Determination of thermal conductivity of high porosity organic ... - NOPR

Indian Journal of Engineering & Materials Sciences Vol. 11, April 2004, pp. 125-129

Determination of thermal conductivity of high porosity organic foams at varying temperatures and pressures using thermal probe method Jagjiwanram & Ramvir Singh* Thermal Physics Laboratory, Department of Physics, University of Rajasthan, Jaipur 302 004, India Received 27 August 2003; accepted 1 March 2004 The thermal conductivity of organic foams at varying temperatures (-20 to 30°C) and interstitial air pressures has been measured using thermal probe method. Experiment has been conducted on different cell sizes of organic foam samples covering a vide range of porosities. Results show that the effective thermal conductivity decreases with increasing porosity and increases by increasing temperature and interstitial air pressure values. Data obtained from the experiment has been compared with the reported model and found good agreement between experimental and theoretical results at room temperature and normal pressure. IPC Code: Int. Cl.7 G01N 25/18

Measurement of thermal conductivity of high insulating materials is indeed one of the major concerns in the development of heat transfer technology. The main functions of thermal insulation are conservation of energy, control of temperature and control of overall heat transfer. The low thermal conductivity can be achieved in evacuated systems because the gaseous conductive and convective heat transfer modes are not present in vacuum conditions. Therefore, the prominent heat transfer modes in organic foams are thermal radiation and solid-solid conduction at low-pressure conditions. Typically, to achieve insulating performance with a porous medium, it is necessary that the internal pressure is of the order of 0.1 Torr be maintained for the duration of the intended application. The probe method is a transient method for the determination of the thermal conductivity of non-metal materials such as building materials, e.g., bricks, concrete and even some insulating materials. This method derives from the large term behaviour of a lineheating source buried in an infinite body of the material under test1. Considering the simplicity of the method and the extremely low cost of instrumentation compared with that for the steady-state methods, probe method offers an attractive means for the determination of thermal conductivity. On the other hand, the accuracy, of the method is good enough to —————— *For correspondence (E-mail: [email protected])

give results comparable to those obtainable from standard equipments1-4. The objective of the present work is to report data on thermal conductivity of organic foams at various environmental conditions using transient probe method. Experimental measurements were carried out on different cell sizes of organic foam samples having various densities after removal of moisture. Organic foams that have been selected for this study are manufactured and used in India by Sweet Dream, Tirupati and Foam Limited Ahmedabad (Gujarat). Theoretical The method is based on the principle that when a line source of heat, is buried in an infinite sample, the temperature rise with time at a point near to the line source depends upon the rate of energy input and various thermal properties of the surrounding. Using this method the effective thermal conductivity (ETC) of the system is calculated by the relation1

λe

Q ln(t2 /t1 ) . 4π (θ 2 − θ1 )

… (1)

where θ1 and θ2 are the temperatures at times t1 and t2 respectively. Q the rate of heat generation in line source per unit length per unit time. From Eq. (1), it is evident that the thermal conductivity λe of the material under test can be determined by measuring the rate of heat generation in the heating

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INDIAN J. ENG. MATER. SCI., APRIL 2004

source per unit length and the values of temperature at two times t1 and t2, respectively. Carslaw and Jeager1 has given the theory of transient thermal conductivity method in detail and discussed its various limitations. Theoretically a line heat source should not occupy space and should have no mass. But in practice a fine heater wire housed in a hollow cylindrical needle is used as the line heat source and a copper-constantan thermocouple housed at its middle point, which possesses a finite radius and whose thermal characteristics differ considerably as compared to the material under test. Errors are also introduced because of the contact resistance between heater wire and test material. These discrepancies have been investigated by Vander Held and Drunen5 and DE Vries and Peck6. Experimental The probe used for this study was a thin needle of 1 mm diameter having 14 cm length. It had a resistance of 27.6 Ω. The heating current used was low of the order of 50 mA, so that the power dissipated in the sample was low. The probe constructed in the laboratory has been standardized by measuring the thermal conductivity of pure glycerin to be 0.29 W/m K at 30oC. Since the value reported in literature7 is 0.286 W/m K at 30°C, the error is not more than 1.4%. The experimental arrangement used in association with thermal probe is shown in Fig. 1. The power was supplied by the constant power source having high capacity. The reference junction of thermocouple was kept at ice point. The voltage generated corresponding

