrigerateur domestique ; Modelisation ; Simulation ; Convection ; Air ; Condenseur a air

1. Introduction

Household refrigerators are cyclic systems that consume

a reasonable amount of electric energy to fulfill a certain job.

The performance of the different components of the refrig-

erator is of interest for many researchers to investigate and

analyze. These refrigerators prove to be durable, reliable,

and provide a satisfactory service for over 15 years (Cengel

and Boles, 1999). Improper operation and placement of

a refrigerator would certainly degrade its performance anddurability.

The basic vapor-compression refrigeration cycle remained

more efficient than the absorption refrigeration cycle and the

thermoelectric refrigeration cycle. Fig. 1 shows a general

schematic of a household refrigerator with a wire-and-tube

condenser attached to the back of the refrigerator. The figure

also shows the domain of interest in the present study. The

performance of each component of the refrigerator affects its

* Tel.: þ20 16 391 6415; fax: þ20 86 2346674.E-mail address: [email protected]

w w w . i i fi i r . o r g

a v a i l a b l e a t w w w . s c i e n c e d i r e c t . c o m

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m/ l o c a t e / i j r e f r i g

0140-7007/$ – see front matter ª 2009 Elsevier Ltd and IIR. All rights reserved.

doi:10.1016/j.ijrefrig.2009.03.011

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 1 6 4 5 – 1 6 5 6

mailto:[email protected]

http://www.iifiir.org/

http://www.sciencedirect.com/

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

http://www.sciencedirect.com/

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http://www.iifiir.org/

mailto:[email protected]



overall performance. The challenge for the designer is to

control noise, vibration, heat rejection, and minimize the

power consumption of the compressor; keeping the system

operates at higher efficiencies and capacities.

The condenser is the main component in the refrigerating

system.It is responsible for rejecting the heat, absorbed by the

refrigerant in the evaporator, out of the refrigerator

compartment into its surroundings. It may be cooled by

Nomenclature

A area (m2)

C p air specific heat, J kg 1 K1

d diameter (m)

g gravitational acceleration (m s2)

G flow rate per unit area (kg s1 m2)

Gr Grashof number (–)

H condenser height (m)

h heat transfer coefficient (W m2 K1)

k thermal conductivity (W m1 K1)

l tube length (m)_m mass flow rate, kg s1

N number of wires (–)

p pressure (N m2)

P Pitch (m)

Pr Prandtle number (–)

Q heat rejected (W)

Ra Rayleigh number (–)

s surrounding gap thickness (m)

T temperature (K)

U overall heat transfer coefficient (W m2 K1)

u, v velocity (m s1)

W condenser width (m)

x, y coordinate system (m)

Subscripts

a air

avg average

c condenser, convection

ev evaporator

e element

eq equivalenti inner, element number

l liquid

o outer

r radiation

R refrigerant

s surface

t tube

v vapor

w wall

Greek letters

a thermal diffusivity (m2 s1)

b coefficient of expansion (K1)

N ambient conditions

n kinematic viscosity (m2 s1)

r air density (kg m3)

Refrigerator

compartment

Compressor

Refrigerator

condenser

Evaporator

tube

Refrigerator

door

Capillary

tubeDrier

Rubber gasket

H

WRefrigerator

back-wall

wire

s

Interested parameter

Condenser tube

cross-section

air

current

Fig. 1 – A schematic of a household refrigerator and the interested domain.




natural draft on freestanding refrigerators and freezers or fan-

cooled on larger models and on models designed for built-in

applications. The natural-draft condenser is attached to the

back wall of the compartment, Fig. 1, and is cooled by natural

air convection under the refrigerator cabinet and up the back.

Mainly a natural-draft condenser consists of a flat serpentine

of copper tubes of 4.5 mm outer diameter, and steel wires of

almost 1 mm diameter welded 6 mm apart normal to thecondenser tubes. Generally, one of the most important design

requirements for a condenser includes sufficient heat dissi-

pation at peak-load conditions. Insufficient surrounding air

passage or blocking this passage by a cabinet above the

refrigerator level will degrade the performance of the

condenser and thus the refrigerator (Cengel and Boles, 1999).

