# An experimentally validated model to predict the thermal conductivity of closed-cell pipe insulation systems with moisture ingress.

INTRODUCTIONMechanical pipe insulation systems are commonly used around cold pipes in HVAC field to reduce heat transfer between the pipelines and the surrounding ambient. When pipe insulation systems are applied to cold surfaces in which the surface temperature is below ambient room temperature, such as in water chiller applications, water vapor in the ambient is drawn inside the insulation and it might condensate if the pipe temperature is below the ambient dew point temperature. The insulation system apparent thermal conductivity is affected by the moisture that accumulates in the insulation system but limited modeling efforts are available in the open domain literature that properly account for the effect of moisture on the pipe insulation system apparent thermal conductivity. For porous type of insulation, Luikov (1966) proposed that the apparent thermal conductivity ([k.sub.app]) is equal to the summation of the conductive ([k.sub.cond]), convection ([k.sub.conv]) and radiative ([k.sub.rad]) components of thermal conductivity, according to:

[k.sub.app] = [k.sub.cond] + [k.sub.conv] + [k.sub.rad] (1)

Bankvall, referred by Batty et al. (1981), firstly proposed series arrangement and parallel arrangement to model fibrous insulation under dry condition and Batty et al. (1981) cataloged the moisture distribution models as series, parallel, bead and foam arrangements with moisture content. Wijeysundera et al. (1996) observed that the apparent thermal conductivity of moist insulation depends on the manner that the liquid distribute in the insulation, and they considered bead, series and parallel arrangements when modeling the moisture status in porous insulation. However, both studies above did not fully consider a combination of different moisture distribution configurations. Ochs et al. (2008) developed a model to predict effective thermal conductivity of moistened porous insulation based on flat slab. The conductive component of the apparent thermal conductivity was considered as a combination of series and parallel arrangement of the cells, and the radiation effect was included with pore specifications, while the convection effect was ignored due to the low Rayleigh number. Wijeysundera et al. (1993) proposed analytical solution for the effective thermal conductivity of flat-slab and round-pipe insulations in the presence of condensation. The solution requires the value at the wet-dry interface, which was determined from the local temperature profile. Choudhary et al. (2004) computed the effective thermal conductivity as a combination of solid, gas and liquid phases by considering phase saturation coefficient. However, predicting the thermal conductivity variation at different moisture contents is not a trivial task when considering their approach. To this end, it is obvious that while some work exists in the literature, a general comprehensive model that predicts the thermal conductivity of pipe insulation system in dry and wet conditions with moisture ingress is not available. One reason can be due to the lacking of experimental data suitable for model validation. Based on authors' previous work (Cremaschi et al., 2012b) and current experimental efforts in this work, such experimental data were made available and this paper builds upon such data to develop a first principle model of thermal conductivity of pipe insulation systems.

MODEL FOR CLOSED-CELL PIPE INSULATION SYSTEMS

A 2-D analytical model for closed-cell pipe insulation was originally developed from Ochs et al.'s (2008) and a similar approach was used in the present work. The overall thermal resistance was considered as a combination of the thermal resistances from insulation material, air gaps and joint sealant, as shown in Figure 1. The actual configuration of the pipe insulation system as installed on a cold pipe is illustrated in Figure 1a. The assumptions for the present model are as follows: 1) the convection term is neglected due to the low Rayleigh number (<<1708); 2) the insulation materials are essentially composed of solid and gas layers, plus liquid layer if in wet condition, and only two arrangements of the cells are taken into consideration: series and parallel, as shown in Figure 1c to e. Each arrangement in Figure 1c, for dry conditions, Figure 1d and e, represents a limiting case for the resistance to the heat flow through the materials. Under wet conditions, the solid layer remained the same as in dry condition, but the gas layer is affected by water vapor and condensate and it has to be divided further to include water layer, moist pores layer and the residual gas layer, as shown in Figure 1d and e. Additional underlying assumptions of the present model are 3) the insulation materials are homogeneous; 4) the fraction of series and parallel configuration remain constant for the same type of pipe insulation under both dry and wet conditions; and 5) the air gap exists only at the interface between the bottom pipe wall surface and the bottom interior surface of the insulation system and the thickness of the air gap was assumed uniform within the 180[degrees] angle of the bottom shell, as shown in Figure 1b. According to the above mentioned assumptions, the thermal resistance and thermal conductivity for the insulation material become as follows:

