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Applicability of multilayered phase-change-material modeling in building simulation.

INTRODUCTION

Building energy consumption and its resulting greenhouse gas emissions can be substantially reduced if solar energy is adequately utilized. Storage of thermal energy in buildings has gained prominence in the past two decades due to a strong need to reduce the total thermal energy requirement (both heating and cooling) in buildings (Zalba et al. 2004). The integration of phase-change materials into building fabrics can accumulate the gain from solar radiation during the day and release the stored energy at night. Athienitis et al. (1997) performed an experimental analysis on a test room with PCMs and found that peak room temperature was reduced by 4% and reduced the heating load at night. Darkwa and O'Callaghan (2006) performed an experimental study of drywalls with PCMs at different phase-change temperature ranges during cooling season. It was found that due to the corresponding heat capacity, a narrow phase-change range of PCMs was most effective to reduce room temperature (by 17%). Therefore, the energy requirement at peak hours can be reduced and precooling or heating becomes possible. Furthermore, the implementation of PCMs can reduce the indoor temperature fluctuations and improve the thermal comfort of occupants.

Phase-change material can be used for heating and cooling. Stritih and Novak (1996) used a paraffin wax to heat air for ventilation. Onishi et al. (2000) performed a CFD analysis of a house in winter conditions with a Trombe wall containing PCMs. This system stored daytime solar heat gain and released it at night. They found that the PCMs reduced heating costs. Gonzalez and Alva (2002) used a paraffin-wax-based solar collector to provide solar-assisted cooling in subtropical regions. They found that it reduced the cooling loads. Lin et al. (2003) used night time ventilation with PCM as a means of daytime cooling in an office building. Yamaha and Misaki (2006) found that PCMs can reduce peak temperatures when incorporated into the ventilation system. Zhou et al. (2007) used PCM for passive solar heating and found a 46% reduction in indoor temperature swing using PCM/gypsum material. Arkar and Medved (2007) created a heat storage device that can be integrated into ventilation systems to provide free cooling of a building.

Due to the potential of phase-change material, there have been many numerical studies and implementations in building simulation software. Stritih and Medved (1994) and Ahmad et al. (2006) used a finite element approach to model PCMs in TRNSYS (Klein 2004). Kim and Darkwa (2002), Kissock and Limas (2006), and Kuznik et al. (2010) developed a finite difference scheme to capture the heat transfer phenomena. Heim and Clark (2004) used the built-in special material facility in ESP-r to model a house with PCM/gypsum walls. Zhang et al. (2007) studied the behavior of solid-to-solid PCM using the finite element method (FEM). A simplified model of PCM was incorporated into TRNSYS by Ibanez et al. (2005).

ANALYSIS

In order to understand the heat transfer process in PCMs, mathematical models for PCMs are briefly reviewed here. The governing equations for the heat transfer in the solid-liquid PCMs are composed of the Navier-Stokes (momentum) equation, the mass conservation equation, and the energy conservation equation. From a mathematical point of view, the momentum and mass conservation equations can be neglected for the PCMs because the convective term is negligible in the PCMs (Zalba et al. 2003). This conclusion significantly simplifies the numerical analysis.

Consider the heat transfer process through PCM which can be described by the full Navier-Stokes equations. Due to the above assumption, the energy equation becomes the only governing equation for the analysis of PCMs, and it reduces to Fourier's law of conduction given as,

[partial derivative]([rho]H)/[partial derivative]t = [nabla](k[nabla]T) (1)

where [rho], H and k are the density, enthalpy, and thermal conductivity of PCMs, respectively. There are two types of numerical methods, namely, enthalpy method and effective heat capacity method. The effective heat capacity method will be utilized in the current work since this is the method used by ESP-r.

In the effective heat capacity method, the heat capacity is described as a function of temperature. The effective heat capacity of the material ([C.sub.eff]) is a linear function of the latent heat of fusion on both the heating and cooling processes. It is inversely proportional to the temperature difference between the onset and the end of the phase transition. The effective heat capacity of the PCM during the phase change is given as:

[C.sub.eff] = [L/[T.sub.e] - [T.sub.o]] + [C.sub.p] (2)

where L is the latent heat of fusion, [T.sub.o] is the onset temperature of phase transition happens, and [T.sub.e] is the temperature when the phase transition completely finishes.

