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This work is licensed under a CC BY-NC-ND 4.0 License (Creative

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more information see https://creativecommons.org/licenses/by-nc-nd/4.0/.

Paul, A., Baumhoegger, E., Elsner, A., Moczarski, L., Reineke, M., Sonnenrein, G., Hueppe, C.,

Stamminger, R., Hoelscher, H., Wagner, H., Gries, U., Freiberger, A., Becker, W., & Vrabec, J. (2020).

Determining the heat flow through the cabinet walls of household refrigerating appliances. International

Journal of Refrigeration. https://doi.org/10.1016/j.ijrefrig.2020.10.007

Andreas Paul, Elmar Baumhögger, Andreas Elsner, Lukas Moczarski,

Michael Reineke, Gerrit Sonnenrein, Christian Hueppe, Rainer

Stamminger, Heike Hoelscher, Hendrik Wagner, Ulrich Gries, Alfred

Freiberger, Wolfgang Becker, Jadran Vrabec

Determining the heat flow through the

cabinet walls of household refrigerating

appliances

Accepted manuscript (Postprint)Journal article |

Determining the heat flow through the cabinet walls of household

refrigerating appliances

Andreas Paul a, b, Elmar Baumhögger a, Andreas Elsner a, Lukas Moczarski a, b,

Michael Reineke a, Gerrit Sonnenrein a, Christian Hueppe c, Rainer Stamminger c,

Heike Hoelscher d, Hendrik Wagner d, Ulrich Gries e, Alfred Freiberger f,

Wolfgang Becker g, Jadran Vrabec b *

a Thermodynamics and Energy Technology, University of Paderborn,

Warburger Str. 100, 33098 Paderborn, Germany

b Thermodynamics and Process Engineering, Technical University of Berlin,

Ernst-Reuter-Platz 1, 10587 Berlin, Germany

c Institute of Agricultural Engineering – Section Household and Appliance

Engineering, University of Bonn, Nussallee 5, 53115 Bonn, Germany

d BASF Polyurethanes GmbH, Elastogranstraße 60, 49448 Lemförde, Germany

e Secop GmbH, Mads-Clausen-Str. 7, 24939 Flensburg, Germany

f Secop Austria GmbH, Jahnstraße 30, 8280 Fürstenfeld, Austria

g BSH Home Appliances GmbH, Robert-Bosch-Straße 100, 89537 Giengen an der

Brenz, Germany

*corresponding author

Highlights

•A measurement method for determining the 𝑘𝑘∙𝐴𝐴 value of household

refrigerating appliances is presented.

•A latent heat sink is a suitable alternative to the reverse heat leak method.

•Air flow and storage temperatures in the refrigerator compartment are

comparable to the real operating conditions.

•Temperature gradients between the storage room and the ambient of the

refrigerating appliances are more realistic.

•An age-related increase of the 𝑘𝑘∙𝐴𝐴 value of between 3.6 % and 11.5 % is found

over a period of 14 months.

Keywords

Household refrigerating appliances, PUR foam, 𝑘𝑘∙𝐴𝐴 value, Insulation, Measurement

method

Accepted manuscript of: Paul, A., Baumhoegger, E., Elsner, A., Moczarski, L., Reineke, M., Sonnenrein, G.,

Hueppe, C., Stamminger, R., Hoelscher, H., Wagner, H., Gries, U., Freiberger, A., Becker, W., & Vrabec, J.

(2020). Determining the heat flow through the cabinet walls of household refrigerating appliances.

International Journal of Refrigeration. https://doi.org/10.1016/j.ijrefrig.2020.10.007

https://creativecommons.org/licenses/by-nc-nd/4.0/

Abstract

The increase of the thermal conductivity of PUR foam in the insulation of the cabinet

is an important cause for aging processes of household refrigerating appliances. To

determine the influence of the PUR foam aging on energy consumption, the

development of a new measurement method is necessary because current methods

influence the aging behavior of household refrigerators and are therefore not

applicable in general. Based on a latent heat sink, constructed as an ice water bucket,

a new measurement method is developed to determine the 𝑘𝑘∙𝐴𝐴 value over time. With

this method, the 𝑘𝑘∙𝐴𝐴 value of four household refrigerating appliances was determined

over an interval of 14 months. The 𝑘𝑘∙𝐴𝐴 value increased between 3.6 % and 11.5 %

during this period.

Nomenclature

𝐴𝐴 Surface (m2)

𝐴𝐴𝑎𝑎 Outer surface (m2)

𝐴𝐴𝑖𝑖 Inner surface (m2)

𝐴𝐴𝑗𝑗 Average surface of material layer j (m2)

𝑐𝑐𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖 Specific isochoric heat capacity of ice (kJ/(kg K)

𝑑𝑑𝑗𝑗 Material thickness of layer j (mm)

𝑘𝑘 Heat transfer coefficient (W/(m2 K))

(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 𝑘𝑘∙𝐴𝐴 value related to the ice water bucket (W/K)

(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 𝑘𝑘∙𝐴𝐴 value related to the fresh food compartment (W/K)

𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖 Mass of ice of the second addition (kg)

𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Power of pump (W)

𝑄𝑄󰇗𝑖𝑖𝑖𝑖𝑖𝑖 Heat flow absorbed by the ice (W)

