Asme Plan Hot Method

Draft
ASME 2013 Summer Heat Transfer Conference
ASME2013
July 14-19, 2013, MINNEAPOLIS, MINNESOTAL, USA

HT2013-17359

MEASUREMENT OF THERMAL CONDUCTIVITY FOR INSULATION MATERIALS IN HIGH TEMPERATURE BASED ON TRANSIENT HOT-PLANE METHOD

|Guanfu Pan |Fan Yu |
|Thermal Engineering Department, University of Science and Technology |Thermal Engineering Department, University of Science and Technology |
|Beijing |Beijing |
|Beijing, China,100083 |Beijing, China,100083 |
|[e-mail] |[e-mail] |

Abstract Acquiring the thermal conductivity in high temperature accurately has important implications for using insulation materials. In this paper, the measurement principle of the transient hot plane method is introduced. For rising the operating temperature, the plane heat source with film is changed to no film one. So the measurement errors caused by film can be eliminated. Because of the low thermal conductivity of insulation materials and the sample should be heat up until high temperature. The preheating time will be too long. In order to shorten the time of preheating sample before measuring, this text introduce an original preheating method called center preheating method which is verified by the numberical simulating result. After the experimental apparatus has been established, practical measurements about thermal conductivity and thermal diffusivity have been made with ceramic fibre material in environment temperature 23.9~746.9℃. These experiments demonstrate favorable reproducibility and accuracy under the established apparatus high temperature environment.

1 INTRODUCTION Insulation materials are intensively used in aerospace, chemical industry and construction industry [1,2]etc. It is well known that the thermal conductivity as well as the thermal diffusivity vary extensively depending on the structure, density, porosity, electrical conductivity, etc., of different materials [3]. The thermal conductivity as an crucial evaluation parameter may change significantly with the temperature change. Since insulation materials are normally under high temperature, acquiring the thermal conductivity in high temperature accurately has important implications for proper utilization of insulation materials. Other thermal properties, like the thermal diffusivity and specific heat capacity, are also important only under transient conditions [4]. It is very necessary to have a well-suited and accurate method for measuring the thermal conductivity and diffusivity for insulation materials in high temperature [5]. The transient hot-plane method introduced in this article is proved can be effectively used to measure thermal conductivity for insulation materials in high temperature. Because of the low thermal conductivity of insulation materials [6], and the sample should always be test when heat up to high temperature. However, the preheating time can be too long by the conventional heating up method, even the physical and chemical properties would change in high temperature during such long time. So in the first two parts this paper will introduce an original preheating method, center preheating method. This center preheating method will shorten the preheating time substantially and control the measuring point temperature in an easier manner. Numberical simulations are made in the third part for models with experimental heat transfer conditions, verified the effects of center preheating method. The fourth part implements this transient hot-plane method to test thermal conductivity of ceramic fiber in high temperature with experimental apparatus established for the measurement of thermal conductivity. The preheating time was also gotten to verify the effects of center preheating method. Then the final part concludes.

2 measuring principle of transient hot-plane method[7] Thermal conductivity and thermal diffusivity are two important heat transfer properties of materials. Transient hot-plane method is able to detect both two thermophysical parameters. The rationale, as shown in Fig.1, is that the constant-current source can output as step current or pulse current, by which the plane heat source will generate heat with the flow of current in it. Then the heat will transfer into sample and make the temperature of sample rise. The excess temperature-time curve can be drawn by measuring the temperature response of one certain point in the sample (usually the centre point in a cross section of sample). According to the mathematic model of transient hot-plane method, the thermal conductivity λ and thermal diffusivity[pic]can be gotten by the modified Gauss-Newton method [8,9].