The effective heat capacity method can be introduced into Equation 1 by defining enthalpy as a function of specific heat during the phase-change range as follows,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

By assuming the change in density to be negligible with time, the time derivative term in Equation 1 can be expanded as,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

Thus, the governing equation (Equation 1) for the PCM can be expressed as

[rho][C.sub.p] (T)([partial derivative]T/[partial derivative]t) = [nabla](k[nabla]T) (5)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

Where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the average specific heat of the liquid ([T.sub.o]) and solid ([T.sub.e]) states.

To aid in analyzing the behavior of the PCM, an investigation of Biot number and Fourier number is useful. Hensen and Nakhi (1994) studied the effect of varying Biot number and Fourier number in ESP-r on the accuracy of the diffusion equation for heat flow. The Biot number gives an indication to the effectiveness of treating a lumped mass with the same thermophysical properties during a transient heat transfer analysis. Biot number (Bi) and Fourier number (Fo) are defined as (Hensen and Nakhi 1994):

Bi = 0.5 hd/k (7)

[F.sub.o] = [alpha][DELTA]t/[DELTA][x.sup.2] (8)

where h is the convective heat transfer coefficient, d is the layer thickness, [alpha] is the thermal diffusivity, [DELTA]t is the time step, and [DELTA]x is the node spacing.

The main objective of this work is to determine the applicability of a multilayered approach to model PCM in ESP-r. This work is an extension of the multilayered PCM modeling work of Almeida et al. (2010). For a given thickness of PCM placed in the walls of a building, it may be necessary to discretize the PCM material into multiple layers in order to capture the transient effects of phase-change process. To study this, comparisons will be made by using different material thickness, number of layers, and time steps.

PROBLEM DEFINITION

Building Energy Simulation Test (BESTEST) and Model Definition

The Building Energy Simulation Test (BESTEST) is a set of tests and procedures to help validate building energy simulation software (Judkoff and Neymark 1995; Haddad et al. 2001; ASHRAE 2004). The test has been developed by the International Energy Agency (IEA), U.S. Department of Energy (DOE), the U.S. National Renewable Energy Laboratory (NREL), and ASHRAE. It consists of a combination of empirical validation and analytical calculations. BESTEST also includes a procedure for diagnostic analysis to determine any discrepancies in building simulation software.

The test includes a series of building cases that vary from simple buildings to complex buildings. The simple cases are meant to isolate specific heat transfer mechanisms while the complex cases help to diagnose errors in building inputs. The different tests are broken down into cases which start with a baseline simple building and incrementally increase the complexity. For example, case 600 is a low-mass building with a single zone and two south facing windows. Case 610 is the same as case 600 but includes an external shade, and case 620 includes east and west facing windows. For the current research, case 600 was used due to its simplicity in order to highlight the effect of phase-change material. Along with the building description, there is corresponding weather data for the 600 series, which is designed to go through a large temperature swing in a 24 hour cycle.

A simple, single-zoned house was modelled in ESP-r, as shown in Figure 1. The house has dimensions of 8 m by 6 m (26.2 ft by 19.7 ft) and a height of 2.7 m (8.9 ft). There are two south-facing windows which take up 12 [m.sup.2] (129.2 [ft.sup.2]) of the wall. The floor construction is made up of two layers consisting of foam and timber. All four of the vertical walls are made up of the same three layers, consisting of wood, fibre, and plaster. The BESTEST house has a ceiling made up of three layers, and for this work, a PCM layer was placed in the interior surface of the ceiling, giving four total layers. For the multilayered PCM model, the single layer PCM was replaced with eight layers of PCM with the total thickness remaining the same. The multilayered PCM allows the Biot number to be varied by changing the layer thickness. A summary of the house construction and materials is shown in Tables 1.

PCM Definition

The phase-change material used is technical-grade paraffin. The material properties are based on differential scanning calorimetry (DSC) curve experiments and numerical studies from Lamberg et al. (2004). There is flexibility in the choice of phase-change temperature range and latent heat of fusion. The recommended phase-change temperature range is from 25[degrees]C to 27[degrees]C (77[degrees]F to 80.6[degrees]F) and the latent heat of fusion is 23,0132 J/kg (98.9 Btu/lb). The physical properties are summarized in Table 2.