𝑄𝑄󰇗𝑖𝑖𝑎𝑎𝑐𝑐. Heat flow through the cabinet (W)

𝑄𝑄󰇗𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 Heat flow related to the ice water bucket (W)

𝑄𝑄󰇗𝑓𝑓𝑓𝑓𝑖𝑖 Heat flow related to the fresh food compartment (W)

𝑇𝑇𝑎𝑎 Ambient temperature (°C)

𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖 Time averaged ice temperature (°C)

𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,𝑖𝑖 Instantaneous ice temperature (°C)

𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,1 Storage temperature of the ice (°C)

𝑇𝑇𝑖𝑖 Temperature inside (°C)

𝑇𝑇𝑝𝑝𝑎𝑎 Time averaged temperature of heat sink measurements (°C)

𝑇𝑇1 Temperature at measurement point 1 (°C)

𝑇𝑇2 Temperature at measurement point 2 (°C)

𝑇𝑇3 Temperature at measurement point 3 (°C)

𝛼𝛼𝑎𝑎 Heat transfer coefficient outside (W/(m2 K))

𝛼𝛼𝑖𝑖 Heat transfer coefficient inside (W/(m2 K))

∆ℎ𝑝𝑝 Enthalpy of fusion of ice (kJ/kg)

∆(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 Measurement error related to the ice water bucket (%)

∆(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 Measurement error related to the fresh food compartment (%)

∆(𝑘𝑘∙𝐴𝐴)𝑝𝑝𝑎𝑎𝑚𝑚 Maximum measurement error (%)

∆𝜏𝜏𝑝𝑝 Melting time (s)

∆𝑇𝑇 Temperature difference (K)

𝜆𝜆𝑗𝑗 Thermal conductivity of material layer (W/(m K))

𝜆𝜆𝑃𝑃𝑃𝑃 Thermal conductivity of HIPS (W/(m K))

𝜆𝜆𝑃𝑃𝑃𝑃𝑃𝑃 Thermal conductivity of PUR foam (W/(m K))

𝜆𝜆𝑃𝑃𝑆𝑆 Thermal conductivity of steel (W/(m K))

1 Introduction

Due to the increasing customer awareness of global warming and the necessary

reduction of greenhouse gas emissions, the EU energy label has become an essential

selling point for modern household refrigerating appliances [1]. It compares household

refrigerating appliances with respect to their energy consumption, storage volume as

well as construction type and classifies them according to their energy efficiency. For

this purpose, standardized measuring methods are used to sample these quantities of

new household refrigerating appliances. However, like any technical system,

household refrigerating appliances are subject to considerable technical degeneration

over their lifespan of up to 20 years in some cases. An Australian study from 1990 on

household refrigerating appliances, most likely with CFC-containing PUR foams,

showed no aging influence on energy consumption in the first two years [2]. Typically,

CFC-11 was used in PUR foams at the time when that study was carried out [3-5]. First

prototypes of CFC-free household refrigerating appliances were developed in 1992 [6].

Around 1994, the first models of this appliance type were brought into the market in

significant numbers [7, 8]. Due to a low water content in the raw materials,

CFC-containing PUR foams are typically less susceptible to aging processes than

current state-of-the-art cyclopentane-blown PUR foams [9]. Elsner et al. showed an

increase of energy consumption between 20 % and 35 % over a period of 18 years for

household refrigerating appliances with PUR foams that do not contain CFC [10].

Harrington examined the influence of the energy saving potential by replacing old

appliances through modern appliances [11]. The study showed that the replacement

of older appliances has an energy saving potential of about 60 %. In his dissertation

[12], Harrington examined the influence of consumer behavior on energy consumption

of household refrigerating appliances. Among others, he determined the influence of

temperature and humidity in the storage room, ambient temperature, evaporator

defrosting, door openings and the general choice of the model. Wagner developed

methods to simulate heat transfer through PUR foam as a part of his dissertation [13].

The method described in this paper is part of a larger project that aims to determine

the energy consumption increase of new household refrigerators over a period of three

years with non-destructive measurement methods.

1.1 Aging of PUR foams

With a share of 45 % to 55 %, the heat flow entering the storage room through the

cabinet represents the largest driver for the energy consumption of a household

refrigerating appliance [14]. The cabinet essentially consists of an approximately 1 mm

layer of galvanized sheet steel on the outside, a 40-60 mm thick core made of PUR

foam and an approximately 0.6-2 mm layer of high impact polystyrene (HIPS) on the

inside towards the storage room. During the manufacturing process, isocyanates and

polyols react in a polyaddition reaction to PUR. A second blowing reaction between

isocyanates and water leads to CO2-formation. The CO2 and the additional physical

blowing agent cyclopentane (isopentane) cause foam rise of the PUR. After the

manufacturing process, the cell gas of the PUR foam primarily consists of CO2 and

cyclopentane. Through diffusion processes, CO2 is replaced over time by nitrogen and

oxygen from the ambient air [9, 15-17]. This leads to an increase of the thermal

conductivity of the PUR foam (𝜆𝜆𝑃𝑃𝑃𝑃𝑃𝑃) and thus to an increase of the energy consumption

of household refrigerating appliances [18-23]. This process is strongly dependent on

the temperature that the PUR foam is exposed to [18-22]. Current research projects

are examining the replacement of the blowing agent pentane with CO2-water mixtures.