[pic]
Figure 1. Schematic diagram of transient hot-plane method

[pic]
Figure 2. Schematic diagram of ideal semi-infinite and one-dimensional model

Since the heat may loss from the sample surface, the heat conduction process in solids should be considered as a three-dimensional process. In order to simplify the analysis, here we assume this heat transfer as an ideal one-dimensional process instead. Under this assumption, no heat exchange exists between the sample and surroundings, which means, as the Fig.2 shown, the heat only transfer along the direction of thickness. Transient hot-plane method is based on this one-dimensional model. Thereby the heat conduction differential equations, boundary and initial equations can all derived from it as follow. [pic] (1) where z is the coordinate in the direction of heat transfer, t is time , λ is the thermal conductivity, a is the thermal diffusivity, q(t) is the flux of heat source. T(z , t) is the excess temperature at position z and time t, it’s the difference between real temperature T1 and initial temperature T0. When the current is step current. [pic] (2)
Where q is the heat flux density, I is the heating current, U is the voltage of two ends of plane heat source, R is the resistance of plane heat source, Q is the heating power, S is the area of plane heat source. When the heating current is step current, q=cones, the mathematic model can be derived after Laplace transform and inverse Laplace transform: [pic] (3)
Where erfc(y) is complementary error function. The T—t curve is what can be achieved during the step heating process. Since the thermal conductivity and thermal diffusivity are linearly independent, they can be figured out through the least square parameter-estimated method

3. CENTER PREHEATING METHOD When measuring the thermal conductivity of insulation materials in high temperature, the sample must be heated to the experimental temperature before measurement. The conventional prheating method is putting the sample into a furnace directly. By heat exchange between the sample surface and environment in the furnace，the sample temperature will rise to the target temperature. However, due to the low thermal conductivity of insulation materials, the consequent preheating process will be unconscionably long. The physical and chemical properties of sample are prone to change in high temperature over such long time. On the top of that, the conduction of heat is from outside to inside, which leads to the temperature close to the surface rising faster than the internal temperature, but the temperature measuring point is in the internal sample. Then the temperature closed to surface usually exceeds the experimental temperature when the temperature of measuring point reaches the experimental temperature. As a result, the heat will flow from not only the plane heat source but also the surface of sample. It is clear to distort measurement accuracy. To solve this problem, taking center preheating method, the plane heat source starts during the preheating process, so the plane heat source will transfer heat to the sample to make the sample temperature rise together with the surface heat transfer. During this preheating process, the heating power of plane heat source should be less than rated load of the constant-current source and prevent the sample temperature rising too fast. At the meantime, the preheating time will be reduced substantially and temperature of the measuring point will be able to control subtly. The result of numberical simulation will verify the efficiency of this method as follows. [pic] Figure 3. Diagram of three-dimensional model

Geometry size of plane heat source: length of the sample size L=89.94mm [10,11], width of heating plate l=2.37mm, gap j=0.50mm , half-thickness of plane heat source z1=0.05mm [12]. Thermal properties of plane heat source (0Cr21Al6Nb): thermal conductivity λ = 12.81W/(m[pic]K), volume specific heat = 3.5074×107J/(m3[pic]K) [13]. The integrated heat transfer coefficient are different in different temperature, the concreted value from value from calculating were shown in table1.

Table 1. The integrated heat transfer coefficient
|Temperature |Integrated heat transfer coefficient |
|℃ |W/(m2[pic]℃) |
|600 |148 |
|800 |230.69 |
|1000 |383.40 |
|1200 |664 |

In center preheating method, the heating power of plane heat source was set at 8W. This heating power can convert to an internal heat source of g1 = 12.4603×106W/m3. Four types heat resisting sample materials are chosen to be calculated, and the thermal conductivity of the four kinds of materials are λ＜0.1, 0.1≤λ≤1 and λ＞1 respectively. So the result of numberical simulation has reference value for both insulation materials and ordinary materials [14].