ESP-r

ESP-r is a building-energy simulation tool that allows for detailed thermal and optical description of buildings. The software discretizes the problem domain in a control volume scheme and solves the corresponding conservation equations for mass, momentum, energy, etc. The system of equations are solved using the Crank-Nicolson scheme. ESP-r can integrate the effect of a variety of factors including weather, external shading, occupancy gains, HVAC systems, and many others. More information about ESP-r can be found in Clarke (2001). For the current simplified simulation, no ventilation and no HVAC system was used. The simulation period is from July 1st to August 1st, using ASHRAE BESTEST weather data.

To ensure that all cases start the simulation with the same initial conditions, no presimulation start-up days were chosen. The simulation was run with a variety of time steps ranging from 1 minute to 1 hour in order to obtain varying Fourier numbers. ESP-r has a built-in capability to take into account the effect of phase-change material. This is done through ESP-r active material module where the label of phase change is assigned to a material layer. From there, ESP-r will incorporate the affect of phase change by determining the effective specific heat, thermal conductivity, and energy stored in the material. The simulation was performed for five different cases by considering the following: with and without PCM, 8 mm versus 60 mm (2.362 in. versus 0.315 in.) of PCM, and single layer-versus 8-layers of PCM. For each case, different time steps were also considered. The different cases are summarized in Table 3.

NUMERICAL RESULTS

Effect of PCM on Room and Surface Temperatures

First, the effect of phase-change material on room and surface temperatures is studied. The effect of PCMs (single layer) on the room temperature is shown in Figure 2 and it is compared with the no-PCM case. Here each peak represents a midafternoon, daytime peak temperature. Thus, each sinusoidal cycle can be thought of as a single day (a 24 hour period) What is displayed is a 18-day period (or 18 cycles) There is an approximately 3[degrees]C (37 4[degrees]F) difference in room temperature on most days for the first 9 days between the PCM and no-PCM case However, for the last nine days there is a less appreciable difference The PCM cases have a reduced room peak temperature At nighttime however, the PCM case has a higher room temperature than the no-PCM case This is caused by the PCM releasing its stored energy While this nighttime effect might be advantageous in the winter, it is problematic during the summer (which is the case during the current simulation) This issue could be fixed by including nighttime ventilation so that the PCM discharges more quickly and thus the house stays cooler. The current study does not consider the effect of nighttime ventilation due to the simple model of the house.

In order to understand what has happened, it is necessary to look at the surface temperature of the PCM in Figure 3. Here, the surface temperature is the interior room-side surface temperature of the ceiling, which is in contact with the room air. Again the PCM has a significant effect on surface temperature for the first seven days, then little difference for the rest of the simulation. It is between the 8th day and 9th day that the surface temperature of the PCM goes above 27[degrees]C (80.6[degrees]F) and is no longer discharging latent energy overnight. It is therefore behaving as a regular material with no latent heat storage. Thus, as long as the phase-change material can go through the charge-and-discharge cycle of its latent heat, then there will be a noticeable effect on room temperature. In the current model no HVAC system is in place, so the room temperature is allowed to increase. However in a realistic situation, the operation of an air-conditioning system would cap the peak daytime temperatures and thus allow the PCM to discharge its latent heat overnight.

For comparison, a thicker PCM layer (60 mm [2.362 in.]) is considered and its effect on room temperature is shown in Figure 4. Now with a larger potential of latent heat storage, there is an even greater affect of PCM on the room temperature. While in this case the weather conditions are the same, due to the larger latent heat storage, the peak temperature remains significantly lower throughout the 18 days. This is due to the fact that the PCM is never fully charged and is always within the phase-change range at some point throughout the day. So the PCM goes through a charge-and-discharge cycle within every 24 hour cycle.

Comparison of One- and Eight-Layer PCM Models

Figure 5 illustrates the effect of using 8-layers versus 1-layer for the 8 mm (0.315 in.) PCM case. As it can be seen, there is little to no difference. Only during the daytime peaks is a small difference seen between the 1-layer and 8-layer model of about 1[degrees]C (33.8[degrees]F). For the other times, the two sets of data are practically the same.

