# Evaluation of refrigerator/freezer gaskets thermal loads.

Introduction

Over the past decades, household refrigerator/freezer manufacturers have made significant efforts to improve energy efficiency by increasing the cabinet insulation and improving door gasket and refrigeration system designs. Continued improvement of refrigerator/freezer energy efficiency requires appropriate methods to quantify the loads due to specific components. The objective of this research is to develop a method to quantify the total thermal loads due to the gasket. The latter is calculated as the heat transfer load, that is, the thermal load due to convective, radiative, and conductive heat transfer mechanisms plus the infiltration load.

The open literature about gasket studies is relatively scarce. In a review by Ghassemi and Shapiro (1991), the energy consumption associated with the gasket heat transfer load varied from 10% to 30% of the unit total thermal load, and the gasket infiltration load ranged from 1.5 to 29.3 W (5 to 100 Btu/h). The authors presented two analytical and two experimental methods to estimate the gasket heat transfer load. The two analytical methods are based on the use of coefficients obtained for a specific gasket model, which limits their applicability. Each one of the two experimental methods is based on two reverse heat leakage (RHL) tests. In an RHL test, the refrigerator/freezer unit is put inside a temperature-controlled chamber, an electrical heat source is placed inside of each one of the compartments, and the power input to each heat source is measured along with the inside and outside temperatures. In both methods, the first RHL test measures the total heat loss through the unit (baseline unit). The second RHL test uses modified units, which differ in both methods. The first method uses two identical units whose doors have been removed and are connected by the gaskets, forming one cavity for each compartment. This method is not useful for side-by-side refrigerator/freezers and relies on some speculation regarding the door loss. In the second method, the second RHL test is performed with the unit heavily insulated around the gasket area. This is useful for any refrigerator/freezer configuration. The accuracy of this second method depends on taking the difference between two values that are nearly equal. The authors also estimated the gasket infiltration load, which is the sum of the sensible heat load and the latent load, both functions of the leakage flow rate. To estimate the latter, they used an empirical model, where the leakage flow rate per unit length depends exponentially on the pressure drop. They used values of the exponent and pressure drop that are not valid in general.

Studies of the heat transfer load were performed by Abramson et al. (1990) and Boughton et al. (1996). Abramson et al. (1990) calculated gasket heat transfer load using a computer simulation model based on heat transfer principles with special corrections to deal with nonplanar surfaces and the effects of corners and edges. Unfortunately, they did not give details about the model. Boughton et al. (1996) developed a method to estimate cabinet heat transfer loads. Conduction heat transfer into the refrigerator cabinet is quantified using a combination of numerical simulations and experiments. They assumed that the boundaries between the gasket and the door, and gasket and cabinet walls, are adiabatic. This allowed them to consider the wall, gasket, and door separately, but with a large uncertainty on the actual percentage heat leakage due to the gasket, which must be between the value estimated for the edge loads (28.5%) and the value estimated by this model for the gasket (2.7%).

To estimate the infiltration load through the gasket, the tracer gas method has been used (Tiax Llc 2002). In this method, a gas is injected into the unit until a suitable initial concentration is established. The exponential decay of the concentration indicates the infiltration rate. Two tests are done--one for the baseline unit and the other for the gasket-sealed unit. An alternative method to estimate the infiltration load through cabinet door gaskets was presented by Stein et al. (2002). They studied closed-door moisture transport in refrigerator/freezers by putting water pans to mimic moist foods, and they measured the amount of water defrosted from the evaporator that is collected in a sealed container. The differences between the pan water evaporation rate and the evaporator frost accumulation rate is attributed mainly to the infiltration rate of water through the gaskets. The load is calculated, taking into account the energies required to freeze and melt the water during defrost cycles, neglecting sensible cooling and sensible warming loads. They emphasized that the vapor transport through gasket regions is significantly affected by ambient conditions.

In this study, a method to evaluate the heat transfer through the gasket is presented. This considers conduction and convection in the gasket bulk and convection and radiation over the internal and external surfaces of the gasket, both as functions of the position along the perimeter of the gasket. This method is based on a quasi-one-dimensional theoretical model and uses experimental and numerical results to evaluate thermal coefficients. The infiltration load through the gasket is evaluated using the tracer gas method. The result of gasket total thermal load is compared with the load estimated by the reverse heat leak method.

The method was applied to evaluate the gasket total thermal load of the freezer gasket of a 708 L (25 [ft.sup.3]), side-by-side refrigerator/freezer. This unit has a multiple bubbles magnetic gasket made of extruded PVC. The perimeter of the freezer gasket is 4.072 m (13.360 ft). The freezer cavity has a height H of 1.830 m (6.004 ft.) and a width of 0.508 m (1.667 ft). All experimental measurements and numerical simulations are done at steady-state closed-door conditions. The results reported in this article are forafreezertargettemperatureof-25[degrees]C(-13[degrees]F) and average temperature difference between freezer and room of [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F).

Convective, radiative, and conductive heat transfer loads

Gasket heat transfer load due to the convective, radiative, and conductive mechanisms of heat transfer is calculated using a theoretical model combined with experimental and numerical results.

Heat transfer theoretical model

The steady-state, one-dimensional heat transfer equations (Incropera and De Witt, 2002) are modified to a quasi-one-dimensional model using two factors [c.sub.1] and [c.sub.2] that take into account the heat transfer from the door and cabinet walls in contact with the gasket. This model considers convection and radiation over the internal and internal surfaces using film coefficients [h.sub.o] and [h.sub.i], respectively, and considers convection and conduction in the gasket bulk using an effective conduction coefficient [k.sub.eff]. Figure 1 shows the diagram of the model and the equivalent thermal resistances circuit, where q is the gasket heat transfer load per unit length, L is the gasket width, TO is the room temperature, TSO and TSI are the temperatures at the external and internal surfaces of the gasket, respectively, and TI is the temperature at the inside of the freezer or refrigerator cavity.

[FIGURE 1 OMITTED]

The thermal resistances at the external surface of the gasket [R.sub.o], the gasket bulk [R.sub.eff], and the internal surface of the gasket [R.sub.i], are given by

[R.sub.o] = 1 / [h.sub.o][d.sub.o], [R.sub.eff] = L / [k.sub.eff]d, and [R.sub.i] = 1 / [h.sub.i][d.sub.i], (1)

where [d.sub.o], d, and [d.sub.i] are the depths of the of the gasket at the external surface, the center, and the internal surface, respectively.

The factor [c.sub.1] is the fraction of the heat q that enters through the external surface of the gasket, and the factor [c.sub.2] is related to the heat that enters the gasket through the cabinet and door walls. As the heat transfer through the gasket bulk is evaluated in the central plane between external and internal surfaces, and assuming that the heat flow through the walls increases linearly from the exterior to the interior,

[c.sub.2] = 0.5(1 + [c.sub.1]). (2)

From the equivalent thermal resistances circuit,

[c.sub.1]q = TO - TSO / [R.sub.o], [c.sub.2]q = TSO - TSI / [R.sub.eff], and

q = TSI - TI / [R.sub.i] (3)

In this model, the temperatures and geometrical parameters are known values taken from experimental measurements, and [c.sub.1] is taken from numerical simulations. Thus, Equation 3 constitutes a nonclosed system of three linear equations for four unknowns, the heat transfer load per unit length q, and the three thermal coefficients [h.sub.o,] [k.sub.eff], and [h.sub.i]. A closed system is obtained by adding, to the exterior part of the gasket, a frame made of a material with a known thermal conductivity [k.sub.F], as shown in Figure 2.

The thermal resistance of the frame is given by

[R.sub.F] = [L.sub.F] / [k.sub.F][d.sub.F], (4)

where [L.sub.F] and [d.sub.F] are the length in the q direction and the width of the transversal section of the frame. Then

[c.sub.1]q = TO - TFO / [R.sub.o], [c.sub.1]q = TFO - TSO / [R.sub.F],

[c.sub.2]q = TSO-TSI / [R.sub.eff], and q = TSI-TI / [R.sub.i] (5)

[FIGURE 2 OMITTED]

From the last equations,

[k.sub.eff] = [k.sub.F](1+[c.sub.1] / 2[c.sub.1])(TFO-TSO / TSO-TSI) x (L / [L.sub.F])([d.sub.F] / d). (6)

The effective conduction coefficient [k.sub.eff] is calculated by substituting the temperatures from experimental measurements in the unit with the frame and [c.sub.1] from numerical simulations. The heat transfer load per unit length q and the film coefficients [h.sub.o] and [h.sub.i] of the gasket are obtained by substituting [k.sub.eff], the temperatures taken from the experimental results in the baseline unit, and [c.sub.1] into Equations 1 and 3, giving

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

To estimate the value of the factor c;, the following numerical simulation is done.

