United States
Environmental Protection
Agency
Air and Radiation
(ANR-445)
EPA/430/R-92/009
October 1992
&EPA
Finite Element Analysis of Heat
Transfer Through the Gasket
Region of Refrigerator/Freezers
25
-------
-------
Finite Element Analysis of Heat Transfer
through the Gasket Region of Refrigerator/Fr
-------
Finite Element Analysis of Heat Transfer
through the Gasket Region of Refrigerator/Freezers
ABSTRACT
Heat flow through the gasket region- of a refrigerator/freez-
er (R/F) cabinet is a significant fraction of the total R/F
thermal load. Reductions in this mode of heat transfer will thus
result in lower R/F energy consumption.
Finite element analyses (FEA) of two gasket used in U. S.
R/Fs are developed. These models show that the thermal proper-
ties of the gasket have little influence on heat transfer in the
gasket region, while heat flow down the metal door and cabinet
flanges greatly impacted the overall rate of heat transfer into
the cabinet.
Gasket designs incorporating the modifications suggested by
the FEA were developed and tested in prototype R/Fs. Total R/F
energy consumption reductions of 5 to 8 percent were achieved.
These reductions were slightly less than the 5 to 11 percent
reductions predicted by the models.
ii
-------
Contents
tract ii
ores iv
les v
•*
reduction f 1
ite Element Models. 2
. Results - Current Designs 6
.
i Results - New Designs 14
isurements - New Designs 26
Delusions *...... 28
i
cnowledgenents 29
ferences *. 29
iii
-------
Figures
mber
Finite element model of Subzero gasket region 3
Finite element model of GE gasket region 4
Temperature profiles in SubZero gasket « • 8
Temperature profiles in SubZero gasket
without decorative cover... •, 10
> Finite element model for the GE gasket ..*
including the foam in the door and cabinet 11
6 Temperature profiles in GE gasket 12
7 Finite element model and temperature profiles
for modified SubZero gasket containing a low _
conductivity gas • 15
8 Finite element model and temperature profiles for
modified GE gasket containing a low conductivity gas 16
9 Finite element model and temperature profiles for
uncoupled heat flow in modified SubZero gasket. 18
10 Finite element model and temperature profiles for
modified SubZero gasket region which includes a
plastic clip and approximately half plastic door
and cabinet flanges. « ... 20
11 Finite element model and temperature profiles for
modified GE gasket region which includes a plastic
clip and approximately half plastic door and cabinet
flanges ........ v'... « •
12 SubZero gasket region load reductions for various
flange modifications • 22
13 GE gasket region load reductions for various flange
modifications 25
-------
Tables
Number
1 Properties of Materials.
2 Variation of Subzero Gasket-Region U-value
with R/F Temperatures.
3 Variation of Subzero Gasket-Region U-Values
with Heat Transfer Coefficients <.... 7
4 Effect of Flange/Foam Boundary Condition on
Overall Gasket Heat Transfer Coefficient 13
5 Comparison of U-values for Gaskets containing
Air and Krypton 14
6 Comparison of U-values for the SubZero Gasket
with Coupled and Uncoupled Flanges. 17
7 U-Values for Subzero Gasket Region with a Portion
of the Flanges changed to Plastic , 23
8 U-Values for GE Gasket Region with a Portion of
the Flanges changed to Plastic , 24
9 Effect of Flange/Foam Boundary Condition on
U-Value of Modified GE Gasket Region 26
-------
INTRODUCTION
Heat transfer through the gasket region significantly
contributes 'to the thermal load through the refrigerator/freezer
(R/F) cabinet. Recent finite element analyses of
refrigerator/freezers to assess the impact of the addition of
super insulation on the energy consumption of R/Fs showed approx-
imately 25 percent of the total thermal load entered the cabinet
through the gasket region, i.e. the gasket and flanges. (1) This
load increased to over 35 percent of the total for a cabinet
that was nearly completely covered with super insulation. Clear-
ly, heat transfer through the gasket region is an important
portion of the overall heat transfer flux, and becomes even more
important as the rest of the cabinet becomes more insulated.