The refrigerator performance and energy savings are of

great importance for many researchers. Laguerre and Flick

(2004) investigated natural convection inside the refrigerator

compartment. This is important to visualize the cabinet air

movement that will greatly help placing foods in places with

effective heat transfer.

To minimize the radiation effect of the condenser andcompressor surfaces on the interior temperature of refriger-

ator–freezers, a suggestion of covering the refrigerator wall

near the condenser and compressor with an aluminum foil

was studied in Afonso and Matos (2006). The authors

mentioned that putting this aluminum foil reduced the inte-

rior air temperature by 2 K.

The wire-on-tube condensers, used in the R-12 based

refrigerators, were numerically and experimentally studied by

Ameen et al. (2006) when used with R-134a based refrigera-

tors. The authors used the FEM method to analyze free

convection around this type of condensers. They tracked the

refrigerant flow to check the location where condensation

inception occurs. The authors investigated two differentcondenser coils with different tube-and-wire pitch, number,

and length. They reported that the two-phase change loca-

tions are shifted downstream with either the increase in the

refrigerant mass flowrate or increase in ambient temperature.

Bansal and Chin (2003) presented a useful analysis for the

wire-and-tube condenser. They optimized the condenser

capacity per unit weight by varying wire-and-tube pitches and

diameters. They reached an optimization factor that led to an

improved design with 3% gaining capacity and 6% reduced of

condenser weight. In the same study, the authors reported

that the outer heat transfer resistance contributes to about

80% for single-phase flow and 83–95% for two-phase flow.

Further, the dominant heat-transfer mode is by convection,which contributes to 65% of the total heat transfer.

Bansal and Chin (2002) studied the performance of the hot-

wall condensers, as a replacement of the wire-and-tube

condensers. The authors analyzed the heat transfer charac-

teristics for the condenser. They claimed that a 10% over-

prediction in condenser capacity was attributed to the heat

infiltration into the refrigerator compartment, which they did

notconsiderin their model.Theyconcludedthatthe outer heat

transfer resistance contributes to about 80% and 83–95% of the

total heat transfer for single and two-phase flow respectively.

The temperature of the space, in which the refrigerator is

placed, is of importance since it affects the heat dissipation

driving force. Saidur et al. (2002) experimentally studied the

effect of this ambient temperature on energy consumption.

The room temperature was varied from 14 C to 32 C in an

environmentally controlled chamber located in a laboratory.

The authors mentioned that, according to ASHRAE, 60–70% of

the total refrigerator load is due to the temperature difference

between the air surrounding the refrigerator and the refrig-

erator interior temperature. The most significant conclusion

drawn by the authors is that the room temperature has thehighest effect on energy consumption.

The motivation behind this paper was the waya household

refrigerator is placed in a kitchen or a room. In some narrow

places, the refrigerator backside, where the condenser is

attached, is pushed against a wall leaving a very small gap of

air to carry the condenser rejecting heat. Therefore, it was

thought that there should be a sort of optimization through

quantifying the effect of this gap on condenser rejected heat,

compressor consumed power, and accordingly the refriger-

ator performance.

The present analytical model did benefited from a previous

effective model (Bansal and Chin, 2003), but was modified to

serve a different purpose in this study.

2. Problem formulation

The temperature difference between the condenser-surface

temperature, Ts, and the surrounding air temperature, Ta, is

the driving force for rejecting the heat librated from the

refrigerator’s occupants. In most household refrigerators, the

condenser cooling process takes place naturally. Therefore, it

is very necessary to have an enough free space around the

condenser to allow this cooling process to occur effectively.

Being a part of the space in which the refrigerator is placed,

the condenser surrounding air has essentially the sameconditions as this space. Hence, the temperature of the

refrigerator surrounding affects the condenser effectiveness,

and accordingly the refrigerator performance. It is expected

that as the condenser surrounding space is narrowed or

blocked, the air flowing through gets hotter. This would

prolong the compressor time of operation to reach an internal

thermostat set point, and would decrease the refrigerator

coefficient of performance as a result.