Numerical simulations

A 3D numerical simulation of a vertical section (height of 101.6 mm [4 in.]) of the gasket (including its internal air cavities and magnet), door, cabinet, room air, and inside freezer has been developed to estimate the value of [c.sub.1]. Figure 3 shows a cross-section plane of the computational domain; the gravity force is in the -z direction.

Governing equations

Fluid dynamics and heat transfer phenomena are governed by Navier-Stokes and energy equations. The following assumptions are considered: laminar flow, Boussinesq approximation (i.e., density variation is only relevant in buoyancy terms of momentum equations), Newtonian fluid, negligible viscosity dissipation, constant physical properties, and negligible radiation heat transfer (although radiation heat transfer is taken into account in the theoretical model).

[FIGURE 3 OMITTED]

Boundary and initial conditions

The boundaries of the computational domain for room air and inside freezer air are considered as openings (i.e., [partial derivative][u.sub.n]/[partial derivative][x.sub.n] = 0, where n denotes the boundary-normal component). The temperature of the air coming into the domain from the room is 25.65[degrees]C (78.17[degrees] F), and that coming from the freezer is TI = -18.15[degrees]C (-0.67[degrees]F), respectively, implying [DELTA]T = 43.8[degrees]C (78.8[degrees]F), to reproduce experimental conditions. For gasket internal air cavities, both bottom and top boundaries of the computational domain are also considered as openings. The temperature of the air coming into the domain from the top is the minimum calculated in that boundary from previous iteration, and the temperature of the air coming into the domain from the bottom is the maximum on that boundary in the previous iteration. These assumptions were made trying to emulate the buoyancy effects. For solids, the boundaries of the computational domain are considered adiabatic. The velocity of the fluid in the interface with solid walls is [u.sub.i] = 0.

The following initial conditions were used. Freezer air temperature of -18.15[degrees]C (-0.67[degrees]F), room air temperature of 25.65[degrees]C (79.97[degrees]F), gasket and internal cavities air temperatures of 14.45[degrees]C (58.01[degrees]F) (media between TSO and TSI ; values were taken from experimental results presented below). The reference density for the buoyancy term was the density corresponding to the initial temperature of each subdomain. Air velocity is zero. The temperatures of the solid elements is 3.75[degrees]C (38.75[degrees]F) (the media between TO and TI).

Numerical model

The computational fluid dynamics software employed was CFX[R] v 11.0. It uses the finite control volume technique with a total temporal implicit differentiation (ANSYS 2006). The mesh is nonstructured with tetrahedron elements. The mesh was refined at fluid-solid interfaces to better represent the boundary effects. Diffusive terms are evaluated with a central difference scheme. In advection terms, a high-resolution scheme has been used; this scheme is based in an upwind scheme plus a function that evaluates its changes in the control volume. The time step for fluids considered was [DELTA][t.sub.f] = 0.1 s and for solids [DELTA][t.sub.s] = 1.0 s. The resulting algebraic system equation is solved in a coupled way. As steady-state results are sought, the iterative process is truncated when the rms of the residuals from the equations is less than [10.sup.-4].

[FIGURE 4 OMITTED]

Numerical results

Figure 4 shows the temperature map in the middle cross-section plane, i.e., height 50.8 mm (2 in.).

Table 1 shows a comparison between numerical and experimental temperatures for TSO and TSI. Experimental temperatures are taken at steady state using thermocouples located in section 8 (see Figure 5). Numerical results are taken at corresponding positions.

Numerical results for TSO and TSI differ by 0.2[degrees]C(0.4[degrees]F) and 2.8[degrees]C(5.0[degrees]F) from experimental results, respectively; numerical results for TSO-TSI differ by 2.6[degrees]C(4.7[degrees]F). Thus, the heat transfer results from the numerical model can be considered a good approximation to the experimental conditions, in spite of the approximations made. The heat flow across each one of the gasket interfaces is calculated and is shown in Table 2. From gasketroom and gasket-freezer values, [c.sub.1] = 0.55.

[FIGURE 5 OMITTED]

Assuming the same heat flow along the whole gasket length (same for vertical and horizontal sections), the total computed heat transfer from the freezer gasket would be [Q.sub.ht] = 6.28 W (21.43 Btu/h).

Temperature measurements

According to the developed method, two types of experiments are needed--one with the baseline unit (baseline experiments) and the other with the frame of a known thermal conductivity material covering the gasket (frame experiments). Expanded polystyrene (EPS) was used in the experiments reported in this article. In both types of experiments, the air ducts (air duct supply and air duct return) between freezer and refrigerator cavities were closed. All temperatures were measured using thermocouples (Type T, 36 AWG, electrically welded) connected to a data acquisition system and individually calibrated. The gasket perimeter was divided into eight sections, and temperatures were measured at a representative point within each section, as shown in Figure 5.

The heat transfer load through the ith gasket section, [Q.sub.i], is given by

[Q.sub.i] = [q.sub.i][l.sub.i], (8)

where [q.sub.i] and [l.sub.i] are gasket heat transfer rate per unit length and the length of the ith section, respectively.

The heat transfer load through the freezer gasket due to convection, conduction, and radiation [Q.sub.ht] is given by the sum of the [Q.sub.i].

Room temperature TO was measured 25.4 cm (10 in.) away from the center of the freezer lateral wall at a height of 91.5 cm (3 ft) from the unit base. The corresponding TO thermocouple was pasted to a copper mass cylinder of length and diameter of 29 [+ or -] 6 mm (1.12 [+ or -] 0.25 in.) using thermocouple cement. Internal freezer temperature TI is the average of the measured temperatures at three vertical positions along the central axis of the freezer cavity at heights H/4, H/2, and 3H/4 from the bottom. Each thermocouple was pasted to a copper mass cylinder equal to the one used to measure TO. The copper cylinders were held using insulating threads and stands.

For each gasket section, differential thermocouples were used to measure TFO-TSO and TSO-TSI in the frame experiments, and TSO-TSI, TSI-TI, and TO-TSO in both experiments. The use of differential thermocouples to measure these quantities was preferred because of the smaller uncertainty compared to the one obtained using two thermocouples to measure the corresponding temperatures. The thermocouple-end corresponding to TI was pasted to the cylinder at H/2 inside the freezer; the thermocouple-end corresponding to TO was pasted to the cylinder where TO was measured. Each thermocouple-end corresponding to TFO, TSO, and TSI was pasted at the width center of the exterior surface of the EPS, of the gasket external surface, and of the gasket internal surface, respectively. These ends were pasted with Omega thermocouple cement and were covered with an insulating tape. For the frame experiments, a rectangular cross-section EPS frame was used. The width of the EPS was the same as that of the gasket external surface [d.sub.F] = d = 20 [+ or -] 0.01 mm (0.7874 [+ or -] 0.0004 in.), and the length [L.sub.f] was 9.26 [+ or -] 0.01 mm (0.3657 [+ or -] 0.0004 in.). To achieve a good thermal contact between the gasket and the EPS frame, the frame was pasted to the door and cabinet walls using sealing extruded rubber mastic.

[FIGURE 6 OMITTED]

Results

The effective conduction coefficient [k.sub.eff], the film coefficients [h.sub.o] and [h.sub.i], the heat transfer load per unit length [q.sub.i], and the heat transfer load [Q.sub.i], for each section of the freezer gasket are presented in Figure 6. The uncertainty associated is calculated using the error propagation theory, taking into account the uncertainty associated to the thermocouple calibration, but the uncertainty associated to the location of the thermocouples is not considered due to the impossibility to estimate it.

Detailed observations indicate that the variation of [k.sub.eff] is mainly due to small changes in the distance between the door and cabinet. The small differences in [k.sub.eff]between vertical and horizontal positions indicate that air convection inside the gasket is not relevant, which is in agreement with numerical results. The smallest value of hi at section 2 can be attributed to the protection from convection and radiation given at this section by the door interior compartments and the largest value of [h.sub.o] at section 2 to the convection at this position produced by the airflow from front to back at the bottom of the freezer during compressor operation. Due to their much larger lengths, the two vertical sections have much larger values of [Q.sub.i].