Fig. 1–Experimental arrangement of the determination of thermal conductivity of organic foams using thermal probe [PS = power supply and power measuring unit, DMV = digital microvoltmeter, and RF = reference junction]

to the rise in temperature at the probe surface was recorded using a digital micro-voltmeter. The organic foam samples were cut in shape of cylindrical container having diameter 8 cm and height 15 cm and housed into it. The probe was inserted into the centre of the cylindrical sample. When the sample-probe system attained thermal equilibrium the power to the heater circuit was switched on. The initial rise in temperature before 30 s was dropped according to the approximation taken in deriving the Eq. (1). Each measurement lasted approximately for 5 to 6 min and the rise of temperature at the probe surface was usually of the order of 5 to 6oC. A plot for temperature rise versus logarithm of time for each measurement was made. Experimental observations were made for organic foams at varying temperatures and pressures using temperature and pressure chambers. The temperature chamber is maintained at constant temperature from – 20 to 30oC by circulating liquid from constant temperature bath. The air pressure inside the pressure chamber having the sample was brought to 0.2 mm of Hg with the help of a rotary pump. The chamber was allowed to remain at this pressure for some time to establish uniform interstitial air pressure throughout the chamber. The pressure was altered and the chamber was left to itself, for some time. To measure the pressure inside the chamber, Pirani gauge was used. An attempt has also been made to estimate λs (thermal conductivity of solid phase), by measuring λe (effective thermal conductivity) of the organic foam [φ (volume fraction of the solid phase) = 0.065] sample saturating it with different fluids (air, glycerin, engine oil, mustard oil and water). The curve between λe and λs, meets the straight-line λe = λs and it is evident that this point of intersection should give λs (ref. 8). From Fig. 2, we get λs = 0.0485 W/m K which is in agreement with the one obtained earlier

Fig. 2 – Plot for effective thermal conductivity of organic foam (φ = 0.065 and density = 28 kg/m3) with the conductivity of saturating fluid (air, glycerin, engine oil, mustard oil and water).

JAGJIWANRAM & SINGH: THERMAL CONDUCTIVITY OF HIGH POROSITY ORGANIC FOAMS

127

through the method of extrapolation to zero porosity. The various fluids used for the present work and their thermal conductivities are given in Table 1. Results and Discussion Representative curves for the organic foams of different densities, showing the variation of thermal conductivity with respect to temperature, are shown in Figs 3-5. Figs 6-8 show the variation of thermal conductivity with interstitial air pressure. It is evident from Figs 3-5 that the ETC of organic foams increases with increasing temperature from –20 to 30°C. The reason is that as the temperature rises, the average energy of the molecules increases, so that in the solid

Fig. 5 – Variation of effective thermal conductivity of organic foam (density = 50 kg/m3) with temperature.

Table 1—Various fluids used for the present work and their thermal conductivities Temp., o C

λf W/m K

Air

20

0.026

Wooside9

2

Glycerin

30

0.286

Eckert7

3

Engine oil

30

0.145

Eckert7

4

Mustard oil

30

0.215

Verma10

5

Water

30

0.620

Wooside9

Sl No.

Samples

1

Source of information



Fig. 6 – Variation of effective thermal conductivity of organic foam (density = 10 kg/m3) with pressure.



INDIAN J. ENG. MATER. SCI., APRIL 2004

128

Table 2 —Comparison of ETC values of organic foams using Eq. (2) at normal pressure and room temperature. The thermal conductivity is in W/m K φ

λs

λf

λe (exptl)

λe (theor.) By Eq.2

% Error

Organic foam/air

0.028

0.0485

0.026

0.0268

0.0267

0.3

Organic foam/air

0.065

0.0485

0.026

0.0283

0.0290

2.6

Sl No.