The physical domain to be studied is shown in Fig. 1. The

air surrounding the condenser is sandwiched between the

refrigerator back wall to which the condenser is attached and

the room wall. Through this width, s, the air temperature

surrounding the condenser importantly varies. Hence, thedriving force to reject the condenser heat intothe surrounding

will be affected.

The analysis considered a certain refrigerant temperature,

and a fixed refrigerant flow rate. This assumption helps

keeping the compressor working on a fixed pressure ratio. The

goal was the effect of moving a refrigerator against a room

wall on the condenser heat rejected driving force.

3. Mathematical formulation

The mathematical analysis of this natural convection process

is based on an elemental energy balance. So, the element

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 1 6 4 5 – 1 6 5 6 1647



approach with variable conductance and air temperature over

the elements is employed. Fig. 2 shows an element of the

condenser. Theelement length is equal to the tube length, and

its height equals to the tube pitch, Pt. Heat is rejected from

tube and wires by both convection and radiation. Therefore,

the heat transfer over an element can be represented by the

following equation:

Q e ¼ UAe

TR Ta;avg

(1)

where UAe is the conductance, and Ta,avg is the air average

temperature over the element. It is calculated in a weighting

fashion between the temperature of the air entering the

element, Tai, and the temperature of the air leaving the

element, Taiþ1, as follows:

Ta;avg ¼ uTai þ ð1 uÞTaiþ1 ¼ Taiþ1 þ uðTai Taiþ1Þ (2)

where u is a weighting factor that is considered 0.5 in this

study for the sake of equally dividing the contribution of inlet

and exit air temperatures over the element. For heat to flow

from the refrigerant inside the tubes to the ambient air

surrounding the tubes, it should overcome a series of resis-

tances. These resistances are the inner convection resistance,

the conduction resistance, and the outer convection resis-

tance. The resistances are connected between refrigerant

temperature, inner wall temperature, outer-surface equiva-

lent temperature, and the average ambient temperature. The

surrounding air temperature was averaged in a weighted

fashion (eq. (2)) between the inlet and exit air temperatures

over the studied element. In addition, the condenser outer-

surface equivalent temperature was related to both the tube

temperature and wire temperature. The conductance is the

reciprocal of the summation of all these resistances. It can be

written as:

UAe ¼ 1

1hiAi

þlnðro=riÞ

2pkwl þ

1hoAo

(3)

The outer area includes the area of the tube and the area of

the wires. It can be written as:

Ao ¼ At þ Awire ¼ pdtl þ 2pdwirePtN

The outer convective heat transfer is required. This coeffi-

cient represents both convection and radiation so, it can be

written as:

ho ¼ hc þ hr (4)

Knowing that convection and radiation take place from

both tube and wires, it is necessary to define tube outer

temperature, Tt,o, andwire temperature, Twire. The wires act as

fins, so the fin efficiency concept is adopted for the case of

finite length. Therefore, the fin efficiency is given as ( Holman,

1981):

hwire ¼tanhðmPt

2

mPt

2

; where m ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

4hwire

dwirekwire

s (5)

The wire temperature can then be calculated as follows:

Twire ¼ hwireTt;o þ uð1 hwireÞTai þ ð1 uÞ ð1 hwireÞTaiþ1 (6)

knowing that hwire ¼ ðTwire Ta;avg =Tt;o Ta;avg Þ and using

equation (2).