The heat transfer load through the freezer gasket, due to convection, conduction, and radiation is [Q.sub.ht] = 2.68 [+ or -] 0.04 W (9.1 [+ or -] 0.1 Btu/h). The contribution of the condenser hot loop mullion periodic heating to [Q.sub.ht] is estimated to be 5%. This quantity is not the real impact of the presence of the condenser hot loop. To measure [Q.sub.ht], experiments without the condenser hot loop must be carried out, which is beyond the scope of the present study.

Infiltration load

To evaluate the gasket infiltration load, two different experiments are necessary. One with the gasket uncovered (baseline experiment), the other with the gasket artificially sealed to avoid infiltration through it (gasket-sealed experiment). The gasket sealing is done using extruded rubber mastic. In both types of experiments, any other source of infiltration is not modified.

The gasket infiltration load [Q.sub.ing] is calculated as the difference between infiltration load in the baseline experiment [Q.sub.inb] and infiltration load in the gasket sealed experiment [Q.sub.ins],

[Q.sub.ing] = [Q.sub.inb] - [Q.sub.ins]. (9)

For each one of the experiments, the infiltration load [Q.sub.in] has two components--the sensible heat load [Q.sub.s] and the latent heat load [Q.sub.l] (Kuehn et al. 2001),

[Q.sub.in] = [Q.sub.s] + [Q.sub.l]. (10)

The sensible heat load Qs is given by

[Q.sub.s] = [??][bar.Cp][DELTA]T, (11)

where [??] is the infiltration air mass flow

[??] = [[rho].sub.a]V A; (12)

[[rho].sub.a] = 1.2 kg/[m.sup.3] (0.07 lb/[ft.sup.3]) is the air density; V = 0.25 [m.sup.3] (8.8 [ft.sup.3]) is the cavity volume; A is the interchange rate of air between the cavity and the room, relative to the volume of the cavity, in inverse time units. The average specific heat of the humid air, [bar.Cp], is defined as

[bar.Cp] = [Cp.sub.a] + [bar.W][Cp.sub.w], (13)

where [Cp.sub.a] = 1.006 kJ/[kg.sub.a][degrees]C (0.240 Btu/lb[degrees]F) is the specific heat of dry air; the term [bar.W][Cp.sub.w] is the contribution to the sensible load of water vapor in the air, with [bar.W] the average during the experiment of the absolute humidity and [Cp.sub.w] = 1.882 kj/[kg.sub.w][degrees]C (0.999 Btu/lb[degrees]F) the water specific heat. The latent heat load [Q.sub.l] is given by

[Q.sub.l] = [??][bar.[h.sub.w]][DELTA]W, (14)

where [bar.[h.sub.w]] = 2,700 kJ/[kg.sub.w] (1,162 Btu/lb) is the average water vaporization enthalpy, and [DELTA]W is the absolute humidity difference between the cavity and the surroundings.

The interchange rate of air between the cavity and the room relative to the volume of the cavity infiltration A is evaluated using tracer gas dilution method, as described below.

Infiltration by a tracer gas dilution method

In this method, a small volume of gas is introduced inside the cavity, and its concentration is measured as a function of time. The concentration, C, defined as the ratio of gas volume to air volume, decreases with time t exponentially;

C = [C.sub.0][e.sup.At], (15)

where [C.sub.0] is the initial concentration, and A is a negative constant. Equation 15 can be written as

1n C = At + 1n [C.sub.0]. (16)

The value of A can be obtained by fitting the experimental data to Equation 16.

Infiltration experiments

The infiltration is a function of the temperature difference between the interior and exterior of the cavity [DELTA]T. Thus, these temperatures must be measured during the experiment. This was done with the thermocouples used to measure TO and TI at H/2. The air ducts (air duct supply and air duct return) between freezer and refrigerator cavities and the air ducts at ice and water dispensers were sealed.

[FIGURE 7 OMITTED]

Due to safety reasons (ASTM 2006) and sensors availability, C[O.sub.2] was used as the tracer gas in the experiments. A C[O.sub.2] cylinder tank with a security valve and a pressure regulator was used. The normal concentration of C[O.sub.2] in air is about 300 ppm; thus, it is recommended that the sensor's upper limit be close to 4,000 ppm. The C[O.sub.2] sensor used (10 to 4,500 ppm) was located at the center of the freezer cavity. The ambient relative humidity was measured using a data logger (5 to 95%HR, [+ or -]2.5%HR). Data were recorded using an acquisition system. The C[O.sub.2] was introduced through the water input tube of the icemaker. For sealed experiments, the gasket was sealed with the same EPS frame and the sealing extruded rubber mastic used in previous experiments.

Once the temperature at the freezer cavity had achieved a steady state, the corresponding C[O.sub.2] concentration was recorded (this concentration is called the base value). Then, the gas tank valve was opened and, using the pressure regulator, the cavity was filled with gas until the desired maximum concentration was obtained. In order to have the best possible resolution, the maximum concentration in the experiments was about 4,450 ppm. Concentration, temperatures, and relative humidity were recorded every minute, and the experiment finished when the gas concentration approached the base value. Figure 7 shows the natural logarithm of C[O.sub.2] concentration as a function of time for baseline and sealed experiments. Using Equation 16, A = -0.1123 [+ or -] 0.0007 [h.sub.-1] for the baseline experiment, and A = -0.0531 [+ or -] 0.0002 [h.sub.-1] for the gasket sealed experiment. The uncertainty of A increases to 0.01 due to test repeatability as far as how uniformly the door seals after each opening-closing process.

[FIGURE 8 OMITTED]

For both experiments, the average of the absolute humidity was [bar.W] = 0.0075 [+ or -] 0.0004 [kg.sub.w]/[kg.sub.a] (0.0075 [+ or -] 0.0004 [lb.sub.w]/[lb.sub.a]), and the absolute humidity difference between the cavity and the surroundings was [DELTA]W = 0.015 [+ or -] 0.0008 [kg.sub.w]/[kg.sub.a] (0.015 [+ or -] 0.0008 [lb.sub.w]/[lb.sub.a]). These quantities were estimated using the measured ambient absolute humidity during the experiments and assuming, based on previous measurements, that the absolute humidity inside the cavity is zero.

Infiltration load results

Substituting experimental results into Equations 9-14, the gasket infiltration load is estimated as [Q.sub.ing] = 0.44 [+ or -] 0.19 W (1.50 [+ or -] 0.64 Btu/h) for a temperature difference between freezer and room of [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F) and an absolute humidity difference between the cavity and the surroundings of [DELTA]W = 0.015 [kg.sub.w]/[kg.sub.a] (0.015 [lb.sub.w]/[lb.sub.a]). For this condition, the infiltration through the gasket contributes to the frost in 0.14 g/h (0.0003 lb/h). Considering the same [DELTA]T, but assuming an extreme case where [DELTA]W = 0.05 [kg.sub.w]/[kg.sub.a] (0.05 [lb.sub.w]/[lb.sub.a]) and a room temperature of 40[degrees]C (104[degrees]F), the gasket infiltration load would increase up to [Q.sub.ing] = 0.92 [+ or -] 0.19 W (3.14 [+ or -] 0.65 Btu/h) and the frost to 0.45 g/h (0.0010 lb/h).

Reverse heat leak tests

RHL tests were performed in a controlled chamber using a variation of the second method described by Ghassemi and Shapiro (1991) instead of insulating the unit around the gasket area; for the second test, a unit with two equal gaskets was used. The aforementioned test uses a unit with a modified gasket area; two identical gaskets are overlapped, and the distance between the door and the cabinet is equivalent to the double of the original distance (using only one gasket).

Reverse heat leak results

The temperature difference between freezer and room was the same as in previous experiments. The total thermal load of the freezer obtained by the first test is [Q.sub.fzRHL] = 56.80 [+ or -] 1.01 W (829 [+ or -] 10 Btu/h). The gasket load obtained by the two tests is [Q.sub.gRHL] = 3.0 [+ or -] 2.4 W (10.24 [+ or -] 8.2 Btu/h).

Conclusions

A method is developed to evaluate gasket heat transfer load due to convective, radiative, and conductive mechanisms. It combines a quasi-one-dimensional theoretical model with experimental and numerical results. This method allows estimating heat transfer coefficients along the gasket perimeter. Tracer gas dilution and humidity measurements were conducted to evaluate the infiltration load through the gasket. The gasket total thermal load is calculated as the addition of these two loads.