Type of the sample

1 2 3

Organic foam/air

0.123

0.0485

0.026

0.0333

0.0337

1.1

4

Organic foam/glycerin

0.028

0.0485

0.286

0.282

0.282

0.0

5


0.065

0.0485

0.286

0.270

0.268

0.6

6


0.123

0.0485

0.286

0.250

0.248

0.6

7

Organic foam/engine oil

0.028

0.0485

0.145

0.144

0.143

0.1

8


0.065

0.0485

0.145

0.143

0.143

0.0

9


0.123

0.0485

0.145

0.142

0.141

0.2

10

Organic foam/mustard oil

0.028

0.0485

0.215

0.187

0.183

1.7

11


0.065

0.0485

0.215

0.179

0.178

0.3

12


0.123

0.0485

0.215

0.176

0.172

2.1 0.8 %

Average deviation

part of the sample the molecules collide with each other exchanging energy and momentum. Therefore, energy brought in to a colder region by an energetic molecule is rapid shared with its fellows and in the pore space the velocities of the air molecules in a hot region are greater than in a cold region. It is observed from the Figs 6-8 that: (i) As the pressure is increased from 0.2 mm of Hg towards normal, value of ETC increases. But above 100 mm of Hg pressure, there is only a slight variation in ETC. (ii) The rate of variation of ETC with pressure is large in the range 0.2-100 mm of Hg and small in the range 100 mm of Hg to normal pressure. This is because in low-pressure region the number of air molecules inside the sample becomes negligibly small. The contribution to heat transfer in the region below 1 mm of Hg is mainly through radiative heat transfer by an evacuated pore. In the region 1-760 mm of Hg the density of air molecules increases at the same rate the mean free path decreases on increasing the interstitial air pressure. The mode of heat transfer changes from radiative to conductive. Therefore, ETC in this pressure region is increased. (iii) At normal pressure, ETC approaches to a constant value because only conductive mode of heat transfer dominates in this region. It is observed from the Table 2 that for high porosity (volume fraction of fluid phase) organic foam-air system, the ETC is low as compared with low porosity organic foam. An increase in porosity of organic

foam means decrease in density so that there will be more space available for the air molecules in turn the sample into a better insulator. It is also observed from the Table 2 for organic foam-glycerin, organic foamengine oil and organic foam-mustered oil as the porosity increases, effective thermal conductivity of the sample increases due to high thermal conductivity of the fluid phase in comparison with solid phase. Comparison of experimental results of ETC of organic foams and calculated values from Eq. (2) are shown in Table 2. The average deviation is 0.8%, which is good agreement between experimental and theoretical results at room temperature and normal pressure. Conclusions The effective thermal conductivities of organic foams measured in this study were found to be in good agreement with the reported theoretical results. It was also observed that the effective thermal conductivity decreased with increase in porosity and increased with increase in temperature and interstitial air pressure. Acknowledgement The authors would like to thank Professor D R Chaudhary for critical comments and helpful discussion. JR is grateful to the CSIR, New Delhi for the award of SRF.

JAGJIWANRAM & SINGH: THERMAL CONDUCTIVITY OF HIGH POROSITY ORGANIC FOAMS

Appendix

References

1 Carslaw H S & Jeager J C, Conduction of heat in solids, 2nd ed (Oxford: Clarendon) 1959, p 261. 2 Jain P C et al., Indian J Technol, 14 (1976) 583-584. 3 Agrawal M P & Bhandari R C, Appl Sci Res, 23 (1970) 113120. 4 Blackwell J H, Canad, J Phys, 34 (1956) 412-417. 5 Vander Held E F M & van Drunen, Physica, 15 (1949) 865. 6 De Vries D A & Peck A J, Aust J Phys, 11 (1958) 255. 7 Eckert E R G & Drake R M, Analysis of Heat and Mass Transfer, (McGraw-Hill, New York), 1972. 8 Chaudhary D R, Some problems of heat transfer in disperse and porous media-Rajasthan desert sand, Ph.D. Thesis, University of Rajasthan, Jaipur, 1968, p 44. 9 Woodside W & Messmer J H, J Appl Phys, 32(9) (1961) 1988-1699. 10 Verma L S, Prediction and Estimation of thermal coefficients of multi-phase systems, Ph.D. Thesis, University of Rajasthan Jaipur, 1991, p 190.

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The cylindrical particle model is

λe =

λ f [(λs − λ f ){√ (π/4)}F 1/ 2 + λ f ] [(1 − {√ (4/π )}F 1/ 2 (λs − λ f ){√ (π/4)}F 1/ 2 ] + λ f

and F1/2 = C1 φ1/2exp(λf/λs) + C2 where λf is the thermal conductivity of solid phase and other symbols have the same meaning as in the previous part in the paper. C1 and C2 are constants. These constants are different for different type of materials. The values of these constants for organic foamair are 1.3137 and -0.194, for organic foam-glycerin are -0.0052 and 0.1836, for organic foam-engine oil are -0.0226 and -0.4038 and for organic foam-mustard oil are -0.0084 and -0.4038, respectively.