Since the wires are normally welded to the tubes, a contact

resistance exists. Due to the wire small diameter, an equiva-

lent temperature taking into consideration the wire-and-tube

temperatures is proposed in Bansal and Chin (2003) as follows:

Teq ¼

AtTt;o þ AwireTwire

Ao ¼

dtlTt;o þ 2dwirePtNTwire

dtl þ 2dwirePtN (7)

Substituting equation (6) into equation (7) gives:

Teq ¼dtlTt;o þ 2dwirePtNTwire

dtl þ 2dwirePtN ¼ a1Tt;o þ a2Tai þ a3Taiþ1 (8)

where the coefficients are defined as:

a1 ¼1 þ 2NFhwire

1 þ 2NF ; a2 ¼

2uNFð1 hwireÞ

1 þ 2NF ;

a3 ¼2ð1 uÞNFð1 hwireÞ

1 þ 2NF

and the factor F represents a geometric ratio defined as:

F ¼

dwire

dt

Pt

l

The outer-radiation heat transfer coefficient, hr is calculated

based on the energy balance between the radiation and

analogy to convection. The walls were assumed to have the

same temperature of the air since this free convection and the

air velocities are very small. Therefore, this outer-radiation

heat transfer coefficient, hr is calculated using the following

relation:

hr ¼ 3appsT4eq T4

a;avg

Teq Ta;avg

(9)

where 3app represents the apparent emissivity, which is anidentification parameter for the heat exchanger. It is taken

0.88 as a reasonable value (Bansal and Chin, 2003). The Stefan–

Boltzmann constant, s, is 5.67 108 W/m2 K4.

Tagliafico and Tanda (1997) proposed a correlation to

compute the outer convective heat transfer coefficient for the

wire-and-tube condenser. This correlation is given as:

hc ¼Nuka

H ; where Nu

¼ 0:66

RaH

dt;o

0:25(

1

1 0:45

dt;o

H

0:25!

eðsw=4Þ

) (10)

and Ra ¼ Gr Pr ¼ bgðTt;o TNÞH3=na.

Tai

Tai+1

Pt

Single

tube

Wires

Tube length

Qe

Fig. 2 – One-element layout for wire-and-tube

configuration.




The parameter 4 ¼ ð28:2=HÞ0:4sw0:9st1:0 þ ð28:2=HÞ0:8

264=

Tt;o TN

0:5sw1:5st0:5

while sw ¼ pwire dwire /dwire, and st ¼ pt dt /dt.

The solution procedure is presented in the flow chart

shown in Fig. 3. It is not easy to model the process without

setting some assumptions. In this study, the airflow was

assumed to be steady state, laminar (Ra < 109), and the wiresand tube have constant temperatures. The refrigerant satu-

ration temperature corresponding to the condenser pressure

is dominant over the condenser length. In this analysis,

a degree of superheating and subcooling was assumed to be

5 C. As a result, a theoretical cycle was plotted on the pres-

sure–enthalpy diagram of R-12, and an average condenser

temperature was calculated based on the condenser inlet

temperature in the superheated region, the saturation

temperature at Pc, and the condenser exit temperature in the

compressed liquid region.

The inner convective heat transfer coefficient can be

calculated based on ASHRAE (1997) correlation for condensa-

tion in horizontal tubes. This correlation is in the form of:

hDkl

¼ 0:026mlC p

kl

1=3DGeq

ml

0:8

(11)

where Geq ¼ Gvðrl=rvÞ0:5 þ Gl.

Equation (11) is reported in ASHRAE (1997) (eqn. (13) by

Ackers et al. table (3), chapter 4) for a film-type condensation

in horizontal tubes. The parameter G is the mass velocity

(mass flow rate/area), i.e. Gv¼mv /Av, and Gl¼ml /Al. Knowing

that m ¼ mv þ ml or 1 ¼ x þ ml=m, and A ¼AvþAl. The mass

No

Yes

No

yes

No

yes

hwire = ho

Correct guessed

T t,o

y = y + Pt

T a i = T a i+1

Start

Input refrig. Temp., refrig. flow rate, tube and

wire element geometric data, conductivity

Calculatewire , T wire , T eq , hr

Update air properties based on T eq, and obtain hc and ho

Calculate hi, and then Qe based on the resistances eq.(1)

Print T ai , T ai+1 , Qe

Stop

Initial guess of T t,o, hwire, and T a i

Calculate T t,o, and element exit temp. T a i+1

|T t,o - T t,o, g|< 0.01

| ho-hwire | < 0.01

First tube and wire element, y = 0, Pt

Is y = condenser

height

Fig. 3 – Flow chart of the analytical solution procedure.




velocities can be approximated as: Gv¼G, and Gl¼ (1 x)G for

a certain refrigerant flow rate.