For a temperature difference between freezer and room [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F) and an absolute humidity difference between the cavity and the environment [DELTA]W = 0.015 [kg.sub.w]/[kg.sub.a] (0.015 [lb.sub.w]/[lb.sub.a]), the gasket total thermal load is [Q.sub.g] = 3.12 [+ or -] 0.05 W (10.65 [+ or -] 0.17 Btu/h); 86% corresponds to the heat transfer load through the freezer gasket and 14% to the gasket infiltration load. The gasket load obtained in RHL tests with the same AT is QgRHL = 3.0 [+ or -] 2.4 W (10.24 [+ or -] 8.2 Btu/h). In the RHL tests, the infiltration load is only due to the sensible load. Thus, to compare the results, the latent heat load is subtracted, which gives [Q.sub.g*] = 3.08 [+ or -] 0.05 W (10.51 [+ or -] 0.17 Btu/h). This value is equal to [Q.sub.gRHL], within the uncertainty of the latter. The developed method has the advantage of giving results with smaller uncertainty than the RHL method and provides information about the heat transfer along the perimeter of the gasket.

It is known that, on RHL tests, the heat transfer between two gaskets is different from the one between gasket and cabinet; however, the results are similar. The total heat transfer of the freezer gasket obtained from the numerical simulation is more than two times the one calculated with the quasi-one-dimensional model and is close to the upper estimation from RHL tests. This overestimation by the numerical simulation of the heat transfer could be due to the assumptions made at the bottom and the top boundaries of the gasket internal air cavities and that all the perimeter of the gasket has the same heat transfer behavior. Nevertheless, it can be considered that the overestimation is similar for all air cavities, resulting in no change in the value for the coefficient [c.sub.1].

From the total thermal load of the freezer obtained by an RHL test, the freezer gasket total thermal load obtained by the developed model, [Q.sub.g], represents 5.3% of [Q.sup.fzRHL]; and the gasket heat transfer load [Q.sub.ht] represents 4.7% of [Q.sub.fzRHL]. Ghassemi and Shapiro (1991) reported values between 10% and 30%. This indicates that the tested gasket has an improved design.

DOI: 10.1080/10789669.2011.543251

Acknowledgments

This work was supported by Mabe. The authors are thankful to Jose Berrondo Mir (Mabe TyP operation's vice president), Agustin Soto (refrigerators engineering's manager), as well as Francisco Anton (I+D manager), for their support to this project, and to the refrigerators laboratory staff for their experimental data recompilation in RHL tests.

Nomenclature

A = interchange rate of air between the cavity and the room

[c.sub.1] = proportion of the heat transfer from the outside

[c.sub.2] factor related to the heat transfer from the door and cabinet walls

C = gas concentration

[C.sub.0] = initial gas concentration

[bar.Cp] = average specific heat of the humid air

[Cp.sub.a] = air specific heat

[Cp.sub.w] = water specific heat

d = depth of the transversal section of the gasket bulk

[d.sub.F] = depth of the transversal section of the frame

[d.sub.i] = depth of the transversal section of the internal surface of the gasket

[d.sub.o] = depth of the transversal section of the external surface of the gasket

[h.sub.i] = internal surface film coefficient

[h.sub.o] = external surface film coefficient

[bar.[h.sub.w]] = average water vaporization enthalpy

H = freezer cavity height

[k.sub.eff] = effective conduction coefficient

[k.sub.F] = frame thermal conductivity

[l.sub.i] = length of the ith section of the gasket

L = gasket width

[L.sub.F] = frame width

[??] = infiltration air mass flow

q = gasket heat transfer rate per unit length

[q.sub.i] = gasket heat transfer rate per unit length of the ith section of the gasket

[Q.sub.fzRHL] = total thermal load of the freezer obtained by the first RHL test

[Q.sub.gRHL] = gasket load obtained by the RHL tests

[Q.sub.ht] = heat transfer load through the freezer gasket, due to convection, conduction, and radiation

[Q.sub.i] = heat transfer through the ith gasket section

[Q.sub.inb] = infiltration load in the baseline experiment

[Q.sub.ing] = gasket infiltration load

[Q.sub.ins] = infiltration load in the gasket sealed experiment

[Q.sub.l] = latent heat load

[Q.sub.s] = sensible heat load

[R.sub.eff] = thermal resistance at the gasket bulk

[R.sub.i] = thermal resistance at the internal surface of the gasket

[R.sub.o] = thermal resistance at the external surface of the gasket

t = time

TI = temperature at the inside of the freezer or refrigerator cavity

TO = room temperature

TSI = temperature at the internal surface of the gasket

TSO = temperature at the external surface of the gasket

[u.sub.n] = flow velocity normal component to the boundary

V = cavity volume

[bar.W] = average during the experiment of the absolute humidity

[x.sub.n] = spatial coordinate normal to the boundary

[[DELTA]t.sub.f] = time step for fluids in the numerical model

[[DELTA]t.sub.s] = time step for solids in the numerical model

[DELTA]T = temperature difference between freezer and room

[DELTA]W = absolute humidity difference between the cavity and the surroundings

[[rho].sub.a] = air density

References

Abramson, D.S., I. Turiel, and A. Heydari. 1990. Analysis of refrigerator-freezers design and energy efficiency by computer modeling: A DOE perspective. ASHRAE Transactions 96:1354-8.

ANSYS. 2006. CFX-Solver Theory Guide. Canonsburg, PA: ANSYS, Inc.

ASTM. 2006. Standard E741-00. Standard test method for determining air change in a single zone by means of a tracer gas dilution.West Conshohocken, PA: ASTM. E741-00 (Reapproved 2006).

Boughton, B.E., A.M. Clausing, and T.A. Newell. 1996. An investigation of household refrigerator cabinet loads. HVAC&R Research 2(2):135-48.

Ghassemi, M., and H. Shapiro. 1991. Review of energy efficiency of refrigerator/freezer gaskets. Report no. EPA600/2-91-060. Environmental Protection Agency (EPA), North Carolina.

Incropera, F.P., and D.P. De Witt. 2002. Fundamentals of Heat and Mass Transfer, 5th ed. New York: John Wiley and Sons.

Kuehn, T.H., J.W. Ramsey, and J.L. Threikeld. 1998. Thermal Environmental Engineering, 3rd ed. Upper Saddle River, NJ: Prentice Hall.

Stein, M.A., C. Inan, C. Bullard, and T. Newell. 2002. Closed door moisture transport in refrigerator/freezers. International Journal of Energy Research 26:793-805.

Tiax LLC. 2002. Application of best industry practices to de design of commercial refrigerators. Development of a high efficiency reach-in refrigerator. Final report to National Energy Technology Laboratory, U.S. Department of Energy, Cambridge, MA.

Dr. Guadalupe Huelsz, (1) * Fabrisio Gomez, (1) Miguel Pineirua, (1) Jorge Rojas, (1) Mauricio de Alba, (2) and Victor Guerra (2)

(1) Universidad Nacional Autonoma de Mexico, Centro de Investigacion en Energia, Temixco, Mexico

(2) Mabe, Centro de Tecnologia y Proyectos, Queretaro, Mexico

* Corresponding author e-mail: ghl@cie.unam.mx

Received March 12, 2010; accepted October 17, 2010

Dr. Guadalupe Huelsz is researcher. Fabrisio Gomez, EM, is project associate researcher. Miguel Pineirua, EM, is project associate researcher. Dr. Jorge Rojas is researcher. Mauricio de Alba is researcher. Victor Guerra, ESM, is researcher.

Over the past decades, household refrigerator/freezer manufacturers have made significant efforts to improve energy efficiency by increasing the cabinet insulation and improving door gasket and refrigeration system designs. Continued improvement of refrigerator/freezer energy efficiency requires appropriate methods to quantify the loads due to specific components. The objective of this research is to develop a method to quantify the total thermal loads due to the gasket. The latter is calculated as the heat transfer load, that is, the thermal load due to convective, radiative, and conductive heat transfer mechanisms plus the infiltration load.