Figure 6 compares the room temperatures of the 8-layer and 1-layer models for the 60 mm (2.362 in.) case. For a given 24-hour cycle, the difference is largest during the daytime hours and smallest overnight. For simplicity, the 18-day simulation can be broken up into three sections. The first section is from days 1 to 7, second section is from days 8 to 12, and the third section is from days 13 to 18. In the first section there is a small difference between the two models of approximately 1.5[degrees]C (34.7[degrees]F) until day 7, and the temperature of the 8-layer model is higher than the 1-layer. The next 'section' is between days 8 and 12. Largest error is in this section with a temperature difference as high as 3[degrees]C (37.4[degrees]F) and the 1-layer model is at a higher temperature than the 8-layer. On the 11th day, the average day temperature for the 8-layer and 1-layer model is 29.18[degrees]C and 32.15[degrees]C (89.87[degrees]F and 84.52[degrees]F), respectively (giving a 3[degrees]C [37.4[degrees]F] difference in temperature). The third section is from days 13 to 18. Here, both the 1-layer and 8-layer models are almost the same.

In order to better understand this discrepancy between the two models, the ceiling surface temperatures of the 1- and 8-layer models for the 60 mm (2.362 in.) case are shown in Figure 7. In this figure it is easier to see the three sections of the simulation. During the first eight days, the temperature is within the phase-change range for both models. During this time, the 8-layer model fluctuates more than the 1-layer model. Thus the 8-layer model gives a higher and a lower room temperature than the 1-layer model. However, in the second section (starting on day 8), the single layer model has reached saturation and it is no longer absorbing heat, and thus the room temperature increases while the 8-layer model is still undergoing a charge-and-discharge cycle. In other words, the 8-layer model delays the onset of full saturation when compared with the single-layer model. Thus, this gives a few days when the 8-layer is absorbing heat while the 1-layer is fully charged. In the third section, both models are fully charged and they both behave in a similar way with the smallest deviation out of the entire simulation. As mentioned previously, the current simulation does not employ any temperature control scheme which would essentially force the PCM into a charge-and-discharge cycle and thus would reduce this deviation of the 1-layer and 8-layer models.

To further illustrate these three sectional behaviors of the PCM, Figure 8, which displays the percent deviation of the room temperature, is considered. The percent deviation is defined as the absolute difference between the room temperature of the 1- and 8-layer models divided by either the 1- or 8-layer room temperature. The solid line is the deviation relative to the 8-layer. And the dotted line is the deviation relative to the 1-layer. The largest percent deviation (up to about 20%) is during the second section between days 8 and 12 when the 8-layer is absorbing heat while the 1-layer is fully charged. In the third section both models are above the phase-change range and the percent deviation varies from 0%~3%. In the first section, both models are in the phase-change range and the deviation in room temperature is as high as 6%.

While a deviation of 8-layer and 1-layer is only seen for a few days (when a charge-and-discharge cycle is occurring), this deviation would be of greater importance in a more realistic house. A deviation is only seen when the PCM goes through a charge-and-discharge cycle. If an air-conditioning system was employed, then that would put an upper limit to the room temperature and the PCM would continue to go through this cycle.

Comparisons of Biot Number

The variation of Biot number with time is shown in Figure 9 for the 8 mm (0.315 in.) PCM. The Biot number was determined based on the thickness of the interior PCM layer of the ceiling. In general the Biot number follows a 24 hour cycle since it scales with the heat transfer coefficient. A Biot number less than 0.1 is considered adequate for transient analysis as a lumped mass and thus there are no spatial effects within the layer allowing the entire layer to be approximated with the same temperature (Incropera and DeWitt 1990). In Figure 9 (8 mm [0.315 in.] case) all the simulations have a Biot number less than 0.1 regardless of the number of layers or the size of the time step. The 8-layer models have lower Biot numbers than the 1-layer models. Also the simulations with an hour step have a relatively flat Biot number profile relative to the 1 min time step simulations. Since Biot number is proportional to convective heat transfer coefficient, one can see that in a 1 hour time step simulation, the convective heat transfer coefficient does not vary greatly with time.

Figure 10 contains the Biot number for the 60 mm (2.362 in.) case. Here not all of the simulation cases are below a Biot number of 0.1. Both of the 1-layer models (1-minute and 1-hour time steps) go above the Biot number condition and reach a Biot number of approximately 0.4. This indicates that a lumped capacitance method may not be suitable. In other words, there may not be enough nodes in the PCM layer to capture the transient behavior. The Biot number peaks correspond to the peak daytime temperatures. The 8-layer model with a 1-hour time step has a relatively flat Biot number at around 0.05. The lowest Biot number corresponds to the 8-layer model with 1-minute time steps.