Since heat transfer from the refrigerant to the ambient

equals to heat transfer from the refrigerant to the outer

surface of the condenser in the steady state, the outer tube

temperature can be calculated as:

Tt;o ¼ TR Q e

lnðro=riÞ2pkl

þ 1hiAi

(12)

The heat rejected by the condenser outer surface is carried

by the airflow surrounding the condenser. Hence, the exit air

temperature over an element is obtained through a heat

balance between the amount of heat rejected by convection

and radiation over that element with the air enthalpy change

and given as:

Ta;iþ1 ¼ Q e_maC p

þ Ta;i (12a)

The gap between the condenser and the room opposite wall

was treated as an enclosure of a rectangular cross-section.

Hence, at the condenser bottom this area along with anassumed very low inlet air velocity and density was used to

estimate the inlet air mass flow rate, neglecting the open-ends

effect, as thestudy focuseson a two-dimensional flow and the

flow was assumed upward due to the buoyancy effect.

A FORTRAN program was written, based on the flow chart

shown in Fig. 3, and used the above-mentioned governing

equations to analyze the wire-and-tube condenser behavior.

4. Experimental measurements

Some measurements were carried out on a wire-and-tubecondenser of a real household refrigerator type (Ideal

RC225LF, 125 W) works on 145 g of R-12. The condenser

configurations are as listed below:

- Tube outer diameter ¼ 0.0045 m

- Wire diameter¼ 0.001 m

- Tube pitch¼ 0.05 m

- Tube length¼ 0.45 m

- Condenser height¼ 0.8 m

- No. of wires per side ¼ 64

- No. of tube elements¼ 16

The refrigerator was placed against a room wall leaving theinterested gap to be studied. Thermocouples were placed into

this gap at the condenser bottom, middle and upper levels to

measure the upward air temperatures at different cross-

distances. Thermocouples were soldered to the outer surface

of the tube and their junctions were wrapped to isolate the

junctions from the convection and radiation effect from

surrounding. The condenser temperature was averaged based

on three values at the bottom, middle, and upper portions.

The thermocouple accuracy was 1 C. For a certain internal

load at a setting evaporator temperature, the condenser

average outer-surface temperature was measured for the

three distances (30 mm, 100 mm, and 200 mm) and was found

to be 51 C, 47 C, and 41 C, respectively. These values were

considered in the analytical model to predict the condenser

heat rejected for the three cooling gaps. The refrigerant

temperature was assumed to be one degree above the outer

surface temperature since the tube thickness is small. The

refrigerant flow rate was considered varies from 0.0005 to

0.0007 kg s1. The whole cycle was plotted on the R-12 p–h

diagram and the condenser heat rejected was found almost

between 120 W and 97 W; as the distance varies from 200 mmto 30 mm. The cycle coefficient of performance was calculated

and found to be approximately from 2 to 3 for the same

refrigerating effect.

5. Numerical analysis

The computational fluid dynamics, CFD, was used as a tool of

numerical visualization to model this buoyancy-driven

problem. Ansys, a commercial finite element program, was

used to predict the flow pattern through the different gap

thicknesses. The flow was assumed to be laminar (Ra < 109),

steady, and two-dimensional.Since the natural flow around the condenser is mainly due

to the buoyancy effect, it is necessary to know the velocity

pattern and temperature variation as a result. This requires

solving for the momentum equations considering the effect of

buoyancy force on the pressure gradient. Then the energy

equation is solved to predict the temperature distribution.