The open literature about gasket studies is relatively scarce. In a review by Ghassemi and Shapiro (1991), the energy consumption associated with the gasket heat transfer load varied from 10% to 30% of the unit total thermal load, and the gasket infiltration load ranged from 1.5 to 29.3 W (5 to 100 Btu/h). The authors presented two analytical and two experimental methods to estimate the gasket heat transfer load. The two analytical methods are based on the use of coefficients obtained for a specific gasket model, which limits their applicability. Each one of the two experimental methods is based on two reverse heat leakage (RHL) tests. In an RHL test, the refrigerator/freezer unit is put inside a temperature-controlled chamber, an electrical heat source is placed inside of each one of the compartments, and the power input to each heat source is measured along with the inside and outside temperatures. In both methods, the first RHL test measures the total heat loss through the unit (baseline unit). The second RHL test uses modified units, which differ in both methods. The first method uses two identical units whose doors have been removed and are connected by the gaskets, forming one cavity for each compartment. This method is not useful for side-by-side refrigerator/freezers and relies on some speculation regarding the door loss. In the second method, the second RHL test is performed with the unit heavily insulated around the gasket area. This is useful for any refrigerator/freezer configuration. The accuracy of this second method depends on taking the difference between two values that are nearly equal. The authors also estimated the gasket infiltration load, which is the sum of the sensible heat load and the latent load, both functions of the leakage flow rate. To estimate the latter, they used an empirical model, where the leakage flow rate per unit length depends exponentially on the pressure drop. They used values of the exponent and pressure drop that are not valid in general.

Studies of the heat transfer load were performed by Abramson et al. (1990) and Boughton et al. (1996). Abramson et al. (1990) calculated gasket heat transfer load using a computer simulation model based on heat transfer principles with special corrections to deal with nonplanar surfaces and the effects of corners and edges. Unfortunately, they did not give details about the model. Boughton et al. (1996) developed a method to estimate cabinet heat transfer loads. Conduction heat transfer into the refrigerator cabinet is quantified using a combination of numerical simulations and experiments. They assumed that the boundaries between the gasket and the door, and gasket and cabinet walls, are adiabatic. This allowed them to consider the wall, gasket, and door separately, but with a large uncertainty on the actual percentage heat leakage due to the gasket, which must be between the value estimated for the edge loads (28.5%) and the value estimated by this model for the gasket (2.7%).

To estimate the infiltration load through the gasket, the tracer gas method has been used (Tiax Llc 2002). In this method, a gas is injected into the unit until a suitable initial concentration is established. The exponential decay of the concentration indicates the infiltration rate. Two tests are done--one for the baseline unit and the other for the gasket-sealed unit. An alternative method to estimate the infiltration load through cabinet door gaskets was presented by Stein et al. (2002). They studied closed-door moisture transport in refrigerator/freezers by putting water pans to mimic moist foods, and they measured the amount of water defrosted from the evaporator that is collected in a sealed container. The differences between the pan water evaporation rate and the evaporator frost accumulation rate is attributed mainly to the infiltration rate of water through the gaskets. The load is calculated, taking into account the energies required to freeze and melt the water during defrost cycles, neglecting sensible cooling and sensible warming loads. They emphasized that the vapor transport through gasket regions is significantly affected by ambient conditions.

In this study, a method to evaluate the heat transfer through the gasket is presented. This considers conduction and convection in the gasket bulk and convection and radiation over the internal and external surfaces of the gasket, both as functions of the position along the perimeter of the gasket. This method is based on a quasi-one-dimensional theoretical model and uses experimental and numerical results to evaluate thermal coefficients. The infiltration load through the gasket is evaluated using the tracer gas method. The result of gasket total thermal load is compared with the load estimated by the reverse heat leak method.

The method was applied to evaluate the gasket total thermal load of the freezer gasket of a 708 L (25 [ft.sup.3]), side-by-side refrigerator/freezer. This unit has a multiple bubbles magnetic gasket made of extruded PVC. The perimeter of the freezer gasket is 4.072 m (13.360 ft). The freezer cavity has a height H of 1.830 m (6.004 ft.) and a width of 0.508 m (1.667 ft). All experimental measurements and numerical simulations are done at steady-state closed-door conditions. The results reported in this article are forafreezertargettemperatureof-25[degrees]C(-13[degrees]F) and average temperature difference between freezer and room of [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F).

Convective, radiative, and conductive heat transfer loads

Gasket heat transfer load due to the convective, radiative, and conductive mechanisms of heat transfer is calculated using a theoretical model combined with experimental and numerical results.

Heat transfer theoretical model

The steady-state, one-dimensional heat transfer equations (Incropera and De Witt, 2002) are modified to a quasi-one-dimensional model using two factors [c.sub.1] and [c.sub.2] that take into account the heat transfer from the door and cabinet walls in contact with the gasket. This model considers convection and radiation over the internal and internal surfaces using film coefficients [h.sub.o] and [h.sub.i], respectively, and considers convection and conduction in the gasket bulk using an effective conduction coefficient [k.sub.eff]. Figure 1 shows the diagram of the model and the equivalent thermal resistances circuit, where q is the gasket heat transfer load per unit length, L is the gasket width, TO is the room temperature, TSO and TSI are the temperatures at the external and internal surfaces of the gasket, respectively, and TI is the temperature at the inside of the freezer or refrigerator cavity.

[FIGURE 1 OMITTED]

The thermal resistances at the external surface of the gasket [R.sub.o], the gasket bulk [R.sub.eff], and the internal surface of the gasket [R.sub.i], are given by

[R.sub.o] = 1 / [h.sub.o][d.sub.o], [R.sub.eff] = L / [k.sub.eff]d, and [R.sub.i] = 1 / [h.sub.i][d.sub.i], (1)

where [d.sub.o], d, and [d.sub.i] are the depths of the of the gasket at the external surface, the center, and the internal surface, respectively.

The factor [c.sub.1] is the fraction of the heat q that enters through the external surface of the gasket, and the factor [c.sub.2] is related to the heat that enters the gasket through the cabinet and door walls. As the heat transfer through the gasket bulk is evaluated in the central plane between external and internal surfaces, and assuming that the heat flow through the walls increases linearly from the exterior to the interior,

[c.sub.2] = 0.5(1 + [c.sub.1]). (2)

From the equivalent thermal resistances circuit,

[c.sub.1]q = TO - TSO / [R.sub.o], [c.sub.2]q = TSO - TSI / [R.sub.eff], and

q = TSI - TI / [R.sub.i] (3)

In this model, the temperatures and geometrical parameters are known values taken from experimental measurements, and [c.sub.1] is taken from numerical simulations. Thus, Equation 3 constitutes a nonclosed system of three linear equations for four unknowns, the heat transfer load per unit length q, and the three thermal coefficients [h.sub.o,] [k.sub.eff], and [h.sub.i]. A closed system is obtained by adding, to the exterior part of the gasket, a frame made of a material with a known thermal conductivity [k.sub.F], as shown in Figure 2.

The thermal resistance of the frame is given by

[R.sub.F] = [L.sub.F] / [k.sub.F][d.sub.F], (4)

where [L.sub.F] and [d.sub.F] are the length in the q direction and the width of the transversal section of the frame. Then

[c.sub.1]q = TO - TFO / [R.sub.o], [c.sub.1]q = TFO - TSO / [R.sub.F],

[c.sub.2]q = TSO-TSI / [R.sub.eff], and q = TSI-TI / [R.sub.i] (5)

[FIGURE 2 OMITTED]

From the last equations,

[k.sub.eff] = [k.sub.F](1+[c.sub.1] / 2[c.sub.1])(TFO-TSO / TSO-TSI) x (L / [L.sub.F])([d.sub.F] / d). (6)

The effective conduction coefficient [k.sub.eff] is calculated by substituting the temperatures from experimental measurements in the unit with the frame and [c.sub.1] from numerical simulations. The heat transfer load per unit length q and the film coefficients [h.sub.o] and [h.sub.i] of the gasket are obtained by substituting [k.sub.eff], the temperatures taken from the experimental results in the baseline unit, and [c.sub.1] into Equations 1 and 3, giving

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

To estimate the value of the factor c;, the following numerical simulation is done.

Numerical simulations

A 3D numerical simulation of a vertical section (height of 101.6 mm [4 in.]) of the gasket (including its internal air cavities and magnet), door, cabinet, room air, and inside freezer has been developed to estimate the value of [c.sub.1]. Figure 3 shows a cross-section plane of the computational domain; the gravity force is in the -z direction.