Comparisons of Fourier Number

To better understand the differences between 8-layer and 1-layer, a comparison of Fourier number is beneficial. Due to the presence of phase-change material, the specific heat can change dramatically during the simulation. Thus, two Fourier numbers are defined for the purposes of this discussion. A sensible Fourier number, based on the specific heat of the PCM, and a latent Fourier number, based on the effective specific heat during the phase-change temperature range. Table 4 presents a summary of the different Fourier numbers for the various simulation cases. Since the sensible Fourier number is always larger than the latent Fourier number, the rest of the discussion will refer to the sensible Fourier number unless explicitly mentioned.

Figure 11 contains the room temperature plots at various Fourier numbers. Two of the five simulations match each other relatively closely. These are the 8-layer model with time steps of 1 minute and 2 minutes. The 1-layer model with a time step of 1 minute matches closely, except for the middle section of the data from days 8 to 12. Both of the 1-hour time step models do not match the other data closely. The 1-layer model with 1-hour time step does not follow the data for the first and second sections, then follows the other data in the third section. This would indicate that during the phase-change temperature range the one-layer models are unable to correctly predict the behavior, but when the material is fully charged (sensible heat only), it matches the other simulations. The 8-layer model with 1-hour time step matches the data during the first section but stays in the phase-change temperature range for the rest of the simulation. Based on the Table 4, the 8-layer model with time steps of 2 minutes and 1 hour are the least accurate (assuming that a Fourier number less than 0.5 is ideal [Hensen and Nakhi 1994]). However, referring to the Biot numbers shown in Figure 10, the 8-layer models are the most accurate, including even the 1-hour time step case. The model with 8-layers and a 1-hour time step has a sensible Fourier number of approximately 33, which is the largest Fourier number for the 60 mm (2.362 in.) of PCM case. This case has a Fourier number of an order of magnitude higher than unity, and thus is not appropriate for an accurate simulation. The other simulations, however, may have a problem with numerical errors. For Fourier numbers larger than 0.5 there may be oscillations that are incurred in the numerical procedure. These oscillation can be thought of as history errors that propagate through the solution (Hensen and Nakhi 1994). However, in the current study the Fourier number decreases when undergoing phase change, as shown in the latent Fourier number in Table 4. Thus, for most of the simulation the latent Fourier number applies.

For comparison, the surface temperatures at different Fourier numbers are shown in Figure 12, for the 8 mm (0.315 in.) family of simulations. Relative to the 60 mm (2.362 in.) case, these appear to behave more uniformly with each other, despite the larger variations of Fourier number. The Fourier numbers vary from 0.49 to 1875. Based on the Fourier numbers it would appear that the 1-layer model with a time step of 1 minute is the most accurate. The least accurate would be the 8-layer model with a 1-hour time step. The 8-layer model with 1-hour time step has a Fourier number of 1875, and the 1-layer model with 1-hour time step has a Fourier number of 29. By inspection of Figure 12, it would appear that the two 1-hour models are the least accurate since they deviate the most from the rest of the simulation cases. This is interesting because the two 1-hour models behave similarly despite having a much different Fourier number. It would appear that the Biot number is a better predictor of accuracy, while the Fourier number is less important except when the value is much greater than unity (order of magnitude of >100).

CONCLUSION

The use of a multilayered approach to model the effect of phase-change material in building energy simulation was investigated. It was found that the presence of PCMs can have a significant effect on the room temperature. Also a comparison of an 8-layered PCM with a more typical 1-layer PCM was made. For a thin 8 mm (0.315 in.) PCM layer there was little to no difference between the 1-layer and 8-layer models. For a thick 60 mm (2.362 in.) PCM layer there was a significant difference between the 1-layer and 8-layer models in both the room and surface temperatures. Looking into the temperature profiles in the PCM layers, it was shown that the thin PCM layer is small enough with respect to its effective thermal capacitance and thus it can be approximated as a single layer. However, the thicker PCM layer needs to be discretized into multiple smaller layers in order for the PCM to behave correctly. In general, the Biot number appears to be a better predictor of accuracy on the simulations than the Fourier number does. The Fourier number is less important except when the order of magnitude is much larger than unity. Also, the Fourier number is relatively easy to change by altering either the time step and/or changing the Crank-Nicolson weighting factor. The Biot number on the other hand is harder to change since it is based on layer thickness, and thus would need to be changed a priori. The results shown here represent a preliminary investigation into the effect of multilayered PCM modeling. A parametric study would be required (and is ongoing) in order to better quantify this effect. Also a validation, either through experiments or a rigorous model, would be beneficial in order to understand the underlying phenomenon.