Analyses and tests performed in the design of a super effi-
cient R/F in 1980 (2) demonstrated that the heat flow through the
gasket region could be halved with the addition of a second
gasket. Difficulties in implementing the double-gasket concept,
however, have prevented its use in production units.
This report presents the results of finite element analysis
(FEA) of heat flow through two gasket/flange designs employed in
1991 in U.S. refrigerator/freezers. Modifications to the designs
that could yield significant R/F thermal load reductions are also
presented and evaluated.
-------
FINITE ELEMENT MODELS
Two gasket designs were selected for analysis in this study,
a gasket employed in Subzero side by side models and a gasket
used in General Electric top-mount freezer units. These gaskets
represent the extremes of complexity of cross section designs for
gaskets found in U.S. R/Fs.
Gasket dimensions were obtained for the finite element
analyses by cutting the gaskets perpendicular to their length.
Photographic transparencies of the cross sections were then made
and projected onto a sheet of paper. The approximately seven
times enlarged images were then traced and measured. Correct
dimensions were achieved by including a scale in the photographs
of the gaskets. Gasket thicknesses of 0.48 and 0.56 inches were
found for the Subzero and GE gaskets, respectively.
Analyses were performed for the gasket region which in-
cluded the gasket, mounting clip, flanges and a small portion of
the outer steel case. A small portion of the liner and foam
insulation was also included in several analyses of the GE gasket
region. Flanges, mounting clip, case and liner were assumed to
have a thickness of 0.024 inches. The finite element models of
the subzero and GE gasket regions are shown in Figures 1 and 2.
The thermal conductivity for the plastic gasket material and
liner, flexible gasket magnet, air contained within, the gasket,
and metal flanges, clip and case used in this analysis are shown
in Table l. £»%ineering units and the values used by the finite
element code ANSYS are given.
-------
Figure 1. Finite element model of Subzero gasket region. Black
areas within model represent metal components, dark
gray are plastic and light gray are air.
-------
Figure 2. Finite element model of GE gasket region. Black areas
within model represent metal components, dark gray are
.
plastic and light gray are air.
-------
Table 1. Properties of Materials
Material
•»*
Plastic
Magnet
Air
Metal
Thermal Conductivity
Engineering Units
(BTU*in)/(hr*ft**°F)
1.016
1.016
0.18
315.0
ANSYS Units
(BTU*in) / (hr*in**eF)
0.007055
0.007055
0.00125
2.1875
Convection heat transfer boundary conditions were employed
for the inner and outer surfaces. In most calculations, heat
transfer from the flanges or case to the foam insulation which
fills the R/F doors and walls was assumed to be negligible com-
pared to that along the metal piece. The foam/metal surfaces
were/ thus, assumed adiabatic. Convection within the gasket
pockets was also assumed to be negligible.
Total heat flow rates through the gasket and flanges were
calculated in the postprocessing module of ANSYS by summing the
fluxes out of the elements which would constitute the surfaces of
the gasket and flanges on the inside of the R/F. The overall
heat transfer coefficient, U or U-value,- was calculated from the
following equation:
U
Q / dT
where Q was the total heat transfer rate out of the gasket re-
gion, and dT was the overall temperature difference.
-------
FEA RESULTS - CURRENT DESIGNS
The Subzero gasket region was analyzed with the steel case
-
extended to form the decorative gasket cover found on production
units, as shown in Figure 1, and with this piece removed. The
results of these analyses and those performed on the GE gasket
follow.
Subzero Gasket - Four combinations of R/F interior tempera-
ture, Tin, and ambient temperature,TQUt, were analyzed. Since
the thermal conductivities were assumed to be independent of
temperature, the heat transfer rate should be proportional to
Tout"Tin' and u should be independent of the temperature differ-
ence. Table 2 shows the results for heat transfer coefficients
of 2 Btu/(hr*ft»*T) at the inner and outer surfaces. The effect
of heat transfer coefficient on the overall heat transfer coeffi-
cient is shown in Table 3.