However, this would not prevent aging due to diffusion processes, since CO2 is also

present in these PUR foam cells as a reaction product [17]. Instead, the aging problem

would be exacerbated with a CO2-water mixture as a blowing agent.

1.2 Heat transfer through the cabinet walls

The heat flow through the cabinet walls (𝑄𝑄󰇗𝑖𝑖𝑎𝑎𝑐𝑐.) can be expressed as a product of the

heat transfer coefficient (𝑘𝑘), the surface area over which the heat transfer takes place

(𝐴𝐴) and the temperature difference (∆𝑇𝑇) between the ambient (𝑇𝑇𝑎𝑎) and the temperature

inside the cabinet (𝑇𝑇𝑖𝑖) of the household refrigerating appliance.

𝑄𝑄󰇗𝐶𝐶𝑎𝑎𝑐𝑐.=𝑘𝑘∙𝐴𝐴∙∆𝑇𝑇 =𝑘𝑘∙𝐴𝐴∙(𝑇𝑇𝑎𝑎−𝑇𝑇𝑖𝑖)

(1)

The heat transfer coefficient 𝑘𝑘 is constituted by the convective heat transfer

coefficients on the outside (𝛼𝛼𝑎𝑎) and inside (𝛼𝛼𝑖𝑖) surface of the cabinet, the material

thicknesses of the various layers of the wall structure (𝑑𝑑𝑗𝑗) and the thermal conductivity

of the materials (𝜆𝜆𝑗𝑗). Equation 2 also considers the typically different surface sizes of

the outside (𝐴𝐴𝑎𝑎) and inside (𝐴𝐴𝑖𝑖) of the cabinet and the middle surfaces of the different

material layers (𝐴𝐴𝑗𝑗).

𝑘𝑘∙𝐴𝐴 =1

𝛼𝛼𝑎𝑎∙𝐴𝐴𝑎𝑎+�𝑑𝑑𝑗𝑗

𝜆𝜆𝑗𝑗∙𝐴𝐴𝑗𝑗

𝑛𝑛

𝑗𝑗=1

𝛼𝛼𝑖𝑖∙𝐴𝐴𝑖𝑖

(2)

A schematic of the cabinet walls and the resulting temperature profile is shown in

Figure 1. With increasing usage time, the thermal conductivity of the PUR foam (𝜆𝜆𝑃𝑃𝑃𝑃𝑃𝑃)

increases, while the thermal conductivity of the galvanized steel sheet (𝜆𝜆𝑃𝑃𝑆𝑆) on the

outside and that of the HIPS inliner (𝜆𝜆𝑃𝑃𝑃𝑃) remain constant. Consequently, the heat flow

entering the cabinet increases and so does the energy consumption of the refrigeration

process.

Fig. 1 Schematic of the cabinet wall structure of a household refrigerating appliance with a

qualitative temperature profile.

1.3 Measurement methods for the 𝒌𝒌∙𝑨𝑨 value

Several measurement methods to determine the heat flow through the refrigerating

appliance cabinet walls have been proposed. Among them, the reverse heat leak

method should be mentioned in particular. Various authors have reported on their

investigations, modifications and improvements of the reverse heat leak method

[24-28], which is also used in R&D departments of refrigerating appliance

manufacturers.

In contrast to the usual temperature conditions in the storage room of a refrigerating

appliance, heat is supplied to the interior of the cabinet by means of an electric heater,

while the ambient temperature is reduced, so that a heat flow occurs from the inside

out. The electrical heating power needed to maintain a stable temperature inside the

cabinet is directly related to the heat flow through the cabinet walls.

However, in practice, there are several problems with this experimental setup:

• Using the reverse heat leak method repeatedly over a period of several years

can lead to accelerated aging, as cell gas diffusion is temperature dependent

and progresses more rapidly at elevated temperatures.

• In order to prevent temperature stratification in the interior, fans are used in the

reverse heat leak method to achieve a more homogeneous temperature

distribution. However, the fans create a forced air flow that differs from natural

convection in real household use. This results in a larger convective heat

transfer coefficient and the ageing-dependent thermal conductivity of the PUR

foam can be falsified.

• Furthermore, the temperature difference between the storage room and the

ambient differs from real household use, where the largest temperature

difference occurs at the lower part of the storage room of the refrigerator, while

the largest temperature difference is at the upper part of the storage room when

the reverse heat leak method is used.

Fig. 2 Representation of the temperature gradient over a fresh food compartment during

conventional use and reverse heat leak method measurement.

The heat flow can also be determined with heat flow sensors which are selectively

placed on the cabinet. The functionality of the heat flow sensors was described by

Lassue et al. [29]. Melo et al. investigated the use of heat flow sensors and compared

the results with the reverse heat leak method [25]. This measuring method was further

refined by Thiessen et al. [30].

However, the heat flow sensor measurement method also turned out to be unsuitable

for the present project. Each refrigerating appliance has an individual cabinet design,

depending on the manufacturer, brand, appliance type and condenser position

arrangement. Cables and refrigerant pipes, which run through the PUR foam at various

places, would have a strong impact on the results of this method.

