Thermal conductivity calculations

Gomes, C.J., M. Madrid, and C.H. Amon. Parallel Molecular Dynamics Code Validation Through Bulk Silicon Thermal Conductivity Calculations, in Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, IMECE 2003-42352. 2003. Washington, DC. Lee, Y.H., R. Biswas, C.M. Soukoulis, C.Z. Wang, C.T. Chan, and K.M. Ho, Molecular-Dynamics Simulation of Thermal Conductivity in Amorphous Silicon. Physical Review B, 1991.43(8) p. 6573-6580. 

Figure 18. The coefficient of thermal conductivity calculated for myoglobin from T = 20 K to 320 K is plotted as a solid curve in (a). The dashed curve gives the thermal conductivity if no anharmonic coupling of normal modes is included in the calculation, (b) Thermal diffusivity calculated for myoglobin is plotted from 20 K to 320 K with (solid) and without (dashed) contributions of anharmonicity.

Curves of Figure 19 compare the data published for (a) boron nitride [37,40] (b) aluminium (c) diamond-[37-39] (d) aluminium nitride [37-42] (e) crystalline silica. It can be seen that, at 45 vol.%, the maximum thermal conductivity achieved with diamond powder is 1.5 W m K, while crystalline boron nitride at 35 vol.% affords 2.0Wm K. The thermal conductivity of silver-filled adhesives was studied by using silicon test chips attached to copper and molybdenum substrates [43]. The authors outline the importance of the shape factor A, related to the aspect ratio of the particles, to achieve the highest level of thermal conductivity. Another study reports the variation of the effective thermal resistance, between a test chip and the chip carrier, in relation to the volume fraction of silver and the thickness of the bond layer [44]. The ultimate value of bulk thermal conductivity is 2 W m at 25 vol.% silver. However, the effective thermal conductivity, calculated from the thermal resistance measurements, is only one-fifth of the bulk value when the silicon chip is bonded to a copper substrate. 

The above equations indicate that values of and Ky are within approximately 5% of the bulk thermal conductivity if T/A fp > 7 (for Ky) and Lj> 4.5 (for K. Therefore, the above relations can be used for determination of thermal conductivity when A fp general guidelines exist for thermal conductivity calculation when < 1. 

Brigand et al. (1992) derived the rock composition ( electrofacies mineralogy and porosity ) from logs and used a four component (sandstone, carbonate, shale, pore fluid) geometric mean equation for thermal conductivity calculation. 

Effect of Uncertainties in Thermal Design Parameters. The parameters that are used ia the basic siting calculations of a heat exchanger iaclude heat-transfer coefficients tube dimensions, eg, tube diameter and wall thickness and physical properties, eg, thermal conductivity, density, viscosity, and specific heat. Nominal or mean values of these parameters are used ia the basic siting calculations. In reaUty, there are uncertainties ia these nominal values. For example, heat-transfer correlations from which one computes convective heat-transfer coefficients have data spreads around the mean values. Because heat-transfer tubes caimot be produced ia precise dimensions, tube wall thickness varies over a range of the mean value. In addition, the thermal conductivity of tube wall material cannot be measured exactiy, a dding to the uncertainty ia the design and performance calculations. 

The thermal conductivity of soHd iodine between 24.4 and 42.9°C has been found to remain practically constant at 0.004581 J/(cm-s-K) (33). Using the heat capacity data, the standard entropy of soHd iodine at 25°C has been evaluated as 116.81 J/ (mol-K), and that of the gaseous iodine at 25°C as 62.25 J/(mol-K), which compares satisfactorily with the 61.81 value calculated by statistical mechanics (34,35). 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

Transport Properties. Viscosity, themial conductivity, the speed of sound, and various combinations of these with other properties are called steam transport properties, which are important in engineering calculations. The speed of sound (Fig. 6) is important to choking phenomena, where the flow of steam is no longer simply related to the difference in pressure. Thermal conductivity (Fig. 7) is important to the design of heat-transfer apparatus (see HeaT-EXCHANGETECHNOLOGy). The viscosity, ie, the resistance to flow under pressure, is shown in Figure 8. The sharp declines evident in each of these properties occur at the transition from Hquid to gas phase, ie, from water to steam. The surface tension between water and steam is shown in Figure 9. 

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). 

Actual temperatures in practical flames are lower than calculated values as a result of the heat losses by radiation, thermal conduction, and diffusion. At high temperatures, dissociation of products of combustion into species such as OH, O, and H reduces the theoretical flame temperature (7). Increasing the pressure tends to suppress dissociation of the products and thus generally raises the adiabatic flame temperature (4). 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

Finally, it is to be expected that the evaporation coefficient of a very stable compound, such as alumina, which has a large heat of sublimation resulting from the decomposition into the elements, will be low. Since the heat of evaporation must be drawn from the surface, in die case of a substance widr a low thermal conductivity such as an oxide, the resultant cooling of the surface may lead to a temperature gradient in and immediately below the surface. This will lower die evaporation rate compared to that which is calculated from the apparent, bulk, temperature of the evaporating sample as observed by optical pyromeuy, and thus lead to an apparently low free surface vaporization coefficient. This is probably die case in the evaporation of alumina in a vacuum. 

Below -10°C, heat is conducted away too quickly to allow this melting - and because their thermal conductivity is high, skis with exposed metal (aluminium or steel edges) are slower at low temperatures than those without. At these low temperatures, the mechanism of friction is the same as that of metals ice asperities adhere to the ski and must be sheared when it slides. The value of jl (0.4) is close to that calculated from the shearing model in Chapter 25. This is a large value of the coefficient of friction - enough... 

A significant rise in temperature AT is calculated in a volume of soil at a distance up to 3 from the anode, where is the anode radius. Factors are the thermal conductivity of the soil, k, length of the anode, L, the grounding resistance, Rq, and the current, I. The rise in temperature can be calculated from these parameters [10]. For deep anodes it amounts to ... 

Fig. 8. Calculated thermal conductivity of neutron irradiated MKC-1 PH composite.

The inputs required for the calculation are the radii, iimer and outer temperatures, and thermal conductivities at the two temperatures. This expression enables an estimate of the heat flow into a spherical storage tank containing liquified gas. 

A unidirectional glass fibte/epoxy composite has a fibre volume fraction of 60%. Given the data below, calculate the density, modulus and thermal conductivity of the composite in the fibre direction. 

For a steel mould of the same dimensions and thickness, a quick calculation (A = 11 W/m K, Cp = 480 J/kg K and p = 7850 kg/m ) shows that the steel mould would take three times longer to heat up. However, in practice, steel moulds are less than a third of the thickness of aluminium. Therefore, although aluminium has a better thermal conductivity, steel moulds tend to heat up more quickly because they are thinner. 

Because direct calculation of thermal conductivity is difficulty 1], experimental measurements on composites with nanotubes aligned in the matrix could be a first step for addressing the thermal conductivity of carbon nanotubes. High on-axis thermal conductivities for CCVD high-temperature treated carbon fibers have been obtained, but have not reached the in-plane thermal conductivity of graphite (ref. [3], Fig. 5.11, p. 115). We expect that the radial thermal conductivity in MWNTs will be very low, perhaps even lower than the c-axis thermal conductivity of graphite. 

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. 

The Nomograph Part 3 (Figure I0-43C) may be used in a number of ways. For example, what will the fouling resistance, R(, be after an arbitrarily chosen time, t, or it can calculate the thickness of a fouling deposit after an arbitrarily chosen time t, providing the thermal conductivity of the deposited material is known. It can calculate thermal conductivity of a deposit, providing thickness is known, or estimated. 

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