ACKNOWLEDGMENT

The authors would like to acknowledge the tremendous help of Bart Lomanowski for his expertise in ESP-r and help in implementing PCM into our model. Financial support provided by Natural Sciences and Engineering Research Council (NSERC) of Canada and the Solar Buildings Research Network (SBRN) for this work is greatly appreciated.

REFERENCES

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Fabio Almeida

Wey H. Leong, PhD, PEng

Member ASHRAE

Alan S. Fung

Member ASHRAE

Fabio Almeida is a PhD candidate and Wey H. Leong and Alan S. Fung are associate professors in the Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada.

Table 1. Building Material Properties

Layer       Name       k, W/m K          Thickness,
                     (Btu/hr x ft         mm (in.)
                     x [degrees]F)

Wall        Wood     0.14 (0.081)        9 (0.354)
           Fibre     0.04 (0.023)        70 (2.756)
          Plaster    0.16 (0.093)        25 (0.984)
Ceiling     Wood     0.14 (0.081)        19 (0.748)
           Fibre     0.04 (0.023)       100 (3.937)
          Plaster    0.16 (0.093)        25 (0.984)
          Paraffin    0.18 (0.1)     8/60 (0.314/2.362)
Floor       Foam     0.04 (0.023)      1000 (39.370)
           Timber    0.14 (0.081)        25 (0.984)

Layer       Name        Density,       Heat Capacity,
                      kg/[m.sup.3]     J/kg K (Btu/lb
                     (lb/[ft.sup.3])   x [degrees]F)

Wall        Wood       530 (33.09)      900 (0.215)
           Fibre        12 (0.75)       840 (0.201)
          Plaster      950 (59.31)      840 (0.201)
Ceiling     Wood       530 (33.09)      900 (0.214)
           Fibre        12 (0.75)       840 (0.201)
          Plaster      950 (59.31)      840 (0.201)
          Paraffin     789 (49.26)      1800 (0.430)
Floor       Foam        10 (0.62)       1400 (0.335)
           Timber      650 (40.58)      1200 (0.287)

Table 2. Properties of Paraffin PCM

Property                                Value

Density, kg x [m.sup.-3]             768 (47.9)
  (lb/[ft.sup.3])
Thermal conductivity, W x            0.18 (0.1)
  [m.sup.-1] x [K.sup.-1]
  (Btu/hr x ft x [degrees]F)
Specific heat, J x                   1.8 (0.430)
  [g.sup.-1] x [K.sup.-1]
  (Btu/lb x [degrees]F)
Phase-change temperature           25~27 (77~80.6)
  range, [degrees]C([degrees]F)
Latent heat of fusion, J x         230,132 (98.9)
  [kg.sup.-1] (Btu/lb)

Table 3. Summary of Numerical Test Cases

Case          Total PCM         Number           Time Steps
Number   Thickness, mm (in.)   of Layers

1              No PCM             --           1 min, 1 hour
2             8 (0.315)            1           1 min, 1 hour
3             8 (0.315)            8       1 min, 7.5 min, 1 hour
4            60 (2 362)            1           1 min, 1 hour
5            60 (2.362)            8        1 min, 2 min, 1 hour

Table 4. Fourier Number of Simulation Cases

Number      Layer Thickness,   Time Step,      Fo        Fo
of Layers       mm (in.)          min       Sensible   Latent

1              8 (0.315)           1          0.49     0.0075
1              8 (0.315)           60        29.30     0.4512
1              60 (2.362)          1          0.01     0.0001
1              60 (2.362)          60         0.52     0.0080
8              8 (0.315)           1         31.25     0.4813
8              8 (0.315)          7.5        234.38    3.6099
8              8 (0.315)           60       1875.00    28.8792
8              60 (2.362)          1          0.56     0.0086
8              60 (2.362)          2          1.11     0.0171
8              60 (2.362)          60        33.33     0.5134
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Author:Almeida, Fabio; Leong, Wey H.; Fung, Alan S.
Publication:ASHRAE Transactions
Article Type:Report
Geographic Code:1CANA
Date:Jan 1, 2014
Words:5731
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