Hueppe et al. [31] developed another measurement method. They determined the

𝑘𝑘∙𝐴𝐴 value through the duration of a temperature rise in the storage compartments with

a temperature rise test. In addition, aging tests on PUR foam samples have been

published and show an increase of thermal conductivity of the PUR foam from

19.5 mW/(m K) to 22.5 mW/(m K) in 420 days.

2 Test setup

A non-destructive measuring method for the 𝑘𝑘∙𝐴𝐴 value was developed in this work

with the following aims:

The natural temperature stratification in the storage room of the refrigerating

appliances and the temperature differences between the storage room and the

ambient should be maintained as far as possible, natural convection should prevail in

the storage room of the appliances and the measurement method should be

integratable into the existing measurement setup of the standard energy consumption

test according to the standard series IEC 62552:2015 (part 1 – part 3) with as little

effort as possible [32-34].

2.1 Methodology

In the present latent heat sink measuring method, the refrigeration cycle of the

appliance does not operate. Instead, the storage room of the appliance is cooled by a

heat sink in the form of an ice water bucket (height 210 mm, diameter 254 mm) with a

volume of 10.64 liters, cf. Figures 3 and 4. To achieve a homogeneous temperature

distribution of the entire bucket surface, several cooling fins were attached to the lid,

which protruded into the ice water. To avoid temperature stratification in the ice water,

a pump was installed at the bottom of the tank to enforce circulation. The electrical

power consumed by the pump was measured and taken into account in the energy

balance for the calculation of the 𝑘𝑘∙𝐴𝐴 value. To monitor the melting process of the ice

water, four thermocouples were attached to the container, which protruded into the ice

water at two different heights. Furthermore, surface temperatures of the tank were

measured with two thermocouples and that of the lid with a third thermocouple.

Fig. 3 Basic measurement setup in the fresh food compartment (left) and in the ice water bucket

(right).

Fig. 4 Ice water bucket: technical drawing (left) and photo of the device (right).

Before the actual start of the experiment, the refrigerating appliance was operating at

a time averaged fresh food compartment temperature of 𝑇𝑇𝑝𝑝𝑎𝑎 = 4 °C to 5 °C, which was

determined as the mean value of the six temperature measuring points (𝑇𝑇1𝑡𝑡 to 𝑇𝑇3𝑡𝑡 and

𝑇𝑇1𝑟𝑟 to 𝑇𝑇3𝑟𝑟 ) located on both sides of the ice water bucket, cf. Figure 3. The

measurements were made at ambient temperatures of 16 °C, 25 °C and 32 °C

following the IEC 62552:2015 series of standards (part 1 and 3) [32, 34]. Depending

on the ambient temperature, the ice water bucket was filled with an amount of liquid

water as shown in Table 1 at the start of each measurement.

In principle, the experiment should measure the time required for the ice melting

process, where the water temperature remains constant. The point in time at which

there is no longer a temperature of 0 °C at all measuring points in the ice water can be

seen as an increase in the temperature curve, cf. Figure 5. However, since there may

still be residual ice in the bucket at this point in time, a solution had to be found to

ensure that the amount of residual ice is the same at the start and the end of the

measurement period. For this purpose, two ice additions were made.

First, a smaller amount of ice was added to the ice bucket. A relatively constant time

period for the first melting phase could be achieved by varying this ice amount

depending on the various ambient temperatures (cf. Table 1). During this phase in the

experiment, the water level in the bucket only reaches the lower thermocouples, cf.

Figure 3.

Table 1 - Comparison of the test parameters of the first ice addition under

different ambient temperatures.

Ambient temperature 16 °C 25 °C 32 °C

Mass of liquid water in the ice water bucket 4000 ± 20 g 3500 ± 20 g 3000 ± 20 g

Mass of the first addition of ice 1000 ± 20 g 1500 ± 20 g 2000 ± 20 g

Time of the first melting phase 7.00 - 7.75 h 6.75 - 7.50 h 7.00 - 7.75 h

When the lower thermocouples indicated that the temperature of the ice water had

risen by 0.2 K, a second quantity of ice was added to the bucket and the actual

measurement was initiated. The evaluation period ended when the average

temperature of all ice water thermocouples again rose by 0.2 K. The evaluation period

was thus the melting time (∆𝜏𝜏𝑝𝑝). Figure 5 shows the temperature profile of the ice water

over the course of a measurement.

Fig. 5 Ice water temperature over time.

Validation tests were performed with a mass of 3500 g ice for the second addition and

the measurements of the aging studies were performed with 3000 g to avoid overly

long total measurement times.

-8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

0.2 K

second melting period

measurement period

first melting period

second quantity of ice added

start of measurement period

ice water temperature [°C]

time [h]

appliance turned off

first quantity of ice added

end of measurement period

2.2 Evaluation

By determining the time interval that the ice needs to melt (∆𝜏𝜏𝑝𝑝), employing the

enthalpy of fusion of water (∆ℎ𝑝𝑝 = 333.5 kJ/kg) and the mass of ice at the second ice

addition (𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖), the heat flow (𝑄𝑄󰇗𝑖𝑖𝑖𝑖𝑖𝑖) is given by equation 3. Since the ice was stored at

temperatures below 0 °C (𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,1), the according enthalpy contribution was taken into

account via the isochoric heat capacity of the ice (𝑐𝑐𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖 = 2.204 kJ/(kg K)). The

electrical power of the pump (𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝) is dissipated by the circulation of the ice water

and was considered in the energy balance.

