Thermal conductivity calculation methods

The determination of the thermal conductivity of grain is based on the comparison of the temperature history data obtained by using the line heat source probe with the approximate analytical and numerical methods [35,54]. The analytical method has the advantage of being quick in calculating thermal conductivity. This method, however, requires a perfect line source and a small diameter tube holding the line heat source. In reality, this requirement is difficult to meet. Therefore, a time-correction procedure has been introduced [52,54,56]. Another objection to the analytical method is that it cannot easily be used to calculate the temperature distribution in the heated grain and to compare it with the measured one. Such a comparison can be easily accomplished by a numerical method, where the estimated accuracy for thermal conductivity is determined and the thermal conductivity of the device is taken into account [54]. 

The correction for the pressure dependence of transport properties of gases can be piade by use of various correlations. These include the gas density which in turn is calculated from the compressibility factor. For viscosity the method proposed by Dean, Stiel [9] can be used, and for the thermal conductivity the method proposed by Stiel, Thodos [54] can be used. For the bulk diffusion coefficient it is normally assumed that it is inversely proportional to the density. 

A guarded hot-plate method, ASTM D1518, is used to measure the rate of heat transfer over time from a warm metal plate. The fabric is placed on the constant temperature plate and covered by a second metal plate. After the temperature of the second plate has been allowed to equiUbrate, the thermal transmittance is calculated based on the temperature difference between the two plates and the energy required to maintain the temperature of the bottom plate. The units for thermal transmittance are W/m -K. Thermal resistance is the reciprocal of thermal conductivity (or transmittance). Thermal resistance is often reported as a do value, defined as the insulation required to keep a resting person comfortable at 21°C with air movement of 0.1 m/s. Thermal resistance in m -K/W can be converted to do by multiplying by 0.1548 (121). 

Conduction takes place at a solid, liquid, or vapor boundary through the collisions of molecules, without mass transfer taking place. The process of heat conduction is analogous to that of electrical conduction, and similar concepts and calculation methods apply. The thermal conductivity of matter is a physical property and is its ability to conduct heat. Thermal conduction is a function of both the temperature and the properties of the material. The system is often considered as being homogeneous, and the thermal conductivity is considered constant. Thermal conductivity, A, W m, is defined using Fourier s law. 

In design considerations for Thermonized process lines, temperatures may be determined by the Stagnation Method. The calculations involved in this method are based on static conditions where process fluid flow is not present, and are independent of the viscosity, density and thermal conductivity of the process fluid. The process temperature may be calculated from the following relationship ... 

Ya.B. ZeFdovich, FizGoreniyaVzryva 7 (4), 463-76 (1971) CA 77, 64194 (1972) The influence of turbulence and nonturbulence is examined relative to a proplnt burning in a gas flow. Equations indicate exptl methods for determining the magnitudes of the thermal conductivity and viscosity under turbulent flow, and permit a study of thermal flow distribution and temps in a gas wherein an exothermic chem reaction occurs. Equations for non turbulent conditions can be used to calculate the distance from the surface of the proplnt to the zone of intense chem reaction and establish the relation of bulk burning rate to the vol reaction rate. 

The complete data series is used to calculate the temperature response, but only certain parts of the experimental data are used to calculate the error. An example of a calibration run is given in Figure 53, the final calibrated TRNSYS model run is shown in Figure 54. Using the first part of the data (with constant heat flux) an estimate of ground thermal conductivity of 2.15 was obtained. Yavatzturk s method yielded an estimate of 2.18, while the estimate obtained with the TRNSYS parameter estimation method was 2.10. 

It is important to note that Vie and Kjelstrup [250] designed a method of measuring fhe fhermal conductivities of different components of a fuel cell while fhe cell was rurming (i.e., in situ tests). They added four thermocouples inside an MEA (i.e., an invasive method) one on each side of the membrane and one on each diffusion layer (on the surface facing the FF channels). The temperature values from the thermocouples near the membrane and in the DL were used to calculate the average thermal conductivity of the DL and CL using Fourier s law. Unfortunately, the thermal conductivity values presented in their work were given for both the DL and CL combined. Therefore, these values are useful for mathematical models but not to determine the exact thermal characteristics of different DLs. 

Therefore, if is necessary to have good interaction between the diffusion layers and fhe FF plafes—nof only from a mass transport standpoint but also to maintain optimal electrical and thermal conductivity between them. Section 4.4.4 explained in detail measurement techniques to determine the electrical resistance in diffusion layers. It is important to note that most of fhose methods can also be implemented in order to calculate the contact resistance between the DLs and the FF plates. In this subsection, we will focus mostly on mass transport interactions between these two components. 

Key material properties for SOFC, such as the ionic conductivity as a function of temperature, are available in refs 36—39. In addition, Todd and Young ° compiled extensive data and presented estimation methods for the calculation of diffusion coefficients, thermal conductivities, and viscosities for both pure components and mixtures of a wide variety of gases commonly encountered in SOFCs. Another excellent source of transport properties for gases and mixtures involved in a SOFC is the CHEMKIN thermodynamic database. ... 