1/[R'.sub.ins] = a/[R'.sub.series] + (1 - a)/[R'.sub.parallel] (2) [k.sub.ins] = [ak.sub.series] + (1 - a) [k.sub.parallel] (3)

where the parameter a represents the volume fraction of the poor conductive layer with different phases positioned in series, and the fraction of resistances in parallel is (1-a). [k.sub.series] represents the lowest thermal conductivity component of the insulation, while [k.sub.parallel] represents the maximum It should be noted that the formulations of [k.sub.series] and kparallel are different when the insulation system is considered dry (i.e., no water vapor and condensate) or wet (that is, water vapor and water condensate present). The sealant on the longitudinal joints behaves as a resistance in parallel to the insulation material and can create a thermal bridge effects based on its thermal conductivity and sealant thickness. These variables on joint sealant and air gaps are considered in the present model for the first time.

In dry conditions, the combined thermal resistance and the overall thermal conductivity of the pipe insulation system are expressed by the thermal resistance of the join sealant, [R'.sub.joint,sealant], the thermal resistance of the top shell of insulation, [R'.sub.ins,t], the thermal resistance of the bottom shell of insulation, [R'.sub.ins,b], and the thermal resistance from the air gap, [R'.sub.airgap]:

[R'.sub.combined] = [1/[1/[R'.sub.joint sealant] + [1/[R'.sub.ins,t]] + [1/[R'.sub.ins,b]] + [1/[R'.sub.ins,b] + [R'.sub.airgap]]] = [ln([D.sub.exterior,ins]/[D.sub.exterior,Al.pipe])/2[pi][k.sub.tot]L] (4)

And there are:

[R'.sub.joint sealant] = [[D.sub.exterior,ins] - [D.sub.exterior,Al.pipe]/4[k.sub.joint sealant][[delta].sub.joint sealant]L] (5)

[R'.sub.airgap] = [ln ([D.sub.exterior,Al.pipe] + [[delta].sub.airgrap]/[D.sub.exterior,Al.pie])/[pi][k.sub.airgap]L] (6)

[R'.sub.ins,t] = [ln ([D.sub.exterior,ins]/[D.sub.exterior,Al.pipe])/[pi][k.sub.ins,t]L] (7)

[R'.sub.ins,b] = [ln ([D.sub.exterior,ins][/.sub.Dexterior,Al.pipe])/[pi][k.sub.ins,b]L] (8)

Where [D.sub.exterior,ins] is the exterior diameter of the pipe insulation; [D.sub.exterior,Al.pipe] is the exterior diameter of test pipe; L is the length of test section; [k.sub.airgap] is the thermal conductivity of the air gap: at dry condition, [k.sub.airgap] = [k.sub.air], and at wet condition, [k.sub.airgap] = [k.sub.water]; [k.sub.joint sealant] is the thermal conductivity of the joint sealant; [[delta].sub.joint sealant] is the thickness of the joint sealant; [[delta].sub.airgap] is the thickness of the air gap, and an equivalent air gap dimension was calculated as annular shape around the bottom half of the tested aluminum pipe surface. The volume of the air gap, Volairgap, can be expressed as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

Sub-Model of Thermal Conductivity for Dry Pipe Insulation Systems

The minimum thermal conductivity factor kmm can be calculated from the thermal resistance, [R'.sub.series], which is determined with either gas phase or solid phase in the interior, as shown in Figure 1c. Since series configuration represents the case of the highest thermal resistance, R series can be determined by comparing these two scenarios:

[R'.sub.series,dry] = [R'.sub.s,series,dry] + [R'.sub.g,series,dry] = max ([R'.sub.series,dry,1], [R'.sub.series,dry,2]) (11)

Where [R'.sub.s,series] and [R'.sub.g,series] are the thermal resistances of solid and gas phases in series configuration. [R'.sub.series,dry,1] represents the thermal resistance when solid phase is in the exterior, and [R'.sub.series,dry,2] represents the one with solid phase in the interior. In terms of thermal conductivity it becomes Equation (12) if the maximum resistance is [R'.sub.series,dry,1], or the thermal conductivity is calculated as Equation (13) if the maximum resistance is [R'.sub.series,dry,2].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