(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 =𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖 ∙�∆ℎ𝑝𝑝+𝑐𝑐𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖 ∙�𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖 −𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,1��

(𝑇𝑇𝑎𝑎−𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖)∙∆𝜏𝜏𝑝𝑝−𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

(𝑇𝑇𝑎𝑎−𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖)

(3)

The equations presented in this way describe the (𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 value for the heat flow

entering the ice water through the appliance cabinet and the storage room. As shown

in Figure 6, almost constant instantaneous temperatures (𝑇𝑇𝑝𝑝𝑎𝑎) were present in the

storage room of the fresh food compartment during the tests. The balance between

the heat flows 𝑄𝑄󰇗𝑖𝑖𝑎𝑎𝑐𝑐. and 𝑄𝑄󰇗𝑖𝑖𝑖𝑖𝑖𝑖 remained practically constant until the end of the second

melting phase. During the first melting phase, there was an increase of the

instantaneous temperatures until a balance between the heat flow entering the storage

room through the cabinet and the heat flow entering the ice water bucket from the

storage room was established. The slightly lower instantaneous temperatures during

the second melting phase can be explained by the higher degree of filling in the ice

water bucket and the resulting larger surface of the bucket wetted by ice water.

Fig. 6 Temperature at the measuring points in the fresh food compartment over time.

-8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18

-2

second melting periodfirst melting period

second quantity of ice added

start of measurement period

temperature [°C]

time [h]

T2m

T3m

Tice,i

first quantity

of ice added

end of measurement period

Constant instantaneous temperatures in the fresh food compartment allow for the

replacement of the ice water temperature with the instantaneous temperature of the

fresh food compartment in equation 3 so that the (𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 value related to the

refrigerating appliance cabinet can be determined (cf. equation 4). For this purpose,

the ice water temperature in the denominator is replaced with the average fresh food

compartment temperature.

(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 =𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖 ∙�∆ℎ𝑝𝑝+𝑐𝑐𝑣𝑣,𝑖𝑖𝑖𝑖𝑖𝑖 ∙�𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖 −𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,1��

(𝑇𝑇𝑎𝑎−𝑇𝑇𝑝𝑝𝑎𝑎)∙∆𝜏𝜏𝑝𝑝−𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

(𝑇𝑇𝑎𝑎−𝑇𝑇𝑝𝑝𝑎𝑎)

(4)

2.3 Refrigerating appliances

For a validation of the present measurement method, a commercially available table-

height refrigerator (Miele, type K12020 S-1) was used. This appliance (V1) was chosen

due to its age of five years. The investigations discussed in section 1 show that the

most pronounced aging effects occur in the first three years [10, 18-23]. Thus, only

small changes of the 𝑘𝑘∙𝐴𝐴 value were expected for this appliance. In addition, aging

tests were carried out for four refrigerators (R1 to R4), cf. Table 2. Contrary to the

requirements of the standard IEC 62552-1:2015, part1, [32] the built-in refrigerators

were operated without wooden cabinets in order to exclude any influences of the wood

on the measurement results.

Table 2 - Technical data of the studied refrigerating appliances.

Test device V1 V2 R1 R2 R3 R4

Refrigerator

model K12020

S-1 KI81RAD

30/04 KS 16-1

RVA+++ KS 16-1

RVA+++ KI81RAD

30/04 KI81RAD

30/04

Manufacturer Miele Siemens Exquisit Exquisit Siemens Siemens

Refrigerator

type

table-

height

refrigerator

built-in

refrigerator

table-

height

refrigerator

table-

height

refrigerator

built-in

refrigerator built-in

refrigerator

Dimensions

(HxWxD) [mm] 850 x 601

x 628 1775 x 560

x 550 845 x 555

x 575 845 x 555

x 575 1775 x 560

x 550 1775 x 560

x 550

Total storage

volume

[l] 167 319 134 134 319 319

Refrigerant

22 g

R600a

46 g

R600a

26 g

R600a

26 g

R600a

46 g

R600a

46 g

R600a

Energy label A+ A++ A+++ A+++ A++ A++

2.4. Measurement system and measurement error analysis

The mass of water and ice was measured with a laboratory scale DE350.5D (Kern &

Sohn GmbH) with an accuracy of ± 2.5 g. Temperatures were sampled by

thermocouple differential measurements, where each measuring point had its own

reference junction in a separate ice water bath. The measurement signal of the

thermocouples was processed by a combination of a pre-amplifier LTC1050 (Linear

Technologies) with adjusted gain of 1000 and a digital-to-analog converter system

OMB-DAQ 55/56 (Omega Technologies), limiting the offset drift to ± 0.025 K. By

calibrating each thermocouple individually and applying a polynomial correction, the

measurement error was reduced from ± 1% x ∆T to ± 0.5% x ∆T. All measurements

were carried out in a climatic chamber with an ambient temperature fluctuation of

± 0.5 K and an air humidity of 50 %. The supply voltage of the pumps was provided by

BT-305 laboratory power supplies (BASETech) with ± 1 % + 0.02 V accuracy and the

electric current with ± 2 % + 0.02 A. Due to cable length, the supply voltage at the

pump was 1 % lower than the output of the power supply, which was taken into account

in the calculations. The pumps (Bilge pump 360GPH) were operated with a supply

voltage of 5 V. In preliminary tests, this turned out to be the best compromise between

the heat introduced by the pump and the necessary circulation of the ice water to

prevent temperature stratification in the bucket.