Table 2.. Variation of SubZero Gasket-Region
U-Values with R/F Temperatures
Temperature
. Tin f FTout
0 & 70
0 & 90
40 & 70
40 & 90
Total Heat
Transfer Rate
Btu/ (hr*in)
0.2825
0.3632
0.1211
0.2018
Overall Heat
Trans. Coeff . ', u
Btu/(hr*in*°F)
4.036E-3
4.036E-3
4.036E-3
4.036E-3
-------
Table 3. Variation of SubZero Gasket-Region U-Values with
Heat Transfer Coefficients
Surface Heat
Trans. Coefficient
Btu/(hr*ft2*°F)
1
2
5
10
Overall Heat
Trans. Coeff., U
Btu/(hr*in*°F)
2.407E-3
4.036E-3
7.347E-3
11.22E-3
Percent Heat
Flow through
Clip & Flanges
17.5
21.0
28.8
37.0
The percentage of heat flow through the two L.etal. flanges
plus the metal clip shown in Table 3 is the percentage of the
total energy entering the R/F cabinet from the gasket region as a
result of convection from the ends of the two flanges and the
clip. The heat flow rates from each of these three surfaces were
nearly identical, and thus contributed equally to the total. As
shown in Figure 3 for the 90°F to 0°F temperature combination and
heat transfer coefficients equal 2 Btu/(hr*ft**°F), all three
surfaces attain the same temperature. As all three were assumed
to have the same thickness, equal heat transfer rates should
result.
The nonlinear nature of the isotherms shown in Figure 3
indicates that the percentage of heat flow through the flanges
anoT clip is not indicative of the importance of their influence
on the overall heat transfer process. In fact, nearly all of the
heat entering the outer surface of the gasket region flows down
the metal pieces avoiding the gasket. The heat flow then dis-
perses across the gasket near the inner surface of the R/F, and
then is transferred into the R/F by convection.
Removing the decorative metal cover, i.e. the extension of
-------
Figure 3.
Temperature profiles in SubZero gasket with 0° and
I
90°F temperature extremes and heat transfer coeffi-
cients at the inner and outer surfaces of
2 Btu / (hr*ft2*°F). :
-------
the metal case over the gasket shown in Figure 1, had an insig-
nificant effect on the temperature profile, as shown in Figure 4.
The minor changes which occurred were primarily in the higher
temperature isotherms and the overall heat transfer coefficient
increased by less than one percent to 4.069E-3 Btu/
-------
Figure 4. Temperature profiles in SubZero gasket without its
decorative cover at 0° and 90°F temperature extremes
and heat transfer coefficients at the inner and
outer surfaces of 2 Btu / (hr*ft2*°F).
10
-------
Figure 5. Finite element model for the GE gasket including the
• foam in the door and cabinet adjacent to the flanges,
11
-------
Figure 6. Temperature profiles in GE gasket with 0« and 90 «F
i
temperature extremes and heat transfer coefficients
a^fctehe inner and outer surfaces of j
2 Btu / (hr*ft**°F).
12
-------
Table 4. Effect of Flange/Foam Boundary Condition on
Overall Gasket Heat Transfer Coefficient
Flange/Foam
Heat Transfer
Assumption
£1
adiabatic
conduction
Subzero
adiabatic
Overall Heat
Transfer Rate
Btu/(hr*in)
0.5940
0.5810
0.3632
Overall. Heat
Trans. Coeff., U
Btu/(hr*in*°F)
6.600E-3
6.456E-3
4.036E-3
Heat flow through the metal flanges was again approximately
20 percent of the total. The rate from the cabinet flange was
nearly identical to that for the Subzero gasket. The rate for
the door flange was nearly four times higher. This was as ex-
pected, however, as the door flange extended beyond the gasket
into the R/F and increased its surface area for convection by
about a factor of four.
Convection from the appendage on the inside of the R/F near
the cabinet side on the GE gasket accounted for about 25 percent
of the total heat flow through the gasket/flange region. Ex-
cluding heat flow from the flanges and the appendage yields a
total heat flux of 0.3217 Btu/(hr*in). This rate is twelve
percent higher than that for the Subzero gasket, excluding heat
flow through the metal clip and flanges. The GE gasket was 16
percent thicker than the SubZero gasket. Thus comparable heat
flow rates per unit thickness would occur, if the gaskets had
similar cross sections.
