Thermal conductivity indirect measurements

Vacuum gauges may be broadly classified as either direct or indirect (10). Direct gauges measure pressure as force pet unit area. Indirect gauges measure a physical property, such as thermal conductivity or ionisation potential, known to change in a predictable manner with the molecular density of the gas. 

Instruments with indirect pressure measurement. In this case, the pressure is determined as a function of a pressure-dependent (or more accurately, density-dependent) property (thermal conductivity, ionization probability, electrical conductivity) of the gas. These properties are dependent on the molar mass as well as on the pressure. The pressure reading of the measuring instrument depends on the type of gas. 

The measurement of total pressure in a vacuum system is essential. Chapter 5 outlined the two general principles involved (direct and indirect). Direct methods included manometric measurements (Examples 5.1 and 5.3) and those involving the mechanical deformation of a sensing element. Indirect methods, which depend on the estimation of a physical property of the gas (e.g. thermal conductivity, ionisation) that depends on number density, were also discussed. Uncertainty of measurement is a parameter associated with the result of a measurement. It may influence the choice of a pressure gauge, and its practical expression was illustrated in Example 5.4. 

For high thermal-conductivity adhesives, such as the silver-glass compositions whose thermal conductivities are greater than 20 W/m K, the indirect laser-flash method is used. Unlike the steady-state methods, the flash method does not measure thermal conductivity directly, but measures thermal diffusivity, from which thermal conductivity is calculated as follows ... 

The common procedures for measur ent of the specific heat of grains at constant pressnre are ice calorimetry [32], mixture methods [33], indirect methods, where the specific heat is calculated from other thermal properties such as thermal conductivity and diffusivity [34-37], method of differential scanning calorimetry (DSC) [38], guarded plate method, and the adiabatic method [28]. Only the most common method— the method of mixtures and the most modem method that utilizes sophisticated instrumentation— the DSC method, are discussed in this section. 

The recommended method [29] for the determination of the thermal diffusivity of individual kernels is to calculate it from experimentally measured values of the thermal conductivity of kernel material, specific heat, and kernel (particle) density—the so-called indirect method. The method may lead to approximate results with a relative error, which is difficult to estimate in respect to a true (real) value, which can only be determined by direct measurements. The results of thermal properties for wheat and corn [44] and for single soybeans [59] confirm the above. 

The cross section 6 (2000) is obviously available from the viscosity, whereas 6(0001) is often available from bulk viscosity or direct or indirect collision number measurements (Millat et al 1988b Millat Wakeham 1989). This leaves only the cross section 6 (1001) to be determined, which could, in principle, be deduced from measurements of Ant according to equation (4.31). Very few measurements of this quantity have yet been performed (see Perron 1990). It is therefore necessary at present to adopt a different approach, which is to use the limited amount of thermal conductivity data available to determine 6 (1001) and to evaluate Ant from it. Such an analysis can be useful because it is then possible to evaluate the experimental value of Am/ as... 

The measurement of very low thermal conductivities is done directly by equilibrium methods, where typically a constant heat flux is measured to maintain a given temperature difference between a hot and a cold side. Dynamic methods rely on a transient heat pulse or wave that is sent from a material interface and travels over a known distance to reach a detector. Indirect methods then rely on physical models to calculate the thermal conductivity based on heat diffusion equations. A detailed review on the physics of heat transport in aerogels was given by Ebert [203] in the aerogels handbook. Various theoretical models exist, which allow one to determine the effective thermal conductivity of superinsulation materials based on dynamic measurement methods. 

Figure 12.12 shows the heat transfer mechanism from a surface-mounted thermal sensor. The total heat transfer to the fluid from the thermal sensor (Qohmic) has two components, that is, the heat transfer to the fluid (<2fluid) and the heat lost to the substrate (Gsubstrate)- Th heat transfer to the fluid has two parts, that is, direct heat transfer from the sensor element (Qfi) and indirect heat transfer from the substrate heated by the conduction of heat from the sensor to the substrate ( 2f2)- The heat transferred to the fluid via the substrate effects the temperature distribution near the sensor. This affects the net heat transfer rate from the sensor element and limits the performance of thermal shear stress measurement. The effective length of the thermal sensor is higher than the size of the sensor element, thus limiting the spatial resolution of shear stress measurement. Therefore, effective thermal isolation between the sensor element and substrate is an important issue for optimum performance, fabrication, and packaging of thermal shear stress sensors. For thermal isolation, the resistor of the sensor sits on the top of a diaphragm above a vacuum cavity (see Figure 12.12). The presence of vacuum cavity and thin diaphragm reduces the convective and conductive heat transfer to the substrate. Better insulation improves the thermal sensitivity of the sensor, that is, higher temperature rise T - Tq) of the thermal sensor is achieved for a particular power input (F).

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