The measurement errors of the various devices are summarized in Table 3. The

fluctuation of the ice storage temperature (𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖,1) was assumed to be ± 1 K due to

transportation and handling of the ice prior to the addition process. The measurement

errors ∆(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 and ∆(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 were calculated with the error propagation law.

Table 3 – Measured properties and their uncertainties.

Measured quantity Measuring device Uncertainty

Temperature Thermocouples ± 0.1 K

Voltage Laboratory power supplies ± 1 % + 0.02 V

Electric current Laboratory power supplies ± 2 % + 0.02 A

Time Personal computer ± 0.1 s/day

Mass Laboratory scale ± 2.5 g

3. Results and discussion

3.1. Validation

For validation, five measurements for each ambient temperature of 16 °C, 25 °C and

32 °C were carried out with refrigerating appliance V1. The aim was to check the

reproducibility and the influence of the ambient temperature on the results. In addition

to the measured values and the results for the 𝑘𝑘∙𝐴𝐴 values of the individual

measurements, the total measurement errors ∆(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 and ∆(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 are specified

in the following.

Overall, the data show a homogeneous distribution of the measurement results with a

scatter on the same order of magnitude as the overall measurement error. As shown

in Table 4, no influence of the ambient temperature on the measurement results was

found.

Table 4 - Results of the validation test series with varying ambient

temperature.

Test series 16 °C 25 °C

32 °C

Ambient temperature

𝑇𝑇𝑎𝑎

[°C] 15.7 24.8

31.8

Mass of the second addition of ice

𝑚𝑚𝑖𝑖𝑖𝑖𝑖𝑖

[g] 3489.0 3490.5

3493.5

Evaluation period

∆𝜏𝜏𝑝𝑝

[h] 22.81 15.83

12.90

Average fresh food compartment

temperatures

𝑇𝑇𝑝𝑝∗

[°C] 6.3 9.8

12.8

Power of the pump

𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

[W] 4.35 4.35

4.29

(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡

[W/K] 0.74 0.75

0.75

∆(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡

[%] 1.9 % 1.2 %

0.9 %

(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖

[W/K] 1.22 1.24

1.25

∆(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖

[%] 1.3 % 0.8 %

0.6 %

Despite the relatively constant results at different ambient temperatures, an ambient

temperature of 25 °C was preferred for this measurement method. At an ambient

temperature of 16 °C there are significantly higher measurement errors (± 1.9 %) and

a time of more than 24 h for an entire test (first and second addition of ice) leads to

additional organizational effort in labor operation. In addition, only for this ambient

temperature, it was observed that an ice layer formed in the bucket on the water

surface. A comparison of the ambient temperatures of 25 °C and 32 °C shows that the

measurement error is lower at 32 °C, but the internal temperatures were significantly

higher than in regular refrigerator operation. Table 5 shows the selection criteria

mentioned for the evaluation of the three ambient temperatures.

Table 5 - Evaluation for the selection of the ambient temperature.

Ambient temperature 16 °C 25 °C 32 °C

Measurement error

∆(𝑘𝑘∙𝐴𝐴)𝑝𝑝𝑎𝑎𝑚𝑚

± 1.9 % ± 1.2 % ± 0.9 %

- 0 +

Measurement time

second melting interval (

∆𝜏𝜏𝑝𝑝

) 22.80 h 15.63 h 12.90 h

total 30.50 h 23.00 h 20.50 h

- 0 +

Ice layer on the water surface yes no no

- - + +

Average fresh food

compartment

temperature

𝑇𝑇𝑝𝑝∗

6.3 °C 9.9 °C 12.8 °C

+ 0 - -

3.2 Aging studies

With the present measuring method, the aging of commercially available refrigerating

appliances was investigated shortly after their manufacturing. For this purpose, two

tests per appliance were carried out on four appliances at an interval of 14 months and

the 𝑘𝑘∙𝐴𝐴 value was determined. The results are listed in Table 6. Figure 7 shows the

results for the (𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 value and the (𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖 value. The results indicate an

increase between 3.6 % and 11.5 % for (𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡 and an increase between 6.1 %

and 11.3 % for (𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖. This difference between the 𝑘𝑘∙𝐴𝐴 values is significantly larger

than the measurement error (∆(𝑘𝑘∙𝐴𝐴)𝑝𝑝𝑎𝑎𝑚𝑚 < 2 %). Hueppe et al. [31] investigated the

change of the thermal conductivity of PUR foam samples over time and observed an

increase of about 15 % over a period of 420 days. The determined increase of the

𝑘𝑘∙𝐴𝐴 value of real refrigerating appliances is of similar magnitude.

Table 6 - Results of the aging study of refrigerating appliances.