Governing equations

Fluid dynamics and heat transfer phenomena are governed by Navier-Stokes and energy equations. The following assumptions are considered: laminar flow, Boussinesq approximation (i.e., density variation is only relevant in buoyancy terms of momentum equations), Newtonian fluid, negligible viscosity dissipation, constant physical properties, and negligible radiation heat transfer (although radiation heat transfer is taken into account in the theoretical model).

[FIGURE 3 OMITTED]

Boundary and initial conditions

The boundaries of the computational domain for room air and inside freezer air are considered as openings (i.e., [partial derivative][u.sub.n]/[partial derivative][x.sub.n] = 0, where n denotes the boundary-normal component). The temperature of the air coming into the domain from the room is 25.65[degrees]C (78.17[degrees] F), and that coming from the freezer is TI = -18.15[degrees]C (-0.67[degrees]F), respectively, implying [DELTA]T = 43.8[degrees]C (78.8[degrees]F), to reproduce experimental conditions. For gasket internal air cavities, both bottom and top boundaries of the computational domain are also considered as openings. The temperature of the air coming into the domain from the top is the minimum calculated in that boundary from previous iteration, and the temperature of the air coming into the domain from the bottom is the maximum on that boundary in the previous iteration. These assumptions were made trying to emulate the buoyancy effects. For solids, the boundaries of the computational domain are considered adiabatic. The velocity of the fluid in the interface with solid walls is [u.sub.i] = 0.

The following initial conditions were used. Freezer air temperature of -18.15[degrees]C (-0.67[degrees]F), room air temperature of 25.65[degrees]C (79.97[degrees]F), gasket and internal cavities air temperatures of 14.45[degrees]C (58.01[degrees]F) (media between TSO and TSI ; values were taken from experimental results presented below). The reference density for the buoyancy term was the density corresponding to the initial temperature of each subdomain. Air velocity is zero. The temperatures of the solid elements is 3.75[degrees]C (38.75[degrees]F) (the media between TO and TI).

Numerical model

The computational fluid dynamics software employed was CFX[R] v 11.0. It uses the finite control volume technique with a total temporal implicit differentiation (ANSYS 2006). The mesh is nonstructured with tetrahedron elements. The mesh was refined at fluid-solid interfaces to better represent the boundary effects. Diffusive terms are evaluated with a central difference scheme. In advection terms, a high-resolution scheme has been used; this scheme is based in an upwind scheme plus a function that evaluates its changes in the control volume. The time step for fluids considered was [DELTA][t.sub.f] = 0.1 s and for solids [DELTA][t.sub.s] = 1.0 s. The resulting algebraic system equation is solved in a coupled way. As steady-state results are sought, the iterative process is truncated when the rms of the residuals from the equations is less than [10.sup.-4].

[FIGURE 4 OMITTED]

Numerical results

Figure 4 shows the temperature map in the middle cross-section plane, i.e., height 50.8 mm (2 in.).

Table 1 shows a comparison between numerical and experimental temperatures for TSO and TSI. Experimental temperatures are taken at steady state using thermocouples located in section 8 (see Figure 5). Numerical results are taken at corresponding positions.

Numerical results for TSO and TSI differ by 0.2[degrees]C(0.4[degrees]F) and 2.8[degrees]C(5.0[degrees]F) from experimental results, respectively; numerical results for TSO-TSI differ by 2.6[degrees]C(4.7[degrees]F). Thus, the heat transfer results from the numerical model can be considered a good approximation to the experimental conditions, in spite of the approximations made. The heat flow across each one of the gasket interfaces is calculated and is shown in Table 2. From gasketroom and gasket-freezer values, [c.sub.1] = 0.55.

[FIGURE 5 OMITTED]

Assuming the same heat flow along the whole gasket length (same for vertical and horizontal sections), the total computed heat transfer from the freezer gasket would be [Q.sub.ht] = 6.28 W (21.43 Btu/h).

Temperature measurements

According to the developed method, two types of experiments are needed--one with the baseline unit (baseline experiments) and the other with the frame of a known thermal conductivity material covering the gasket (frame experiments). Expanded polystyrene (EPS) was used in the experiments reported in this article. In both types of experiments, the air ducts (air duct supply and air duct return) between freezer and refrigerator cavities were closed. All temperatures were measured using thermocouples (Type T, 36 AWG, electrically welded) connected to a data acquisition system and individually calibrated. The gasket perimeter was divided into eight sections, and temperatures were measured at a representative point within each section, as shown in Figure 5.

The heat transfer load through the ith gasket section, [Q.sub.i], is given by

[Q.sub.i] = [q.sub.i][l.sub.i], (8)

where [q.sub.i] and [l.sub.i] are gasket heat transfer rate per unit length and the length of the ith section, respectively.

The heat transfer load through the freezer gasket due to convection, conduction, and radiation [Q.sub.ht] is given by the sum of the [Q.sub.i].

Room temperature TO was measured 25.4 cm (10 in.) away from the center of the freezer lateral wall at a height of 91.5 cm (3 ft) from the unit base. The corresponding TO thermocouple was pasted to a copper mass cylinder of length and diameter of 29 [+ or -] 6 mm (1.12 [+ or -] 0.25 in.) using thermocouple cement. Internal freezer temperature TI is the average of the measured temperatures at three vertical positions along the central axis of the freezer cavity at heights H/4, H/2, and 3H/4 from the bottom. Each thermocouple was pasted to a copper mass cylinder equal to the one used to measure TO. The copper cylinders were held using insulating threads and stands.

For each gasket section, differential thermocouples were used to measure TFO-TSO and TSO-TSI in the frame experiments, and TSO-TSI, TSI-TI, and TO-TSO in both experiments. The use of differential thermocouples to measure these quantities was preferred because of the smaller uncertainty compared to the one obtained using two thermocouples to measure the corresponding temperatures. The thermocouple-end corresponding to TI was pasted to the cylinder at H/2 inside the freezer; the thermocouple-end corresponding to TO was pasted to the cylinder where TO was measured. Each thermocouple-end corresponding to TFO, TSO, and TSI was pasted at the width center of the exterior surface of the EPS, of the gasket external surface, and of the gasket internal surface, respectively. These ends were pasted with Omega thermocouple cement and were covered with an insulating tape. For the frame experiments, a rectangular cross-section EPS frame was used. The width of the EPS was the same as that of the gasket external surface [d.sub.F] = d = 20 [+ or -] 0.01 mm (0.7874 [+ or -] 0.0004 in.), and the length [L.sub.f] was 9.26 [+ or -] 0.01 mm (0.3657 [+ or -] 0.0004 in.). To achieve a good thermal contact between the gasket and the EPS frame, the frame was pasted to the door and cabinet walls using sealing extruded rubber mastic.

[FIGURE 6 OMITTED]

Results

The effective conduction coefficient [k.sub.eff], the film coefficients [h.sub.o] and [h.sub.i], the heat transfer load per unit length [q.sub.i], and the heat transfer load [Q.sub.i], for each section of the freezer gasket are presented in Figure 6. The uncertainty associated is calculated using the error propagation theory, taking into account the uncertainty associated to the thermocouple calibration, but the uncertainty associated to the location of the thermocouples is not considered due to the impossibility to estimate it.

Detailed observations indicate that the variation of [k.sub.eff] is mainly due to small changes in the distance between the door and cabinet. The small differences in [k.sub.eff]between vertical and horizontal positions indicate that air convection inside the gasket is not relevant, which is in agreement with numerical results. The smallest value of hi at section 2 can be attributed to the protection from convection and radiation given at this section by the door interior compartments and the largest value of [h.sub.o] at section 2 to the convection at this position produced by the airflow from front to back at the bottom of the freezer during compressor operation. Due to their much larger lengths, the two vertical sections have much larger values of [Q.sub.i].

The heat transfer load through the freezer gasket, due to convection, conduction, and radiation is [Q.sub.ht] = 2.68 [+ or -] 0.04 W (9.1 [+ or -] 0.1 Btu/h). The contribution of the condenser hot loop mullion periodic heating to [Q.sub.ht] is estimated to be 5%. This quantity is not the real impact of the presence of the condenser hot loop. To measure [Q.sub.ht], experiments without the condenser hot loop must be carried out, which is beyond the scope of the present study.

Infiltration load

To evaluate the gasket infiltration load, two different experiments are necessary. One with the gasket uncovered (baseline experiment), the other with the gasket artificially sealed to avoid infiltration through it (gasket-sealed experiment). The gasket sealing is done using extruded rubber mastic. In both types of experiments, any other source of infiltration is not modified.