Hence, the considered governing equations are the conser-

vation of mass, conservation of momentum, and conservation

of energy equations. Definitely, there is an order of magnitude

between the u and v values as well as their variation. These

equations, as given in Bejan, 1984 and listed below, predict the

air velocity and temperature variation under different

conditions.

vu

vxþvy

vy¼ 0 (13)

uvu

vxþ y

vu

vy¼

1r

v p

vxþ nV2u (14)

uvy

vxþ y

vy

vy¼ nV2yþ gbðT T

NÞ (15)

uvT

vxþ y

vT

vy ¼ aV2T (16)

The y-momentum equation, eqn. (15), adopts the Boussinesqapproximation for the body force term. The momentum

equations (14) and (15) account for the change of momentum

due to free convection, and due to viscous effect due to the

buoyancy force effect. Equation (16) takes care of the energy

balance between heat dissipated by conduction and

convection.

Fig. 4 shows a schematic for the adopted boundary condi-

tions along the computational domain. No slip conditions

were assumed along the walls: the room wall, the refrigerator

back wall, and the condenser tubes’ outer surface. The bottom

inlet air to the condenser was assumed to have the same

temperature as the room air. A very tiny value of air velocity in

the y-direction, vin, was assumed to be a solution trigger. The




6.1. Effect of surrounding space

Fig. 6 depicts a qualitative seen for the temperature contours

around the condenser coil for the three-studied distances. A

remarkable difference is shown in terms of the temperature

variation between the three studied gaps. The figure shows

almost a laminar boundary layer aroundthe tubes at the lower

part of the condenser within almost 150 mm from the inlet.Beyond this point, an intermittent flow disturbance and the

flow wiggle around the tubes. Tagliafico and Tanda (1997)

mentioned that flow around wire-and-tube condensers are of

different regimes depending on the condenser height. More-

over, in the narrow gap (s ¼ 30 mm), almost a symmetrical

temperature distribution is noticed around the condenser

tubes with the higher temperature exists around the tubes’

surface. As the gap width gets bigger, the symmetry trend is

lost. In addition, it can be seen the decrease in the transverse

air temperature across the gap for the 100 mm width

compared to the case of 30 mm. A further move of the

refrigerator from a room wall improves the rate of heat

rejected from the condenser. This can be attributed to theenough sink in which the condenser rejects its heat. These

contours can depict the air plumes trapped around the

condenser tubes and room wall. Practically, as the condenser

can effectively reject the heat absorbed from the interior of

the refrigerator, the compressor time of operation can be

saved. This could improve the refrigerator coefficient of

performance as a result.

Quantitatively, the average air-temperature variation

inside the gap surrounding the condenser is presented in Fig. 7

for an ambient air temperature of 30 C, and a condenser

temperature of 50 C. The figure clearly describes the variation

of air average temperature at different gap widths. The figureindicates that having a sufficient cooling gap around the

condenser (s > 200 mm) would absorb the rejected heat, and

hence slightly affecting the surrounding air temperature

along the condenser. This sufficient space decreases the

convective and radiant resistance in front of the rejected heat,

and accordingly improves the overall heat transfer coefficient.

The figure illustrates the steeper boundary layer for the

narrow width (s¼ 30 mm) compared to that is approaching

a flatten profile at s > 200 mm. It can be quantitatively

concluded that increasing the gap width around the

condenser from 30 mm to 300 mm resulted in almost a 70%

decrease in the air average temperature along the condenser

height, which will accordingly improve the heat transfer rate.The variation of air average temperature and the corre-

sponding heat rejected is shown in Fig. 8. The figure illustrates

the decrease of the average air-temperature as the condenser

surrounding space gets wider. A significant linear drop in the

Fig. 6 – Air temperature contours along the condenser tubes ( T N[30 8C).




air temperature is shown up to a space width of 300 m, and

then the trend intends to approach an asymptotic behavior

beyond this gap thickness. This trend is under certain oper-

ating conditions of fixed: refrigerant flow, condenser capacity

per weight, and cooling capacity. The figure can conclude that

the existence of a sufficient space around the condenser

would improve the heat reject driving force and accordingly,

allow more heat to be rejected from the condenser surface.

It is important to validate the analytical as well as the

numerical predictions through some measurements. Fig. 9

compares the vertical variation of air average temperature at

three different gap widths under the same operating conditions. All trends are qualitatively similar; however,

there was a numerical overprediction at the lower part of

the condenser and a slight underprediction at the upper

part. This could be a result of a round-off error exists in the

numerical analysis.