Test device R1 R2 R3 R4

Refrigerator model

KS 16-1

RVA+++

KS 16-1

RVA+++

KI81RAD

30/04

KI81RAD

30/04

Manufacturer Exquisit Exquisit Siemens Siemens

(𝑘𝑘∙𝐴𝐴)𝑡𝑡𝑡𝑡𝑡𝑡𝑎𝑎𝑡𝑡

new [W/K] 0.56 0.53 0.82

0.78

after 14 months [W/K] 0.58 0.58 0.88

0.87

difference [W/K] + 0.02 + 0.05 + 0.06

+ 0.09

[%] + 3.6% + 9.4% + 7.3%

+ 11.5%

(𝑘𝑘∙𝐴𝐴)𝑓𝑓𝑓𝑓𝑖𝑖

new [W/K] 0.82 0.78 1.65

1.60

after 14 months [W/K] 0.87 0.86 1.79

1.78

difference [W/K] + 0.05 + 0.08 + 0.14

+ 0.18

[%] + 6.1% + 10.3% + 8.5%

+ 11.3%

Fig. 7 Results of the aging study for (𝒌𝒌∙𝑨𝑨)𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 (green) and (𝒌𝒌∙𝑨𝑨)𝒇𝒇𝒇𝒇𝒇𝒇 (brown).

R1 R2 R3 R4

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

k A [W/K]

Refrigerating appliance

(k A)

total

new

(k A)

total

14 months

(k A)

ffc

new

(k A)

ffc

14 months

4 Conclusions

The presented experimental method with a latent heat sink is a suitable alternative to

the reverse heat leak method for determining the heat flow into the cabinet of a

refrigerating appliance. The advantage of the latent heat sink method is that the air

flow and the temperatures in the storage room are comparable to the real operating

conditions. The usage of fans in the reverse heat leak method generates locally

turbulent flows, which increase convective heat transfer. The temperature gradient

between the storage room and the ambient is also more realistic.

An ambient temperature of 25 °C was found to be optimal for using the latent heat sink

method. Application-related temperatures are reached in the storage compartments,

the measurement error is small and the total measurement time can be integrated into

a 24 h cycle. An ambient temperature of 32 °C should not be chosen due to the higher

storage temperature in the compartment and 16 °C should not be chosen due to the

possible formation of ice layers.

By measuring the 𝑘𝑘∙𝐴𝐴 value of new refrigerating appliances over time, an increase of

8.2 % (± 2.1 %) for the table high refrigerators and 9.9 % (± 1.4 %) for the large built-in

refrigerators was found over a period of 14 months. This result is consistent with the

literature for the increase of the thermal conductivity of PUR foam.

Acknowledgements

This work was carried out as part of the ALGE research project funded by the German

Federal Ministry for Economic Affairs and Energy as part of the 6th energy research

program (project funding reference number: 03ET1544A-E).

References

[1] Statista: Haushaltsgroßgeräte. 2018, URL:

https://de.statista.com/statistik/studie/id/7683/dokument/haushaltsgrossgeraete-

statista-dossier/.

[2] Australian Consumers’ Association, 1990. Energy Consumption of Refrigerators

and Freezers Used Under Normal Conditions of Use. Choice, Sydney, Australia.

[3] Kjeldsen, P., Jensen, M.H., 2001. Release of CFC-11 from Disposal of

Polyurethane Foam Waste. Environmental Science & Technology 35, 3055-

3063.

[4] Scheutz, C., Kjeldsen, P., 2002. Determination of the fraction of blowing agent

released from refrigerator/freezer foam after decommissioning the product.

Environment and Resources DTU, Technical University of Denmark.

[5] Yazici, B., Can, Z.s., Calli, B., 2014. Prediction of future disposal of end-of-life

refrigerators containing CFC-11. Waste Management 34, 162-166.

[6] Meyer, A, 1993. Der FCKW-freie Kuehlschrank der FORON-Hausgeraete gmbH

- ein Beitrag fuer eine bessere Umwelt. Luft- und Kaeltetechnik 29, Nr. 1, 3-4.

[7] Stiftung Warentest, 1994. Umwelt geschont – Strom gespart. test 1994, Nr.3, 36-

39.

[8] Stiftung Warentest, 1994. Auch ohne Ozonkiller. test 1994, Nr.6, 24-25.

[9] Delebecq, E., Pascault, J.-P., Boutevin, B., Ganachaud, F., 2013. On the

versatility of urethane/urea bonds: reversibility, blocked isocyanate, and non-

isocyanate polyurethane. Chemical Reviews 2013113, 80-118.

[10] Elsner, A., Müller, M., Paul, A., Vrabec, J., 2013. Zunahme des Stromverbrauchs

von Haushaltskältegeräten durch Alterung. Deutsche Kälte-Klima Tagung 40,

Hannover, Germany, November 20-22, 2013.

[11] Harrington, L., 2017. Quantifying energy savings from replacement of old

refrigerators. Energy Procedia 121, 49-56.

[12] Harrington, L., 2018. Prediction of the energy consumption of refrigerators during

use. Dissertation, Melbourne (Australia): https://minerva-

access.unimelb.edu.au/handle/11343/213357

[13] Wagner, K-E., 2002. Simulation und Optimierung des Wärmedämmvermögens

von PUR Hartschaum, Wärme- und Stofftransport sowie mechanische

Verformung, Dissertation, Stuttgart (Germany): http://dx.doi.org/10.18419/opus-

1579.