Where [k.sub.s] is the thermal conductivity of the solid particles; [k.sub.p] is the thermal conductivity of the pores in closed-cell insulation. The diameters [D.sub.x1] and [D.sub.x2] are calculated as follows:

[D.sub.x1] = [square root of n([D.sub.exterior,ins] - [D.sup.2.sub.Exterior,Al.pipe]) + [D.sup.2.sub.exterior,Al,pipe]] (interior: gas exterior: solid)

[D.sub.x2] = [square root of [D.sup.2.sub.exterior,Al,pipe] - n([D.sup.2.sub.Exterior,ins] - [D.sup.2.sub.Exterior,Al,pipe])] (interior: Solid, exterior: gas)

In order to consider the radiation effects in the cells, the relations originally proposed by Ochs et al. (2008) are applied for this system and the results are as follows:

[k.sub.p] = [k.sub.pg] + [k.sub.rad] (14)

[k.sub.rad] = [4[sigma][d.sub.m]/[2/[epsilon]] - 1] [T.sup.3.sub.k] = [c.sub.rad] [T.sup.3.sub.k] (15)

Where [k.sub.pg] is the gas thermal conductivity; [k.sub.rad] is the effect of radiation; [d.sub.m] is the pore diameter; [epsilon] is the particle surface emissivity and as is the blackbody radiation constant. As suggested by Ochs et al. (2008), [k.sub.md] can be expressed as a function of the radiation constant, [c.sub.rad], and of the absolute temperature, [T.sub.k]. In the present model the radiation constant [c.sub.rad] was determined from Nelder-Mead optimization based on experimental data.

The parallel thermal resistance, [R'.sub.parallel], represents the lowest thermal conductivity when the resistances of solid and gas are in parallel arrangement. Based on the assumption that the porosity is homogenous throughout the entire insulation materials, the parallel thermal resistance and thermal conductivity are calculated as follows:

[R'.sub.parallel] = [R'.sub.s,parallel]/(1 - n) + [R'.sub.g,parallel]/n(16)

[k.sub.parallel] = a[k.sub.s] + (1 - a) [k.sub.p] (17)

Where n is the porosity of the insulation materials, [R'.sub.s,parallel] and [R'.sub.g,parallel] are the thermal resistances of solid and gas phases in parallel arrangement.

It should be noted that the combined thermal conductivity of the insulation material collapses to the solid or to the gas thermal conductivity in the limiting case of no porosity (n [right arrow] 0) or gas filling completely the annular space (n [right arrow] 1) that is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Sub-Model of Thermal Conductivity of Wet Pipe Insulation Systems with Moisture Ingress

For wet insulation in addition to solid and gas phases, layers of liquid phase and moistened pores (i.e. pores with water vapor) are added in the model as described next. Logically the water layer and water vapor in the pores layer takes place in the air-only filled regions and they are modeled as shown in Figure 1d and 1e. Depending on the solid material thermal conductivity and gas trapped in the insulation material, the thermal resistance of these two configurations was computed and the configuration that had highest thermal resistance was selected. For the water vapor diffusion in the moistened pores, the effective thermal conductivity ([k.sub.pd]) is determined from the thermal conductivity due to water vapor diffusion ([k.sub.diff]), which takes into consideration the heat transfer due to the evaporation occurring at the warm side of the pore, and condensation at the cold side. The expressions are as follows:

[k.sub.pd] = [k.sub.p] + [k.sub.diff] (20)

[k.sub.diff] [[D.sub.v]/[R.sup.2.sub.v] [T.sup.2.sub.k] x [[P.sub.amb]/[P.sub.amb] - [P.sub.sat]] [DELTA][h.sup.2.sub.v] (21)

Where [D.sub.v] = 2 3.4 x [10.sup.-6] [([T.sub.k]/273).sup.2.3], is the water vapor diffusion coefficient; [P.sub.sat] = 610.8 x exp (17.08085 x T/234.175 + T), saturation vapor pressure; [P.sub.amb] is the ambient pressure; [h.sub.v] is the latent heat of evaporation; [R.sub.v] is the gas constant. More details for computing diffusion thermal conductivity factor are reported in the work by Ochs et al. (2008). By assuming that the portion of the pores involved in the vapor diffusion ([V.sub.pd]) is proportional to the pores with gas in them, the fraction of moistened pores in the cells (b) is calculated as follows:

[V.sub.pd] = b (n - [V.sub.w]) (22)

b = 1 - [(1 - [V.sub.w]/[V.sub.fs]).sup.9] (23)