6.2. Effect of room air temperature

Masjuki et al. (2001) mentioned that compressor efficiency

declines as the ambient temperature rises, and the refriger-

ator consumption of electricity is sensitive to the ambient

temperature. The authors concluded that energy consump-

tion increasesaround 40 W h for a 1 C increase in theambienttemperature. Hence, as the room air around the condenser

gains heat (room internal loads, the refrigerator is placed close

to a gas stove as in a kitchen, or the refrigerator condenser is

exposed to the sun), the driving force for dissipating the

refrigerator internal load into surrounding decreases. There-

fore, in addition to the space around the condenser, there will

be a problem if the air in the room in which the refrigerator is

placed gains heat before flowing up to the condenser tubes.

Fig. 10 presents an analysis for the effect of room air-

temperature increase on the amount of heat rejected by the

condenser. The analysis considered an average condenser

temperature. The figure shows a linear decrease of the heat

rejected with a line slope that is the heat capacity, UA, as theroom air temperature increased that means the decrease of

heat rejected per 1 C decrease of temperature difference

(TeqTa,avg ) for a constant condenser temperature. The figure

also indicates that the resistance in front of the rejected heat

is strongly existed in the narrow gap thickness, s ¼ 30 mm.

The results showed that for a constant condenser tempera-

ture, increasing the room air temperature decreases the heat

rejected by almost 65%.

6.3. Effect of air blockage

Blocking the air passage around the condenser would signifi-

cantly affect the air behavior and the condenser effectivenessas a result. An example of blocking the air around the

condenser is having a cabinet with a certain depth and at

a certain distance above the refrigerator. Such a cabinet

existence would affect the natural convection process and the

rate of heat reject as a result. The present study visualized

through the CFD the effect of having such a cabinet (15 cm

above the level of a refrigerator). Fig. 11 quantitatively

compares the average air-temperature variation in both cases.

An increase of almost 6 C in the air temperature can be seen

near the upper part of the condenser, when the cabinet exists.

This increase can be attributed to the accumulation of hot

plumes of airbelow the cabinet surface. Thiswouldeventually

decrease the ability of condenser to reject its heat. On the

Air Temperature, °C

25 30 35 40 45

V e r t i c a l D i s t a n c e , m

0.0

0.2

0.4

0.6

0.8

s = 0.03 ms = 0.1 ms = 0.2 ms = 0.3 m

s = 0.4 ms = 0.5 m

Fig. 7 – Average air temperatures’ distribution along the

condenser height.

Cooling Gap Thickness, m

0.0 0.2 0.4 0.6 0.8 1.0

H e a t R e j e c t e d , W

10

20

30

40

50

60

70

80

AverageA

irTemperature,°C

30

32

34

36

38

40

42

44

46

(T = 30 °C)∞

Fig. 8 – Effect of gap thickness on air average temperature

and condenser heat rejected.




other hand, the effect of the cabinet is not felt at the lower part

of the condenser up to a distance of 0.2 m.

Fig. 12 shows a qualitative numerical visualization of the

air temperature contours for the case of s ¼ 100-mm width.

The figure clearly shows the difference when a cabinet is

existed above the refrigerator. The figure depicts the warm

air plumes accumulation near the cabinet due to closing

the vertical passage in front of the buoyant air. This indi-

cates a stratification effect. It can be shown the increase of

air temperature around the condenser tubes as well as

where the upward-flowing air is leaving the refrigerator

back wall.

Room Air Temperature, °C

15 20 25 30 35 40 45

C o n d e n s e r H

e a t R e j e c t e d , W

0

20

40

60

80

100

120

s = 0.03 m

s = 0.1 m

s = 0.2 m

s = 0.5 m

Tc = 50 °C)

Fig. 10 – Effect of room temperature variation on condenser

heat rejected.

Air Average Temperature, °C

0 10 20 30 40 50 0 10 20 30 40 500 10 20 30 40 50


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

s = 0. 03 m (num.)

s = 0. 03 m (analy.)s = 0.03 m (Exp.)