The gasket infiltration load [Q.sub.ing] is calculated as the difference between infiltration load in the baseline experiment [Q.sub.inb] and infiltration load in the gasket sealed experiment [Q.sub.ins],

[Q.sub.ing] = [Q.sub.inb] - [Q.sub.ins]. (9)

For each one of the experiments, the infiltration load [Q.sub.in] has two components--the sensible heat load [Q.sub.s] and the latent heat load [Q.sub.l] (Kuehn et al. 2001),

[Q.sub.in] = [Q.sub.s] + [Q.sub.l]. (10)

The sensible heat load Qs is given by

[Q.sub.s] = [??][bar.Cp][DELTA]T, (11)

where [??] is the infiltration air mass flow

[??] = [[rho].sub.a]V A; (12)

[[rho].sub.a] = 1.2 kg/[m.sup.3] (0.07 lb/[ft.sup.3]) is the air density; V = 0.25 [m.sup.3] (8.8 [ft.sup.3]) is the cavity volume; A is the interchange rate of air between the cavity and the room, relative to the volume of the cavity, in inverse time units. The average specific heat of the humid air, [bar.Cp], is defined as

[bar.Cp] = [Cp.sub.a] + [bar.W][Cp.sub.w], (13)

where [Cp.sub.a] = 1.006 kJ/[kg.sub.a][degrees]C (0.240 Btu/lb[degrees]F) is the specific heat of dry air; the term [bar.W][Cp.sub.w] is the contribution to the sensible load of water vapor in the air, with [bar.W] the average during the experiment of the absolute humidity and [Cp.sub.w] = 1.882 kj/[kg.sub.w][degrees]C (0.999 Btu/lb[degrees]F) the water specific heat. The latent heat load [Q.sub.l] is given by

[Q.sub.l] = [??][bar.[h.sub.w]][DELTA]W, (14)

where [bar.[h.sub.w]] = 2,700 kJ/[kg.sub.w] (1,162 Btu/lb) is the average water vaporization enthalpy, and [DELTA]W is the absolute humidity difference between the cavity and the surroundings.

The interchange rate of air between the cavity and the room relative to the volume of the cavity infiltration A is evaluated using tracer gas dilution method, as described below.

Infiltration by a tracer gas dilution method

In this method, a small volume of gas is introduced inside the cavity, and its concentration is measured as a function of time. The concentration, C, defined as the ratio of gas volume to air volume, decreases with time t exponentially;

C = [C.sub.0][e.sup.At], (15)

where [C.sub.0] is the initial concentration, and A is a negative constant. Equation 15 can be written as

1n C = At + 1n [C.sub.0]. (16)

The value of A can be obtained by fitting the experimental data to Equation 16.

Infiltration experiments

The infiltration is a function of the temperature difference between the interior and exterior of the cavity [DELTA]T. Thus, these temperatures must be measured during the experiment. This was done with the thermocouples used to measure TO and TI at H/2. The air ducts (air duct supply and air duct return) between freezer and refrigerator cavities and the air ducts at ice and water dispensers were sealed.

[FIGURE 7 OMITTED]

Due to safety reasons (ASTM 2006) and sensors availability, C[O.sub.2] was used as the tracer gas in the experiments. A C[O.sub.2] cylinder tank with a security valve and a pressure regulator was used. The normal concentration of C[O.sub.2] in air is about 300 ppm; thus, it is recommended that the sensor's upper limit be close to 4,000 ppm. The C[O.sub.2] sensor used (10 to 4,500 ppm) was located at the center of the freezer cavity. The ambient relative humidity was measured using a data logger (5 to 95%HR, [+ or -]2.5%HR). Data were recorded using an acquisition system. The C[O.sub.2] was introduced through the water input tube of the icemaker. For sealed experiments, the gasket was sealed with the same EPS frame and the sealing extruded rubber mastic used in previous experiments.

Once the temperature at the freezer cavity had achieved a steady state, the corresponding C[O.sub.2] concentration was recorded (this concentration is called the base value). Then, the gas tank valve was opened and, using the pressure regulator, the cavity was filled with gas until the desired maximum concentration was obtained. In order to have the best possible resolution, the maximum concentration in the experiments was about 4,450 ppm. Concentration, temperatures, and relative humidity were recorded every minute, and the experiment finished when the gas concentration approached the base value. Figure 7 shows the natural logarithm of C[O.sub.2] concentration as a function of time for baseline and sealed experiments. Using Equation 16, A = -0.1123 [+ or -] 0.0007 [h.sub.-1] for the baseline experiment, and A = -0.0531 [+ or -] 0.0002 [h.sub.-1] for the gasket sealed experiment. The uncertainty of A increases to 0.01 due to test repeatability as far as how uniformly the door seals after each opening-closing process.

[FIGURE 8 OMITTED]

For both experiments, the average of the absolute humidity was [bar.W] = 0.0075 [+ or -] 0.0004 [kg.sub.w]/[kg.sub.a] (0.0075 [+ or -] 0.0004 [lb.sub.w]/[lb.sub.a]), and the absolute humidity difference between the cavity and the surroundings was [DELTA]W = 0.015 [+ or -] 0.0008 [kg.sub.w]/[kg.sub.a] (0.015 [+ or -] 0.0008 [lb.sub.w]/[lb.sub.a]). These quantities were estimated using the measured ambient absolute humidity during the experiments and assuming, based on previous measurements, that the absolute humidity inside the cavity is zero.

Infiltration load results

Substituting experimental results into Equations 9-14, the gasket infiltration load is estimated as [Q.sub.ing] = 0.44 [+ or -] 0.19 W (1.50 [+ or -] 0.64 Btu/h) for a temperature difference between freezer and room of [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F) and an absolute humidity difference between the cavity and the surroundings of [DELTA]W = 0.015 [kg.sub.w]/[kg.sub.a] (0.015 [lb.sub.w]/[lb.sub.a]). For this condition, the infiltration through the gasket contributes to the frost in 0.14 g/h (0.0003 lb/h). Considering the same [DELTA]T, but assuming an extreme case where [DELTA]W = 0.05 [kg.sub.w]/[kg.sub.a] (0.05 [lb.sub.w]/[lb.sub.a]) and a room temperature of 40[degrees]C (104[degrees]F), the gasket infiltration load would increase up to [Q.sub.ing] = 0.92 [+ or -] 0.19 W (3.14 [+ or -] 0.65 Btu/h) and the frost to 0.45 g/h (0.0010 lb/h).

Reverse heat leak tests

RHL tests were performed in a controlled chamber using a variation of the second method described by Ghassemi and Shapiro (1991) instead of insulating the unit around the gasket area; for the second test, a unit with two equal gaskets was used. The aforementioned test uses a unit with a modified gasket area; two identical gaskets are overlapped, and the distance between the door and the cabinet is equivalent to the double of the original distance (using only one gasket).

Reverse heat leak results

The temperature difference between freezer and room was the same as in previous experiments. The total thermal load of the freezer obtained by the first test is [Q.sub.fzRHL] = 56.80 [+ or -] 1.01 W (829 [+ or -] 10 Btu/h). The gasket load obtained by the two tests is [Q.sub.gRHL] = 3.0 [+ or -] 2.4 W (10.24 [+ or -] 8.2 Btu/h).

Conclusions

A method is developed to evaluate gasket heat transfer load due to convective, radiative, and conductive mechanisms. It combines a quasi-one-dimensional theoretical model with experimental and numerical results. This method allows estimating heat transfer coefficients along the gasket perimeter. Tracer gas dilution and humidity measurements were conducted to evaluate the infiltration load through the gasket. The gasket total thermal load is calculated as the addition of these two loads.

For a temperature difference between freezer and room [DELTA]T = 47.2 [+ or -] 0.3[degrees]C (85.0 [+ or -] 0.5[degrees]F) and an absolute humidity difference between the cavity and the environment [DELTA]W = 0.015 [kg.sub.w]/[kg.sub.a] (0.015 [lb.sub.w]/[lb.sub.a]), the gasket total thermal load is [Q.sub.g] = 3.12 [+ or -] 0.05 W (10.65 [+ or -] 0.17 Btu/h); 86% corresponds to the heat transfer load through the freezer gasket and 14% to the gasket infiltration load. The gasket load obtained in RHL tests with the same AT is QgRHL = 3.0 [+ or -] 2.4 W (10.24 [+ or -] 8.2 Btu/h). In the RHL tests, the infiltration load is only due to the sensible load. Thus, to compare the results, the latent heat load is subtracted, which gives [Q.sub.g*] = 3.08 [+ or -] 0.05 W (10.51 [+ or -] 0.17 Btu/h). This value is equal to [Q.sub.gRHL], within the uncertainty of the latter. The developed method has the advantage of giving results with smaller uncertainty than the RHL method and provides information about the heat transfer along the perimeter of the gasket.