Where [V.sub.w] is the volume fraction of water per volume of the test sample, percentage; [V.sub.pd] is the volume fraction of the cells involved with the vapor diffusion per volume of the test sample, percentage; and [V.sub.fs] is the volume fraction of water condensate in free saturation conditions per volume of the test sample, in percentage. The parallel thermal resistance ([R'.sub.parallel,wet]) was calculated as follow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

And, in terms of overall apparent thermal conductivity of the wet pipe insulation systems ([k.sub.parallel,wet]) results:

[k.sub.parallel,wet] = [V.sub.w][k.sub.w] + [V.sub.w][k.sub.pd] + (n + [V.sub.w] + [V.sub.pd]) [k.sub.p] + (1 - n) [k.sub.s] (25)

Based on the experimental observation that moisture content of the bottom shells was typically higher than the moisture content measured on the top C-shell, the equations (11) to (25) were solved independently for the half shells at the top and bottom, yielding to two values of the apparent thermal resistance [R'.sub.series,wet,t] and R. series, wet, b, respectively.

MODEL VALIDATION FOR DRY CONDITIONS AT BELOW AMBIENT TEMPERATURES

The parameters a and [c.sub.rad] of the present model were derived by regression of data from material samples tested in radial configuration at dry non-condensing conditions. Then, the paramter [c.sub.rad] was adjusted based on the porosity of the insulation samples of the experimental data. The porosity was estimated from the density. The parameter, a, was assumed to be dependent only on the type of insulation material and thus it was assumed constant for the same insulation material with various wall thicknesses and various densities. The experimental data of thermal conductivity of closed-cell type insulation, that is, cellular glass, phenolic and elastomeric pipe insulation systems (Cremaschi et al., 2012a; 2012b), were used as benchmark for the simulation results during a preliminary sensitivity study of the thermal conductivity for the parameters a and [c.sub.rad]. The results of the comparison are shown in Figure 2. The specifications of the samples in the baseline and in the actual experiments are listed in Table 1. As an example, let's consider the cellular glass pipe insulation. First the experimental data of 25.4 mm (1 in) cellular glass pipe insulation was used as a baseline case to derive the two parameters, a and cmd, based on the Nelder-Mead regression optimization approach (Nelder & Mead, 1965). Then for the same type of material with different insulation wall thickness, the parameters a and [c.sub.rad] were kept constant. The thermal conductivity for cellular glass sample A (CGA) and cellular glass sample B (CGB) were predicted with a 17% and 5% deviation with respect to the experimental data. It should be noted that CGA showed a higher thermal conductivity and a slightly flatten trend of the thermal conductivity with temperature with respect to CGB. However, the difference was due to the test methodology used to measure the thermal conductivity of these two samples. If the data reduction procedure used to analyze the experimental data is the same for both cases, the effective thermal conductivity of CGA decreases from group 3 to 4, and the data of CGA and CGB become within the experimental uncertainty. For the purpose of model validation both groups can still be considered, as shown in Figure 2a. The joint sealant effect was also taken into account in the simulation. The thickness of joint sealant was an input to the model. By varying the thickness of joint sealant from 1.6 mm (1/16 in) to 2.1 mm (1/12 in) on the CGA sample, the effective thermal conductivity increased and the difference on the thermal conductivity computed from model to the experimental results reduced from 17% to 10% (dash-dot line 1 to 2, Figure 2a). Phenolic pipe insulation was tested with two nominal wall thicknesses. The 25.4 mm (1 in) sample was considered as the baseline and the simulation results for 50.8 mm (2 in) phenolic (PA) was about 10% higher than the experimental results. By decreasing the thickness of joint sealant from 2.1 mm (1/12 in) to 1.6 mm (1/16 in), the difference decreased to 6% (see Figure 2b dot line 5 to 6). The simulation was also applied on elastomeric rubber pipe insulation system. The baseline case was taken from the data of the sample in 50.8 mm (2 in). The other two test samples, ERA and ERB, had about 20% density difference, most likely because the sample were from a different batch. Thus an adjustment of the [c.sub.rad] parameter was made as previously discussed in this section. Using the same parameter a and the adjusted [c.sub.rad], the simulation results matched well with the experimental values on ERA and ERB and the deviation was 12% and 7%, as shown in Figure 2c.