[14] 2010 ASHRAE Handbook: Refrigeration. SI edition. Atlanta, GA: ASHRAE, 2010.

ISBN 1933742828.

[15] Engels, H.-W., Pirkl, H.-G., Albers, R., Albach, R.W., Krause, J., Hoffmann, A.,

Casselmann, H., Dormish, J., 2013. Polyurethane: vielseitige Materialien und

nachhaltige Problemlöser für aktuelle Anforderungen. Angewandte Chemie 125,

9596-9616.

[16] Tucker, B.W., 1992. Rigid polyurethane foams with low thermal conductivities,

patent document, US005169877A, PCT, 08.12.1992.

[17] Berardi, U., Madzarevic, J., 2020. Microstructural analysis and blowing agent

concentration in aged polyurethane and polyisocyanurate foams. Applied

Thermal Engineering 164, 114440.

[18] Wilkes K.E., Yarbrough D.W., Weaver F.J., 1997. Aging of polyurethane foam

insulation in simulated refrigerator walls. International Conference on Ozone

Protection Technologies, Baltimore Maryland, November 12-13, 1997.

[19] Wilkes, K.E., Gabbard, W.A., Weaver, F.J., 1999. Aging of polyurethane foam

insulation in simulated refrigerator panels: One-year results with third-generation

blowing agents. The Earth Technologies Forum, Washington D.C., September

27-29, 1999.

[20] Wilkes, K.E., Gabbard, W.A., Weaver, F.J., Booth, J.R., 2001. Aging of

polyurethane foam insulation in simulated refrigerator panels: Two-year results

with third-generation blowing agents. Journal of Cellular Plastics 37, 400-428.

[21] Wilkes, K.E., Yarbrough, D.W., Gabbard, W.A., Nelson, G.E., Booth, J.R., 2002.

Aging of polyurethane foam insulation in simulated refrigerator panels: Three-

year results with third-generation blowing agents. Journal of Cellular Plastics 38,

317-339.

[22] Wilkes, K.E., Yarbrough, D.W., Nelson, G.E., Booth, J.R., 2003. Aging of

polyurethane foam insulation in simulated refrigerator panels: Four-year results

with third-generation blowing agents. The Earth Technologies Forum,

Washington D.C., April 22-24, 2003.

[23] Albrecht, W., 2003. Änderung der Wärmeleitfähigkeit von zehn Jahre alten PUR-

Hartschaumplatten mit gasdiffusionsoffenen Deckschichten. Bauphysik 25, 317-

319.

[24] Stovall, T., 2012. Closed Cell Foam Insulation: A review of long term thermal

performance, Oak Ridge National Laboratory report ORNL/TM-2012/583.

[25] Melo, C., da Selva, L.W., Pereira, R.H., 2000. Experimental evaluation of the heat

transfer through the walls of household refrigerators. Eighth International

Refrigeration Conference at Purdue University, West Lafayette, IN, USA, July 25-

28, 2000, 353-360.

[26] Lieghton, D.L., 2011. Investigation of household refrigerator with alternative low

global warming potential refrigerants. Master thesis, University of Maryland, USA.

[27] Sim, J.S., Ha, J.S., 2011. Experimental study of heat transfer characteristics for

a refrigerator by using reverse heat loss method. International Communications

in Heat and Mass Transfer 38, 572-576.

[28] Hermes, C., Melo, C., Knabben. F., 2013. Alternative test method to assess the

energy performance of frost-free refrigerating appliances. Applied Thermal

Engineering 50, 1029-1034.

[29] Lassue, S., Guths, S., Leclercq, D., Duthoit, B., 1993. Contribution to the

experimental study of natural convection by heat flux measurement an

anemometry using thermoelectric effects. Experimental Heat Transfer, Fluid

Mechanics and Thermodynamics 1993, 831-838.

[30] Thiessen, S., Knabben, F.T., Melop, C., 2014. Experimental evaluation of the

heat fluxes through the walls of a domestic refrigerator. 15th Brazilian Congress

of Thermal Sciences an Engineering at Belem, PA, Brazil, November 10-13,

2014.

[31] Hueppe, C., Geppert, J., Stamminger, R., Wagner, H., Hoelscher, H., Vrabec, J.,

Paul, A., Elsner, A., Becker, W., Gries, U., Freiberger, A., 2020. Age-related

efficiency loss of household refrigeration appliances: Development of an

approach to measure the degradation of insulation properties. Applied Thermal

Engineering 173, 115113.

[32] IEC 62552:2015, 2015. IEC 62552-1:2015 Household Refrigerating Appliances –

Characteristics and Test Methods – Part 1: General requirements. International

Electrotechnical Commission (IEC).

[33] IEC 62552:2015, 2015. IEC 62552-2:2015 Household Refrigerating Appliances –

Characteristics and Test Methods – Part 2: Performance requirements.

International Electrotechnical Commission (IEC).

[34] IEC 62552:2015, 2015. IEC 62552-3:2015 Household Refrigerating Appliances –

Characteristics and Test Methods – Part 3: Energy consumption and volumes.

International Electrotechnical Commission (IEC).