Table2. Thermal properties of different samples
| |thermal |volume specific |
|sample name |conductivity |heat |
| |W/(m[pic]K) |J/(m3[pic]K) |
|J703 |0.032 |3.60[pic]105 |
|ceramic fibre |0.06 |2.72[pic]105 |
|refractory brick |0.31 |1.35[pic]106 |
|marble |2.434 |2.73[pic]106 |

The numberical simulation has to simulate the actual preheating process. With the previous preheating method, the sample is heated only by the heat exchange on surface. But when adopting the center preheating method, the sample is heated by the surface heat exchanging and the heat generating of plane heat source together. Through the numberical simulating, the preheating time of these four materials with conventional preheating method and center preheating method are compared. The result has shown that the center preheating method can shorten the preheating time dramatically. The result of refractory brick sample and ceramic fibre sample are offered in graphic form for the sake of comparing the two different preheating methods clearly, shown in Fig.4.

[pic]
(a)
[pic]
(b)
Figure 4. Preheating time curve of different preheating method, where (a):refractory brick; (b): ceramic fibre The Fig.4 above discribes the preheating time curve of refractory brick sample and ceramic fibre sample under different experiment initial temperature. Where, the ordinate value is the preheating time of samples made by different materials; the abscissa value is the half-thickness of sample, and origin is the point of sample closed to the plane heat source center. The experiment initial temperature is set as 600℃, 800℃, 1000℃ and 1200℃ respectively. That the preheating time of center preheating method is much lesser than conventional preheating method is conspicuous in Fig. 5. As for the reason, compare to the conventional preheating method, temperature of the point closer to the plane heat source rise to the experiment initial temperature firstly. For the insulation material ceramic fibre, the high temperature preheating process will cost more time than the low temperature preheating process. But for the material with higher thermal conductivity this process is just opposite. The preheating process of lower experiment initial temperature will cost more time. The reason is that for the high temperature preheating process, in order to heat the sample to a higher experiment initial temperature, the temperature of environment in furnace must reach higher and the integrated heat transfer coefficient in high temperature is also larger than in low temperature. As a result of these, the heat transferred from surface is very large. Hence, since the thermal conductivity is larger than the insulation materials, the heat transferred from surface will reach the internal sample much more quickly.

[pic]
Figure 5. Preheating time curve on the plane 7.5mm away from the plane heat source

In the experiment the thermocouple is usually put on the center of plane 7.5mm away from the plane heat source. In the Fig.5 above, the abscissa origin is the center point of the plane 7.5mm away from the plane heat source. So it is clear to see that the center point in the plane heat up more quickly than the sample edge. The preheating time curve of different initial experimental temperature present the similar shape. The following parts give the numberical simulation result of ceramic fibre at measuring temperature 800℃.

[pic] Figure 6. Temperature rise curve of ceramic fibre in center preheating method

The temperature rise curve in Fig.6 depicts the whole process that the temperature rise of sample was sharp at the beginning of preheating process, then slightly slowed as the temperature approached 800℃. Since the convective heat transfer and radiation heat transfer are both on sample surface, the plane close to the temperature rise much more quickly than the plane close to the plane heat source at the beginning. As the heat of plane heat source fully release and the heat from surface transfer into the sample internal, the temperature of plane close to plane heat source rise more quickly than other areas in turn. Finally, the temperature of point that is nearest to the plane heat source center reached the experiment initial temperature firstly.

[pic] Figure 7. Temperature distribution along x axis

When the preheating process finished, it is indicated that the temperature of plane near heat source is higher than other plane. On the plane perpendicular to the z axis there is an area with nearly the same temperature, which can be regarded as a single dimensional heat transfer area [15]. When the thermocouple is put in this single dimensional heat transfer area, the measured temperature is equal to the center temperature. The temperature distribution along y axis was nearly the same as that along x axis on the same plane. The result of numberical simulation has shown that the center preheating method can shorten the preheating time and make the temperature of measuring point reach experiment initial temperature earlier than other areas near the sample surface.