The simulation results were also compared with published values of thermal conductivity of pipe insulation systems in the literature, as shown in Table 1. Due to the fact that for cellular glass and phenolic pipe insulation there was no information provided on the joint sealant applied between the two pipe insulation half shells, the model was applied without joint sealant, and then compared to the cases with the same joint sealant as used in the baseline samples. Without joint sealant, the simulation results matched the reported values with average differences of 25% for cellular glass, and 25% for phenolic pipe insulation. By considering the joint sealant effects, the differences decreased to 21% on cellular glass with a 1.6 mm (1/16 in) thickness of joint sealant, but the difference increased to 32% on phenolic with a 2.2 mm (1/12 in) thickness, shown in Figure 3a and 3b. For cellular glass, the literature values might be obtained based on the test specimens with joint sealant applied between the two half shells, and the specification of the joint sealant were not clearly identified. Thus, the thermal conductivity and thickness of the joint sealant selected in the model can be different from the one used in the experimental measurement. The simulation model over-predicted phenolic pipe insulation when compared to the literature values because less conductive or a thinner layer of joint sealant might have been present during experimental measurements. Aging effect on phenolic is also another source of uncertainty that might cause the simulation results to deviate from the experimental data in the literature. Elastomeric rubber was not affected by the joint sealant, since it is usually installed as one piece around the pipe, or pre-slimed with a very thin layer of adhesive factory applied. The differences between the simulation results and the values in the literature were within 4%, as shown in Figure 3c.

MODEL VALIDATION UNDER WET CONDITIONS WITH MOISTURE INGRESS

In the present work, phenolic and PIR pipe insulation systems were considered for wet conditions with moisture ingress. The variation on the thermal conductivity with moisture ingress were predicted with the present model and validated with the experimental data from the present work. The experimental data were gathered according to the methodology described in details by Cremaschi et al. (2012a; 2012b). The parameters a and [c.sub.rad] were computed from the baseline test results of dry insulation conditions, and [c.sub.rad] was adjusted based on the material porosity. The parameter [V.sub.fs] must be considered as input for the model. The free saturation condition was assumed to be reached when all the pores were filled with water condensate. With this assumption, the parameter [V.sub.fs] was basically equal to the porosity of the material. The comparison of the predicted thermal conductivity of pipe insulation systems in wet condensing conditions with moisture ingress versus the experimental data are shown in Figure 4a and 4b. The thermal conductivity of phenolic pipe insulation system was measured two times and the test specimens had same nominal wall thickness and similar density, as listed in Table 2. The parameters for the model were obtained from the baseline case selected in Table 1 (Phenolic (Baseline) in dry conditions. Once the insulation material depended parameters of the model were set, the model was run for wet operation conditions. For both sets of data in Table 2, the simulation results under-predicted the thermal conductivity of the phenolic pipe insulation by about 12%. For PIR pipe insulation system with no vapor retarder, the model parameters were obtained from the tests on two different PIR pipe insulation samples (PIR, b1 and PIR, b2), as listed in Table 2, that had similar density but different nominal wall thicknesses and manufacturing time. The physical properties of the sample tested under wet conditions were the same as the sample selected in baseline 1 (PIR, b1). The simulation results are plotted in Figure 4b. Compared to baseline 2, the results computed from baseline 1 was in better agreement with the experimental results. The simulation results deviated from the experimental data by 16% if the moisture content reached 16% by volume. The simulation results obtained by using the parameters from baseline 2 under-estimated the thermal conductivity at the beginning of the wet test and over-predicted the thermal conductivity with high moisture content. These deviations illustrate one limitation of the present model which is the model does not include the "aging" phenomenon, as happened on PIR. The aging effects might lead to different values for a and crad, which lead to different weight for the series and parallel configurations of the thermal resistances.

CONCLUSIONS

A 2-D model for predicting the pipe insulation thermal conductivity was developed for closed-cell pipe insulation systems. The model was based on the insulation material properties, which had to be estimated from a limited set of laboratory experiments. Then, the present model predicted the thermal conductivity of the pipe insulation system at below ambient temperature in dry non-condensing conditions and in wet conditions with moisture ingress. The model included joint sealant effects and the impact of the air gap between the insulation and the pipe wall on the bottom section of the pipe insulation system. The model was validated with the experimental results from the present work and available data from the literature. For three types of closed-cell pipe insulation, the simulation results matched well with the trends of the experimental data and the deviation was about 17%. In wet conditions, the deviation from the simulation results and the experimental data was also found to be satisfactory.