Air Average Temeprature, °C


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

s = 0.1 m (num.)

s = 0.1 m (analy.)s = 0.1 m (Exp.)

Air Average Temperature, °C


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

s = 0.2 m (num.)

s = 0.2 m (analy.)s = 0.2 m (Exp.)

Fig. 9 – Average air temperature along the cooling gap at the three distances considered.

Average Air Temperature, °C

0 10 20 30 40 50

V e

r t i c a l D i s t a n c e , m

0.0

0.2

0.4

0.6

0.8

No Cabinet

With Cabinet

Fig. 11 – Air-temperature variation through the 0.1 m gap

without and with a kitchen cabinet almost 0.15 m above

the level of the refrigerator.




7. Conclusions

A household refrigerator placed in a space where insufficient

surrounding air surrounds the condenser would certainlydegrade its performance. The aim of this paper was to

investigate the effect of this surrounding space on the

condenser capacity to reject heat. Some conclusions can be

drawn from the study. The results showed that having an

enough space (s > 200 mm) around the condenser increases

the driving force of heat transfer from the condenser. On the

other hand, if the room air temperature increased, even for

an enough space, the amount of heat rejected will decrease.

Blocking the space around the condenser will resist the up-

flow of buoyant air and allow for hot air accumulation close

to the upper part of the condenser. Accordingly this would

decrease the driving force to reject heat out of the condenser

surface.

r e f e r e n c e s

Ameen, Ahmadul, Mollik, S.A., Mahmud, Kizir, Quadir, G.A.,Seetharamu, K.N., 2006. Numerical analysis and experimentalinvestigation intothe performanceof a wire-on-tube condenserof a retrofitted refrigerator. Int. J. Refrigeration 29, 495–504.

ASHRAE, 1997. ASHRAE Handbook of Fundamentals. AmericanSociety of Heating; Refrigerating; and Air Conditioning Engineers, Atlanta, GA (Chapter 4).

Afonso, Clito, Matos, Joaquim, 2006. The effect of radiationshields around the air condenser and compressor of a refrigerator on the temperature distribution inside it. Int. J.Refrigeration 29, 789–798.

Bansal, P.K., Chin, T.C., 2002. Design and modelling of hot-wallcondensers in domestic refrigerators. Appl. Therm. Eng. 22,1601–1617.

Bansal, P.K., Chin, T.C., 2003. Modelling and optimisation of wire-

and-tube condenser. Int. J. Refrigeration 26, 601–613.

Fig. 12 – Temperature contours for the 0.1 m gap with and without a kitchen cabinet above the level of the refrigerator

( T N[30 8C, T c[50 8C). (a) No kitchen cabinet, (b) with a kitchen cabinet.




Bejan, Adrian, 1984. Convection Heat Transfer. John Wiley & SonsInc. (Chapters 4 and 7)

Cengel, Yunas A., Boles, Michael A., 1999. Thermodynamics, anEngineering Approach, third ed. McGraw-Hill Co.

Holman, J.P., 1981. Heat Transfer, fifth ed. McGraw Hill Co.Laguerre, O., Flick, D., 2004. Heat transfer by natural convection in

domestic refrigerators. J. Food Eng. 62, 79–88.Masjuki, H.H., Saidur, R., Choudhury, I.A., Mahlia, T.M.I.,

Ghani, A.K., Maleque, M.A., 2001. The applicability of ISO

household refrigerator–freezer energy test specifications inMalaysia. Energy 26, 723–737.

Saidur, R., Masjuki, H.H., Choudhury, J.A., 2002. Role of ambienttemperature, door opening, thermostat setting position andtheir combined effect on refrigerator–freezer energyconsumption. Energy Convers. Manage. 43, 845–854.

Tagliafico, L., Tanda, G., 1997. Radiation and natural convectionheat transfer from wire-and-tube heat exchangers in

refrigeration appliances. Int. J. Refrigeration 20, 461–469.


2. evaluating the effect of the space surrounding the

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