4 Experimental Measurement

4.1 experimental apparatus

[pic]
Figure 8. Test unit of thermal conductivity

The test unit is shown in the Fig.8, and the main components include: temperature-controllable chamber, data collector，constant-current source，cold junction，plane heat source，thermocouple and computer etc [16]. The temperature controllable chamber must be able to control the temperature and pressure at the same time. In the experiment the samples should be stacked up in the temperature controllable chamber. In order to make the heat from plane heat source transfer to the two sides fifty-fifty. The thickness sum of sample I and sample II have to be equivalent to that of sample III. The data collector is used to collect the current and voltage data from the thermocouple and constant-current source outputs steady power and upload the heating power data to computer. One of the computer ports is connected to the cold junction. All above the data are gathered and input into computer, and then the thermal conductivity and thermal diffusivity can be worked out through the calculating programme. In addition, the experimental apparatus are repeatable and the data collector can also be used for the measurement by hot strip method [17].

4.2 result and analysis of measurement In the experiment, the center preheating method was employed on the preheating process. The preheating time is 2326s. The thermal conductivity of ceramic fibre in 800℃ have been gotten and offered in graphic form for further analysis.

Table 3 The result of ceramic fibre in 800℃
|temperature |pressure |thermal |volume specific|heat storage |
|℃ |Pa |conductivity |heat |coefficient |
| | |W/(m.K) |J/(m3.K) |(W.J)1/2/(m2.K) |
|23.9 |100000 |0.08228 |338139 |166.8 |
|386.2 |2000 |0.07801 |403689 |177.5 |
|385.9 |10000 |0.0882 |406264 |189.3 |
|746.9 |10000 |0.1776 |407150 |268.9 |

[pic] Figure 9. Excess temperature curve of 746℃、10000 Pa

[pic]
Figure 10. Relationship between thermal conductivity and temperature

As the experimental results suggested, there is good consistence between the experimental temperature rise curve and the theoretical temperature rise curve. And the experimental temperature rise curve is close to linear. The thermal conductivity will increase since the temperature and pressure going up. This is because of that when the temperature and pressure goes up, the member heat of sample inner part exercises more and more quickly and the distance between the molecules decreases.The experimental error is made up of the deviation between the experimental conditions and theoretical model associated with the measurement error of parameters in equation (2): such as the measurement error of voltage U, current I, temperature T, time t and the position of temperature measurement point z. In this experiment, measurement error of voltage[pic], measurement error of current[pic], error of heat flux density [pic],measurement error of temperature[pic], measurement error of time[pic], measurement error of z is [pic], taken together: [pic], [pic]. From the result the conclusion can be reached that this test unit is operable and repeatable for insulation materials with no more than 4% maximum relative. Notice that the heating power and test time should be set in light of materials and the temperature should keep stable before testing. In addition, the time interval between two tests should be long enough to prevent the warm of last test on following testing.

5 conclusion The transient hot-plane method in this paper is an original way to measure the thermal conductivity of thermal insulation materials under high temperature, with which more than one thermal property can be obtained rapidly and reliably by measuring temperature on one point only. Through the numberical simulation of the actual test the possibility and usefulness of center preheating method have been confirmed. Subsequent experiment study is conducted by employing this method to measure thermal conductivity and thermal diffusivity of ceramic fibre under different pressure and temperature conditions. Further extended study of this method would remain to be confirmed and consummated on other types of insulation materials under potential higher temperature.

acknowledgments The work is supported by the National Natural Science Foundation of China (No.50776009). The authors wish to thank the anonymous reviewers for suggestion that contributed to improvement in the usability of test unit herein.

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References: [9] Wang,X.Z., “theory and application of nonlinear model parameter estimation[M]”, Wuhan, Wuhan university press, 2002, pp.79-113 [10] Zuo L., Zhu S [13] Wang Z.D. and Gong D.S., “electrothermal alloy[M]”, Beijing, Chemical industry press, 2006, pp.306-322 [14] Hu F