13
-------
RESULTS - NEW DESIGHS
Modifications to the current gasket designs including chang-
the gas.inside the gasket and changing the !flfflnge design
were evaluated. The results of these calculations are presented
below.
12S Conductivity Sas. - LOW conductivity ...... such as
Xrypton, have been proposed as alternatives to polyurethane .foams
insulation materials. ,3, „ the air pockets within the gasket
contribute significantly to reduce the u-value of I the gasket
switching the gas within these pockets to a low conductivity gas
could significantly reduce the u-value of the gasketj
The modified Subzero and GE gasket designs showing the
pockets which contain low conductivity gas are presented in
Figures 7 and 8. A comparison of the u-values with air and with
krypton in these pockets is shown in Table 5. The conductivity
of krypton was assumed to equal 0.067 (Btu.in, / (hrWr) or
about 37 percent that of air, and heat transfer coefficients of 2
Btu/Chr*ft*..F) were used for these calculations.
Table 5. comparisons-values for Caskets containing
0-Value [Btu/(hr«in*«F)] containing
-------
Figure 7. Finite element model and temperature profiles for
modified Subzero gasket containing a low conductivity
gas (white areas within gasket).
15
-------
Figure 8. Finite element model and temperature
modified GE gasket containing a low
(white areas within gasket).
profiles for
conductivity gas
16
-------
The overall Subzero and GE gasket heat transfer coefficients
were reduced by 4.4 and 6.4 percent, respectively. While the
reductions are significant, it is relatively small compared to
the 63 percent reduction in the thermal conductivity of the gas
in the pockets. As pointed out earlier, the temperature profiles
within the gasket indicate that heat flows down the metal flanges
and then across the inner portion of the gasket. Thus, changing
the rate of heat flow through the flanges and not the thermal
resistance of the gasket by changing the gas within it, should
have a larger impact on the gasket-region U-value.
Flange Modifications - The hypotheses that heat flow down
the flanges was of primary importance to the overall heat flow
problem was tested by uncoupling the flanges from the Subzero
gasket. This was accomplished in the model by "inserting" an
adiabatic surface between the flanges.and the gasket. The result
was a nearly 50 percent reduction in the U-value of the gasket
region, see Table 6.
Table 6. Comparison'of U-values for the SubZero Gasket
with Coupled and Uncoupled Flanges
Gasket
coupled
uncoupled
U-Value [Btu/(hr*in*°F)] containing
Air
4.036E-3
2.139E-3
Krypton
3.859E-3
1.949E-3
The temperature profiles for the uncoupled model presented
in Figure 9 show that heat must now flow through the gasket when
the flanges are uncoupled from the gasket. Furthermore, while
17
-------
Figure 9.
element aodel and temperature promes ror
heat flow ln modified ^^ ^^^ _ '
batic su«a=6s between «anges and gasket ^ ^^
18
-------
uncoupling reduced the U-value by about a factor of two, replac-
ing the air within the gasket with krypton reduces the U-value by
only an additional ten percent.
Uncoupling heat flow between the flanges and gasket can not,
in practice, be accomplished by placing adiaba±ic surfaces be-
tween the flanges and gasket. Replacing the metal clip which
holds the gasket in place and part of the metal flanges with
plastic as shown in Figures 10 and 11 could be implemented in
production and could produce the same result.
Modifications to the Subzero gasket region shown in Figure
10 include changing the metal retaining clip to plastic, changing
the portion of the door flange between the mounting socket and
interior of the R/F to plastic and changing the portion of the
cabinet flange between the end of the gasket magnet and interior
of the R/F to plastic. The U-value resulting for the modified
gasket region was 1.775E-3 Btu / (hr*in*°F), a nearly 60 percent
reduction.
As it may not be possible to make such drastic changes in
practice on all models, calculations were performed for flange
designs which embodied a fraction of the above described modifi-
cations. U-values which resulted from changing the clip and/or a
fraction of the above metal portions of the flanges to plastic
are summarized in Table 7 and plotted in Figure 12.
19
-------
Figure 10.
Finite element model and temperature profiles for
modified Subzero gasket region which includes a
plastic clip and approximately half plastic door and
cabinet flanges.
