Thermal conductivity of materials

The thermal conductivity of materials has been examined in Chapter 2 and Chapter 3. As we shall see in this chapter, in many cases, at very low temperatures, the heat conduction is not limited by the bulk thermal resistivity of the material but by the contact thermal resistance appearing at the interface of two materials. This is a particularly severe problem, below IK, in the case of the heat transfer between liquid He and a solid (see Section 4.3). Heat transfer by radiation will be considered in Section 53.2.2. 

One final note is appropriate for this section. Dne to the fact that many oxide ceramics are used as insulating materials, the term thermal resistivity is often used instead of thermal conductivity. As will be the case with electrical properties in Chapter 6, resistivity and conductivity are merely inverses of one another, and the appropriateness of one or the other is determined by the context in which it is used. Similarly, thermal conductance is often used to describe the thermal conductivity of materials with standard thicknesses (e.g., building materials). Thermal condnctance is the thermal conductivity divided by the thickness (C = k/L), and thermal resistance is the inverse of the prodnct of thermal conductance and area R = 1/C A). 

The thermal conductance of materials depends on temperature and decreases as the latter increases. It also depends on the density of a solid, increasing with density. The presence of foreign atoms in solid solutions contributes to growth of thermal resistance, i.e., to reduction of thermal conductance (Pampuch, 1971). 

Thermal Conductivity. Figure 1 shows the temperature dependence of a range of materials, and it can be seen that the values of thermal conductivities of materials vary widely. Typical values are as follows ... 

It is well to mention that in some systems like that in Fig. 2- 2 two-dimensional heat flow may result if the thermal conductivities of materials B, C, and D differ by an appreciable amount. In these cases other techniques must be employed to effect a solution. 

From time to time we have mentioned that thermal conductivities of materials vary with temperature however, over a temperature range of 100 to 200°C the variation is not great (on the order of 5 to 10 percent) and we are justified in assuming constant values to simplify problem solutions. Convection and radiation boundary conditions are particularly notorious for their nonconstant behavior. Even worse is the fact that for many practical problems the basic uncertainty in our knowledge of convection heat-transfer coefficients may not be better than 20 percent. Uncertainties of surface-radiation properties of 10 percent are not unusual at all. For example, a highly polished aluminum plate, if allowed to oxidize heavily, will absorb as much as 300 percent more radiation than when it was polished. 

The thermal conductivities of materials vary over a wide range, as shown in Fig. 1-27. The thermal conductivities of gases such as air vary by a factor of 10 from those of pure metals such as copper. Note that pure crystals and metals have the highest thermal conductivities, and gases and insulating materials the lowest. 

The thermal conductivities of materials vary with temperature (Table 1-3). The variation of thermal conductivity over certain temperature ranges is negligible for some materials, but significant for others, as shown in Fig. 1-29. Tlie thermal conductivities of certain solids cxliibit dramatic increases at temperatures near absolute zero, when these solids become superconductors. For example, the conductivity of copper reaches a maximum value of about 20,000 W/m C at 20 K. which is about 50 limes the conductivity at room temperature. The Ihermal conductivities and other thermal properties of various materials are given in Tables A-3 to A 16. 

Thermal conductivity of materials can only be dehned for homogeneous materials, where the thickness is greater than that for which the apparent thermal resistivity of the material does not change by more than 2% with further increase in thickness. The thermal resistance must be sufficiently independent of the area of the specimen and for a flat slab specimen the thermal resistance must be proportional to the thickness. When all these conditions are met ... 

Heat sink thermal conductivity of materials in contact with the weld, for example, anvil and clamping system... 

ASTM C177-71. Test for Thermal Conductivity of Materials by Means of the Guarded Hot Plate. 

ASTM Standard C-177, Thermal conductivity of materials by means of the guarded hot plate, Ann. ASTM Standards, 1(14) 17, 1970. 

Thermal conductivity of material before decomposition, fej, Thermal conductivity of material after decomposition,... 

Table 3.1 Values of the thermal conductivity of materials (to be divided by 10" ), cal/cm/s/deg ...

Pi = volume percentage of material 1 in decimal form ki = thermal conductivity of material 1 2 = volume percentage of material 2 in decimal form k2 = thermal conductivity of material 2... 

There are two basic approaches to measuring the thermal conductivity of materials. The most basic approadi k a steady state a q>roach based on Fourier s definition of thermal conductivity. Steady state me uements often require a long time to reach equilibrium and, as a result, several unsteady state approaches have been developed that are based on the rate of change of temperature of a material suddenly subjected to a new thermal environment. 

Pores and the contacts between grains are barriers for thermal cmiductivity. The thermal conductivity of materials (having equal total porosity) with continuous condensed matter (big closed porosity) is 2-2.5 times higher compared with materials with continuous contacts. The thermal conductivity of fireclay brick at 600 °C is 0.25 W/m-K, while the thermal conductivity of fireclay fiber material is 0.11-0.12 W/m-K (Table 1.6). The thermal conductivity of diatomaceous brick with a different porosity may differ at 200 °C, but it becomes very close at 600-700 °C (Fig. 1.17). 

Below 500 °C, fireclay refractories with small pores are more temperature-conductive compared with fireclay refractories with big pores (at equal total porosity). Above 500 °C, fireclay refractories with big pores are more conductive (compared with fireclay refractories with small pores) due to value of the radiation. For silica refractories, the thermal conductivity of materials with big pores becomes higher compared with the thermal conductivity of materials with small pores beginning at 1,200 °C. 

Other than safe service temperature, usually in vermiculite-based materials there are no defects, and the dimensional tolerances at pressed materials are perfect (Fig. 2.84). If something is not going steadily in the fluidized furnaces, the density of grained vermiculite might increase, which leads directly to an increase in the thermal conductivity of materials. On the contrary, if some problems appear with temperature in a fluidized bed furnace and vermiculite doesn t exfoliate properly, it might start exfoliating during the service, which is not desirable. 

The thermal conductivity of diatomaceous and vermiculite heat insulation materials is similar. Diatomaceous materials have a very fine pore structure in such materials, the radiation effect on the thermal conductivity is low. An interesting dependence of thermal conductivity vs. temperature appears in Fig. 2.86—diatomaceous bricks with density 400, 500, and 600 kg/m have different values of thermal conductivity at 200 °C, but rather similar values at the temperature of service—400-600 °C. At such temperatures, the thermal conductivity of materials... 

High thermal conductivity in these materials provides an additional benefit to these lightweight, high specific stiffness composites. A number of factors can influence the thermal conductivity of particulate based composites such as the conductivity of the individual constituents, the size and volume of particles present, and the interfacial thermal barrier between two materials. Models for predicting the thermal conductivity of materials have been developed and are provided in the literature such as the Hasselman-Johnson model of the form... 

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