NOMENCLATURE

a = fraction of series configuration

b = fraction of moistened pores

c = radiation constant

d or D = diameter, m (in)

[D.sub.v] = water vapor diffusion coefficient, [m.sup.2]/s

h = latent heat of evaporation, kJ/kg

k = thermal conductivity, W/m-K (Btu-in/hr-[ft.sup.2]-F)

L = length, m (in)

n = porosity

P = pressure, Pa

R' = thermal resistance, C/W (hr-ft/Btu)

[R.sub.v] = gas constant, J/kg-K

T = temperature, [degrees]C (K)

[T.sub.k] = absolute temperature, K (R)

V = volume fraction

Vol = volume, [m.sup.3] ([in.sup.3])

[delta] = thickness, m (in)

[epsilon] = emissivity

[sigma] = blackbody radiation constant

Subscripts

amb = ambient

Al = aluminum

b = bottom

diff = diffusion

exp = experiment

fs = free saturation

g = gas

ins = insulation

p = pore

pd = diffusion in the pores

pg = gas in the pores

rad = radiation

s = solid

sat = saturation

t = top

tot = total

w = water

REFERENCES

Batty, W. J., O'Callaghan, P. W., & Probert, S. D. (1981). Apparent thermal conductivity of glass-fiber insulant: effects of compression and moisture content. Applied energy, 9(1), 55-76. doi: 10.1016/0306-2619(81)90042-8.

Choudhary, M. K., Karki, K. C., & Patankar, S. V. (2004). Mathematical modeling of heat transfer, condensation, and capillary flow in porous insulation on a cold pipe. International Journal of Heat and Mass Transfer, 47(26), 5629-5638.

Cremaschi, L., Cai, S., Ghajar, A., & Worthington, K. (2012a). ASHRAE RP 1356 final report: Methodology to measure thermal performance of pipe insulation at below ambient temperatures: ASHRAE, available by request to ASHRAE.

Cremaschi, L., Cai, S., Worthington, K., & Ghajar, A. (2012b). Measurement of pipe insulation thermal conductivity at below ambient temperatures Part I: Experimental methodology and dry tests (ASHRAE RP-1356). Paper presented at the ASHRAE winter conference--Technical papers, January 21, 2012 - January 25, 2012, Chicago, IL, USA.

Luikov, A. V. (1966). Heat and mass transfer in apillary-porous bodies. Oxford, New York: Pergamon Press.

Nelder, J. A., & Mead, R. (1965). A Simplex Method for Function Minimization. The Compiter Journal, 7(4), 308-313.

Ochs, F., Heidemann, W., & Muller-Steinhagen, H. (2008). Effective thermal conductivity of moistened insulation materials as a function of temperature. International Journal of Heat and Mass Transfer, 51(3-4), 539-552.

Tseng, C.-J., & Kuo, K.-T. (2002). Thermal properties of phenolic foam insulation. Journal of the Chinese Institute of Engineers,

Transactions of the Chinese Institute of Engineers, Series A/Chung-kuo Kung Cheng Hsuch Kan, 25(6), 753-758. Whitaker, T. E., & Yarbrough, D. W. (2002). Review of thermal properties of a variety of commercial and industrial pipe insulation materials, Charleston, SC, United states.

Wijeysundera, N. E., Zheng, B. F., Iqbal, M., & Hauptmann, E. G. (1993). Effective thermal conductivity of flat-slab and roundpipe insulations in the presence of condensation. Journal of Thermal Insulation and Building Envelopes, 17, 55-76.

Wijeysundera, N. E., Zheng, B. F., Iqbal, M., & Hauptmann, E. G. (1996). Numerical simulation of the transient moisture transfer through porous insulation. International Journal of Heat and Mass Transfer, 39(5), 995-1004.

Wilkes, K. E., Desjarlais, A. O., Stovall, T. K., McElroy, D. L., Childs, K W., & Miller, W. A. (2002). A pipe insulation test apparatus for use below room temperature, Charleston, SC, USA.

Shanshan Cai

Student Member ASHRAE

Lorenzo Cremaschi, PhD

Member ASHRAE

Shanshan Cai is a PhD student, and Lorenzo Cremaschi is an associate professor in the School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK.