20
-------
25
Figure 11. Finite element model and temperature profiles for
modified GE gasket region which includes a plastic
clip and approximately half plastic door and cabinet
flanges.
21
-------
o
-i-H
O
-------
Table 7. U-Values for SubZero Gasket Region with a Portion of
the Flanges changed to Plastic
% Proposed Modification
clip
0
100
100
100
100
100
100
100
100
100
100
100
100
100
door
*
0
0
25
50
75
100
0
0
0
0
25
50
75
100
cabinet
0
0
0
0
0
0
25
50
75
100
25
50
75
100
U- value
4.036E-3
3.977E-3
3.677E-3
3.409E-3
3.240E-3
3.138E-3
3.459E-3
3.114E-3
2.905E-3
2.780E-3
3.151E-3
2.504E-3
2.068E-3
1.775E-3
% Reduction
0
1.5
8.9
15.5
19.7
22.2
14.3
22.8
28.0
31.1
21.9
38.0
48.8
56.0 '
Changing the metal clip to plastic has a relatively small
effect of 1.5 percent. Changing either the door or cabinet
flange can reduce the heat flow by approximately 25 percent.
Similarly making half of the proposed changes to the door and
cabinet flanges will produce almost a 40 percent reduction. The
effects are also additive as shown by the open circles in Figure
12, which correspond to the sum of the individual reductions.
(Note: When adding values in Table 7, 1.5% must be subtracted
from the sum so that the effect of the clip is not double count-
ed.)
Modifications to the GE gasket region consisted of changing
the clip from metal to plastic, changing the portion of the door
flange from the center of the clip to the interior of the R/F
from metal to plastic and changing the portion of the cabinet
flange from the center of the clip to the interior of the R/F
from metal to plastic. Similar reductions to those for the
23
-------
t •
Subzero gasket are shown in Table 8 and Figures 13
Table 8. U-Values for GE Gasket Region with a Portion of
the Flanges changed to Plastic
% Proposed Modification
.- clip
0
100
100
100
100
100
100
100
100
100
100
100
100
100
door
0
0
25
50
75
100
0
0
0
0
25
50
75
100
cabinet
0
0
0
0
0
0
25
50
75
100
25
50
75
100
U— value
6.600E-3
6.382E-3
6.015E-3
5.304E-3
5.040E-3
4.865E-3
5.479E-3
5.022E-3
4.790E-3
4.695E-3
5..110E-3
3.923E-3
3.376E-3
3.070E-3
% Reduction
0
; 3.3
8.9
19.6
, 23.6
26.3
17.0
23:9
27.4
28.9
22.6
40.6
48.8
53.5
As with the Subzero gasket, the clip has a minor effect on
the U-value, a 3.3 percent reduction. Modifications to the door
flanges produced up to a 26 percent reduction, and up to '29 per-
cent reductions were calculated for modifications jto the cabinet
j
only. Reductions of over fifty percent were, also, possible and
the reductions were cumulative, as shown by the open circles in
Figure 13. |
A final calculation was made to determine if heat flow
through the foam adjacent to the flanges would significantly
affect the reductions described above. A model similar to that
shown in Figure 5 but with the clip and portions of the flanges
described above changed to plastic, was employed in this calcula-
i
tion. As shown in Table 9, including the heat flow through the
24
-------
o
O
3
-d
CD
cd
o
o
• r-t
tJ
CD
0)
Door &: Cabinet
Cabinet Only
——-—• .
^-^
Door Only
0.00
0.25 0.50 0.75 1.00
Fraction Plastic
1.25
Figure 13. GE gasket region load reductions for various flange
modifications.
25
-------
foa* adjacent to the door and cabinet flanges increased the U-
value of the gasket region by less than 2 percent.