Semonian and Manes have devised an approach which provides continuous data from which the desorption isotherm can be constructed. Their method utilizes a calibrated thermal conductivity detector for sensing the effluent concentration from a cell filled with adsorbate and slowly purged with a carrier gas. The amount desorbed at any relative pressure is calculated by integrating the effluent flow rate and thermal conductivity signal. 

Even more interesting and important than the foregoing unique method of measuring thermal conductivities of suspensions is the procedure used to calculate thermal conductivities theoretically. Orr and DallaValle noted that electrical and thermal fields are similar hence the usual equation for calculation of electrical conductivity of a suspension should also be applicable to thermal conductivities. Their extensive tabulated results support this contention to within 3 %. This equation is... 

In order to calculate the numerical values of transfer coefficients, values of the molecular properties are required. In the next section, we present estimation methods for viscosity, diffusivity, thermal conductivity and surface tension, for the high-pressure gas. 

Thermal conductivty can be determined using either equilibrium or dynamic methods. Equilibrium methods involve a heated surface, a thin layer of sample, and a cooled surface. The energy required to maintain a steady state for a given temperature difference is measured and used in the calculations. Dynamic methods are based on thermal dif-fusivity, which is obtained from the curvatures of heating or cooling plots at various depths within the product. Procedures and applications of thermal conductivity measurements to foods have been reviewed (Peeples 1962 Reidy 1968 Woodams and Nowrey 1968). 

The vapor thermal conductivities have been estimated by the method ol Roy and Thoda Sonic vjpin thermal con ductivily data have been reported for acetaldehyde.24 Calculated values agree within an average ot 59r... 

ISOTV4 Tlte method f Roy and Thndos was used to calculate the vapor thermal conductivities over the 0-500T ... 

Liquid thermal conductivities of monocthylamine. di-cthylominc. and iricthylarmne are available in tabular form over a wide range of temperature. Tbc liquid thermal conductivity of ctbylc-nrdtuminc wax calculated with the method t l Robbins and Ktngrea ... 

Tlic vapor thermal conductivities were calculated by the method of Roy and Thodos.17... 

A limited amount uf vapor data arc available for cyclopro pane The vapor thermal conductivity of all four compounds was calculated by ihe method of Roy and Thodo. r... 

Liquid thermal conductivity data for cyclopcntane at 37.JTC and cyclohexane at 20 C and 37.8 C are available.13 Tabulated data are available.1 7 The effect of pressure on the thermal conductivity of cyclohexane is shown in Figure 40-11 API11 provides data on cyclohexane from the freezing point to the boiling point. The data lor cyclopropane and cy-rlobuianc were calculated by the method of Robbins and Kin grea." The data for cyclopcntane were extended by the method of Riedel ... 

Further advancements in the theory of fixed bed reactor design have been made(56,57) but it is unusual for experimental data to be of sufficient precision and extent to justify the application of sophisticated methods of calculation. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on the reaction rate. 

No experimental data on the effective thermal conductivity of an assemblage of micron size zeolite crystals under the conditions of sorption tests used in the examples above could be found in the literature. However, several methods are available for the calculation of k for an assemblage of particles with void fraction f. The thermal conductivities of the solid phase (k ) and the gas phase (k ) in the voids are needed [29]. We Bsed the method develop d by Maxwell. 

Binary diffusion coefficients for the vapor phase and for the liquid phase were estimated via the method proposed by Fuller et al. and Tyn and Calus, respectively (see Ref. 72). Physical properties such as densities, viscosities, and thermal conductivities were calculated from the methods given in Ref. 72. Heat losses through the column wall were measured at pilot scale. 

Recently, Miiller-Plathe suggested a NEMD method [51] for calculation of thermal conductivity in atomic fluids that was subsequently adapted and applied... 

The physical property monitors of ASPEN provide very complete flexibility in computing physical properties. Quite often a user may need to compute a property in one area of a process with high accuracy, which is expensive in computer time, and then compromise the accuracy in another area, in order to save computer time. In ASPEN, the user can do this by specifying the method or "property route", as it is called. The property route is the detailed specification of how to calculate one of the ten major properties for a given vapor, liquid, or solid phase of a pure component or mixture. Properties that can be calculated are enthalpy, entropy, free energy, molar volume, equilibrium ratio, fugacity coefficient, viscosity, thermal conductivity, diffusion coefficient, and thermal conductivity. 

In the present study, the y values of the compounds were determined by measuring the Cp values at very low temperatures. Also, the y values obtained were compared with the DOS calculated by the DV-Xa molecular orbital method [4], In addition, the Debye temperature, the standard entropy of formation, the electric resistivity p and the thermal conductivity k were further determined for each compounds. The physico-chemical properties of the compounds were discussed from both views of the electronic and lattice vibration states. 

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