Table 1. Parameters of the Samples in the Tests and Literature Basic Case/Literature Thickness Density Joint Parameters Sealant mm kg/[m.sup.3] Thickness (in) (lb/[ft.sup.3)] mm (in) Cellular Glass 25.4 (1) 120 (7.5) 1.6 (1/16) (baseline) CG Sample A (CGA) 38.1 (1.5) 120 (7.5) 1.6 (1/16) CG Sample B (CGB) 50.8 (2) 120 (7.5) 1.6 (1/16) Cellular Glass (1) 50.8 (2) 136.2 (8.5) -- Phenolic (baseline) 25.4 (1) 37 (2.3) 2.2 (1/12) P Sample A (PA) 50.8 (2) 37 (2.3) 2.2 (1/12) Phenolic (2) 22 (0.9) 46-67 (2.9-4.2) -- Elastomeric 41.9 (1.5) 50 (3.1) -- Rubber (baseline) ER Sample A (ERA) (1.5) 40 (2.5) -- ER Sample B (eRB) (2) 40 (2.5) -- Elastomeric Rubber (3) 25.4 (1) 66 (4.1) -- Basic Case/Literature Joint Sealant Porosity Parameters Thermal Conductivity W/m-K (Btu-in/hr- [ft.sup.2]-F) Cellular Glass 0.4 (2.77) 0.95 (baseline) CG Sample A (CGA) 0.4 (2.77) 0.95 CG Sample B (CGB) 0.4 (2.77) 0.95 Cellular Glass (1) -- 0.94 Phenolic (baseline) 0.4 (2.77) 0.95 P Sample A (PA) 0.4 (2.77) Phenolic (2) -- 0.94 Elastomeric -- 0.91 Rubber (baseline) ER Sample A (ERA) -- 0.93 ER Sample B (eRB) -- 0.93 Elastomeric Rubber (3) -- 0.88 Basic Case/Literature a [c.sub.rad] Parameters [X10-.sup.10] Cellular Glass 0.8854 7.0648 (baseline) CG Sample A (CGA) 0.8854 7.0648 CG Sample B (CGB) 0.8854 7.0648 Cellular Glass (1) 0.8854 7.0481 Phenolic (baseline) 0.6887 4.1155 P Sample A (PA) Phenolic (2) 0.6887 4.0979 Elastomeric 0.7874 2.4253 Rubber (baseline) ER Sample A (ERA) 0.7874 2.4412 ER Sample B (eRB) 0.7874 2.4412 Elastomeric Rubber (3) 0.7874 2.3994 (1): Specifications from literature, by Whitakar and Yarbrough (2002); (2): Specifications from literature, by Tseng and Kuo(2002); (3): Specifications from literature, by Wilkes (2002) Table 2. Test Samples Specifications in Moisture Tests Basic Case/Literature Thickness Density Joint Parameters Sealant Thickness mm (in) kg/[m.sup.3] mm (in) (lb/[ft.sup.3]) Phenolic Sample 1 (P1) 50.8 (2) 37 (2.3) 2.1 (1/12) Phenolic Sample 2 (P2) 50.8 (2) 36.3 (2.3) 2.1 (1/12) Polyisocyanurate (PIR,b1) 38.1 (1.5) 32 (2) 2.1 (1/12) Polyisocyanurate (PIR,b2) 25.4 (1) Basic Case/Literature Joint Sealant Porosity Parameters Thermal Conductivity W/m-K (Btu-in/hr- [ft.sup.2]-F) Phenolic Sample 1 (P1) 0.4 (2.77) 0.95 Phenolic Sample 2 (P2) 0.4 (2.77) 0.95 Polyisocyanurate (PIR,b1) 0.4 (2.77) 0.95 Polyisocyanurate (PIR,b2) Basic Case/Literature a [c.sub.rad] Parameters x [10.sup.-10] Phenolic Sample 1 (P1) 0.8854 7.0648 Phenolic Sample 2 (P2) 0.8854 7.0648 Polyisocyanurate (PIR,b1) 0.7770 0.00002 Polyisocyanurate (PIR,b2) 0.6948 0.7692

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Author: | Cai, Shanshan; Cremaschi, Lorenzo |
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Publication: | ASHRAE Transactions |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Jan 1, 2014 |

Words: | 5130 |

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