Table 9. Effect of Flange/Foam Boundary Condition on
U-Value of Modifi^ nw «».ir~4. «-_/__. ion. on
Heat Transfer
adiabatic
conduction
Overall Heat
Transfer Rate
Btu/(hr*in)
0.2763
0.2801
Overall H«at
Trans. Coeff., u
Btu/(hr*,in*eF)
3.070E-3
3.119E--3
- NEW DESIGNS
A method to measure the total heat flux through the gasket
region of a R/F cabinet does not exist. Measurements of the
total energy consumption of two prototype R/Fs were t*us used in
conjunction with the SPA Refrigerator analysis (ERR, J1Odel (4, to
determine if the predicted energy reductions could be achieved in
practice. j
Both prototypes had gasket cross sections similar to the
subzero gasket, but neither had the decorative metal gasket cover
shown in Figure 1. other notable differences to the model shown
in Figure 1 were that the cabinet flange was. not as wide as the
gasket for both prototypes and that the plastic liner and not a
»etal clip was used to hold the gasket in place in prototype B.
EMSoiVBe. & - The cabinet flange for this unit1 ended at the
inside edge of the gasket magnet as is shown in Figure 10. The
remainder of the flange was, however, not plastic but rather a
small air gap. still air would produce the same effect: as having
26
-------
plastic in this region. If, however, convection to the R/F
interior occurred in this gap, the flange would behave exactly as
that shown in Figure 1. The exact configuration shown in Figure
10 was then easily obtained by placing plastic insulating tape
between the end of the metallic flange and the inside of the R/F.
No modifications were made to the door flange in prototype A.
The calculations presented in Table 7 suggest that a 30
percent decrease in the total heat flux for the gasket region
would results from this modification, if convection was present
in the air gap. Reducing the gasket heat load by this amount in
the ERA model predicted a 9 percent energy reduction. Measure-
ments yielded 7 to 8 percent.
The agreement between the measurement and models is very
good. It is possible even better agreement would be obtained by
employing a lower heat transfer coefficient in the air gap. This
would be warranted, as some restriction to air flow is likely.
Prototype 1 - The door flange was changed in this unit by
removing the portion of the flange located under the gasket and
between the liner mounting screws. This portion of the flange
accounts for about 80 percent of the heat transfer path and
should produce about that fraction of the 22 percent reduction
for this modification shown in Table 7. Reducing the gasket heat
flow by this amount in the ERA model predicted a 5 percent reduc-
tion in total energy consumption for this unit. This result is
in excellent agreement with the 4 to 5 percent that was measured.
The cabinet flange in this model was similar to that in
prototype A, i. e. it did not extend the entire length of the
gasket. It did, however, extend beyond the magnet approximately
27
-------
one sixth of the way in the freezer and one third of the way in
the fresh food section. As with prototype A, plastic tape was
employed to fill in the air gap in both the freezer and fresh
food sections. Table 7 would suggest an 18 percent reduction for
the fresh food section and a 30 percent reduction for the freezer
section. AS this modification was done after the door flange was
changed the total reductions should be 36 and 48 percent.
The ERA model was again used to simulate the R/F with the
reduced gasket heat input and predicted an 11 percent energy
reduction. Measurements showed a 7 to 8 percent reduction. AS
noted above, better agreement would have been attained with a
lower convective heat transfer coefficient in the air gap.
Agreement was, however, quite good.
CONCLUSIONS
Heat flow through the gasket region of refrigerator/freezers
is modeled using finite element analysis.
Heat flow through the gasket and flanges is highly coupled.
Decreasing the thermal resistance of the gasket by incorpo-
rating a low conductivity gas in the pockets, of the gasket
has a modest effect on the gaskets thermal performance.
Replacing about half of either the metal door flange or
cabinet flange with plastic can reduce the heat flow through
the region by 25 percent.
Replacing about half of the door and cabinet flanges with
28
-------
Plastic can reduce the u-value of the gasket region by half.
Measured and predicted reductions in total R/F energy con-
sumption resulting fro* modified gasket designs are in good
agreement.
ACKNOWI.EDGEMETJ'IPg
The authors wish to thank Mr. oin Zhou, Mr. Kwangil Kim, Dr
Sungpil won and Prof. Reinhardt Radermacher of the Department of
Mechanical Engineering at the University of Maryland for perform-
ing the energy testing on the prototype refrigerator/freezers.
REFERENCES
Resul?s
Panels",
the
Test
Insulation
2, oak
calif ornia
'
S ' Selk°»itz, High-
U.S.
29
------- |