It is known that, on RHL tests, the heat transfer between two gaskets is different from the one between gasket and cabinet; however, the results are similar. The total heat transfer of the freezer gasket obtained from the numerical simulation is more than two times the one calculated with the quasi-one-dimensional model and is close to the upper estimation from RHL tests. This overestimation by the numerical simulation of the heat transfer could be due to the assumptions made at the bottom and the top boundaries of the gasket internal air cavities and that all the perimeter of the gasket has the same heat transfer behavior. Nevertheless, it can be considered that the overestimation is similar for all air cavities, resulting in no change in the value for the coefficient [c.sub.1].

From the total thermal load of the freezer obtained by an RHL test, the freezer gasket total thermal load obtained by the developed model, [Q.sub.g], represents 5.3% of [Q.sup.fzRHL]; and the gasket heat transfer load [Q.sub.ht] represents 4.7% of [Q.sub.fzRHL]. Ghassemi and Shapiro (1991) reported values between 10% and 30%. This indicates that the tested gasket has an improved design.

DOI: 10.1080/10789669.2011.543251

Acknowledgments

This work was supported by Mabe. The authors are thankful to Jose Berrondo Mir (Mabe TyP operation's vice president), Agustin Soto (refrigerators engineering's manager), as well as Francisco Anton (I+D manager), for their support to this project, and to the refrigerators laboratory staff for their experimental data recompilation in RHL tests.

Nomenclature

A = interchange rate of air between the cavity and the room

[c.sub.1] = proportion of the heat transfer from the outside

[c.sub.2] factor related to the heat transfer from the door and cabinet walls

C = gas concentration

[C.sub.0] = initial gas concentration

[bar.Cp] = average specific heat of the humid air

[Cp.sub.a] = air specific heat

[Cp.sub.w] = water specific heat

d = depth of the transversal section of the gasket bulk

[d.sub.F] = depth of the transversal section of the frame

[d.sub.i] = depth of the transversal section of the internal surface of the gasket

[d.sub.o] = depth of the transversal section of the external surface of the gasket

[h.sub.i] = internal surface film coefficient

[h.sub.o] = external surface film coefficient

[bar.[h.sub.w]] = average water vaporization enthalpy

H = freezer cavity height

[k.sub.eff] = effective conduction coefficient

[k.sub.F] = frame thermal conductivity

[l.sub.i] = length of the ith section of the gasket

L = gasket width

[L.sub.F] = frame width

[??] = infiltration air mass flow

q = gasket heat transfer rate per unit length

[q.sub.i] = gasket heat transfer rate per unit length of the ith section of the gasket

[Q.sub.fzRHL] = total thermal load of the freezer obtained by the first RHL test

[Q.sub.gRHL] = gasket load obtained by the RHL tests

[Q.sub.ht] = heat transfer load through the freezer gasket, due to convection, conduction, and radiation

[Q.sub.i] = heat transfer through the ith gasket section

[Q.sub.inb] = infiltration load in the baseline experiment

[Q.sub.ing] = gasket infiltration load

[Q.sub.ins] = infiltration load in the gasket sealed experiment

[Q.sub.l] = latent heat load

[Q.sub.s] = sensible heat load

[R.sub.eff] = thermal resistance at the gasket bulk

[R.sub.i] = thermal resistance at the internal surface of the gasket

[R.sub.o] = thermal resistance at the external surface of the gasket

t = time

TI = temperature at the inside of the freezer or refrigerator cavity

TO = room temperature

TSI = temperature at the internal surface of the gasket

TSO = temperature at the external surface of the gasket

[u.sub.n] = flow velocity normal component to the boundary

V = cavity volume

[bar.W] = average during the experiment of the absolute humidity

[x.sub.n] = spatial coordinate normal to the boundary

[[DELTA]t.sub.f] = time step for fluids in the numerical model

[[DELTA]t.sub.s] = time step for solids in the numerical model

[DELTA]T = temperature difference between freezer and room

[DELTA]W = absolute humidity difference between the cavity and the surroundings

[[rho].sub.a] = air density

References

Abramson, D.S., I. Turiel, and A. Heydari. 1990. Analysis of refrigerator-freezers design and energy efficiency by computer modeling: A DOE perspective. ASHRAE Transactions 96:1354-8.

ANSYS. 2006. CFX-Solver Theory Guide. Canonsburg, PA: ANSYS, Inc.

ASTM. 2006. Standard E741-00. Standard test method for determining air change in a single zone by means of a tracer gas dilution.West Conshohocken, PA: ASTM. E741-00 (Reapproved 2006).

Boughton, B.E., A.M. Clausing, and T.A. Newell. 1996. An investigation of household refrigerator cabinet loads. HVAC&R Research 2(2):135-48.

Ghassemi, M., and H. Shapiro. 1991. Review of energy efficiency of refrigerator/freezer gaskets. Report no. EPA600/2-91-060. Environmental Protection Agency (EPA), North Carolina.

Incropera, F.P., and D.P. De Witt. 2002. Fundamentals of Heat and Mass Transfer, 5th ed. New York: John Wiley and Sons.

Kuehn, T.H., J.W. Ramsey, and J.L. Threikeld. 1998. Thermal Environmental Engineering, 3rd ed. Upper Saddle River, NJ: Prentice Hall.

Stein, M.A., C. Inan, C. Bullard, and T. Newell. 2002. Closed door moisture transport in refrigerator/freezers. International Journal of Energy Research 26:793-805.

Tiax LLC. 2002. Application of best industry practices to de design of commercial refrigerators. Development of a high efficiency reach-in refrigerator. Final report to National Energy Technology Laboratory, U.S. Department of Energy, Cambridge, MA.

Dr. Guadalupe Huelsz, (1) * Fabrisio Gomez, (1) Miguel Pineirua, (1) Jorge Rojas, (1) Mauricio de Alba, (2) and Victor Guerra (2)

(1) Universidad Nacional Autonoma de Mexico, Centro de Investigacion en Energia, Temixco, Mexico

(2) Mabe, Centro de Tecnologia y Proyectos, Queretaro, Mexico

* Corresponding author e-mail: ghl@cie.unam.mx

Received March 12, 2010; accepted October 17, 2010

Dr. Guadalupe Huelsz is researcher. Fabrisio Gomez, EM, is project associate researcher. Miguel Pineirua, EM, is project associate researcher. Dr. Jorge Rojas is researcher. Mauricio de Alba is researcher. Victor Guerra, ESM, is researcher.

Table 1. Numerical and experimental temperatures comparison. TSO Numerical 22.2[degrees]C (72.0[degrees]F) Experimental 22.4 [+ or -] 0.3[degrees]C (72.3 [+ or -] 0.5[degrees]F) TSI Numerical 3.3[degrees]C (38.0[degrees]F) Experimental 6.1 [+ or -] 0.1[degrees]C (43.0 [+ or -] 0.2[degrees]F) TSO-TSI Numerical 18.9[degrees]C (34.0[degrees]F) Experimental 16.3 [+ or -] 0.3 [degrees](61.3 [+ or -] 0.5[degrees]F) Table 2. Heat flows across the gasket. Heat flow % Gasket-room [c.sub.l]q 0.8465 W/m 54.67 (0.8804 Btu/h ft) Gasket-cabinet 0.1821 W/m 11.76 (0.1894 Btu/h ft) Gasket-door 0.5197 W/m 33.57 (0.5405 Btu/h ft) Sum of above 1.5482 W/m 100.00 (1.6101 Btu/h ft) Gasket-freezer, -q -1.5443 W/m 99.75 (1.6060 Btu/h ft) Imbalance 0.0039 W/m 0.25 (0.0040 Btu/h ft)

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Author: | Huelsz, Guadalupe; Gomez, Fabrisio; Pineirua, Miguel; Rojas, Jorge; de Alba, Mauricio; Guerra, Victo |
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Publication: | HVAC & R Research |

Date: | Mar 1, 2011 |

Words: | 6122 |

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