Solids, thermophysical properties

Touloukian, Y.S., Powell, R.W., Ho, C.Y., and Klemens, P.G. (1970) Thermal Conductivity - NonmetalUc Solids -Thermophysical Properties of Matter, vol. 2, IFI/Plenum, New York-Washington. 

Thermophysical Properties of Selected Nonmetallic Solid Substances. 

TABLE 2-382 Thermophysical Properties of Selected Nonmetallic Solid Substances... 

Touloukian, Y.S., and DeWitt, D.P. (1972), Thermal Radiative Properties of Non-metallic Solids, in Thermophysical Properties of Matter, Plenum, New York, pp. 3a-48a. 

Y.S. Touloukian, E.H. Buyco Thermophysical Properties of Matter (Specific Heat) vol. 4, Metallic Elements and Alloy, vol. 5, Nonmetallic Solids, Plenum Press, New York (1970)... 

With the above-described heat transfer model and rapid solidification kinetic model, along with the related process parameters and thermophysical properties of atomization gases (Tables 2.6 and 2.7) and metals/alloys (Tables 2.8,2.9,2.10 and 2.11), the 2-D distributions of transient droplet temperatures, cooling rates, achievable undercoolings, and solid fractions in the spray can be calculated, once the initial droplet sizes, temperatures, and velocities are established by the modeling of the atomization stage, as discussed in the previous subsection. For the implementation of the heat transfer model and the rapid solidification kinetic model, finite difference methods or finite element methods may be used. To characterize the entire size distribution of droplets, some specific droplet sizes (forexample,.D0 16,Z>05, andZ)0 84) are to be considered in the calculations of the 2-D motion, cooling and solidification histories. 

As a result of the time-dependent voidage variations near the heating surface, the thermophysical properties of the packet differ from those in the bed, and this difference has not been included in the packet model. The limitation of this model lies in not taking into account the nonuniformity of the solids concentration near the heating surface. Thus, the packet model under this condition is accurate only for large values of Fourier number, in general agreement with the discussion in 4.3.3. 

The physical and thermophysical properties of density, thermal conductivity, and specific heat are temperature dependent. It is a reasonably good approximation to use constant values for both the solid and molten states. 

As pointed out in the previous section, melting can often be modeled in terms of simple geometries. Here we analyze the transient conduction problem in a semi-infinite solid. We compare the solutions of this problem, assuming first (a) constant thermophysical properties, then (b) variable thermophysical properties and finally, and (c) a phase transition with constant thermophysical properties in each phase. These solutions, though useful by themselves, also help demonstrate the profound effect of the material properties on the mathematical complexities of the solution. 

Example 5.2 Semi-infinite Solid with Constant Thermophysical Properties and a Step Change in Surface Temperature Exact Solution The semi-infinite solid in Fig. E5.2 is initially at constant temperature Tq. At time t — 0 the surface temperature is raised to T. This is a one-dimensional transient heat-conduction problem. The governing parabolic differential equation... 

Example 5.3 The Semi-infinite Solid with Variable Thermophysical Properties and a Step Change in Surface Temperature Approximate Analytical Solution We have stated before that the thermophysical properties (k, p, Cp) of polymers are generally temperature dependent. Hence, the governing differential equation (Eq. 5.3-1) is nonlinear. Unfortunately, few analytical solutions for nonlinear heat conduction exist (5) therefore, numerical solutions (finite difference and finite element) are frequently applied. There are, however, a number of useful approximate analytical methods available, including the integral method reported by Goodman (6). We present the results of Goodman s approximate treatment for the problem posed in Example 5.2, for comparison purposes. 

Example 5.4 Melting of a Semi-infinite Solid with Constant Thermophysical Properties and a Step Change in Surface Temperature The Stefan-Neumann Problem The previous example investigated the heat conduction problem in a semi-infinite solid with constant and variable thermophysical properties. The present Example analyzes the same conduction problem with a change in phase. 

The preceding examples discuss the heat-conduction problem without melt removal in a semi-infinite solid, using different assumptions in each case regarding the thermophysical properties of the solid. These solutions form useful approximations to problems encountered in everyday engineering practice. A vast collection of analytical solutions on such problems can be found in classic texts on heat transfer in solids (10,11). Table 5.1 lists a few well-known and commonly applied solutions, and Figs. 5.5-5.8 graphically illustrate some of these and other solutions. 

A. Goldsmith, L. E. Waterman, L. E. Hirschhorn, Handbook of Thermophysical Properties of Solid Materials, Pergamon Press, Oxford, 1961. 

Empirical approaches are useful when macroscale HRR measurements are available but little or no information is available regarding the thermophysical properties, kinetic parameters, and heats of reaction that would be necessary to apply a more comprehensive pyrolysis model. Although these modeling approaches are crude in comparison with some of the more refined solid-phase treatments, one advantage is that all required input parameters can be obtained from widely used bench-scale fire tests using well-established data reduction techniques. As greater levels of complexity are added, establishing the required input parameters (or material properties ) for different materials becomes an onerous task. 

Y. S. Touloukian, Thermophysical Properties of High Temperature Solid Materials, Macmillan, NY (1967). 

All possible interactions between the K and L groups were taken into account and Akk = 0. The definition contains a minimum number of groups and is satisfactory for most of the binary systems studied. However, it cannot take into account the structural differences which exist between position isomers. This is the case of polycyclic aromatic compounds presenting cycle position isomers or substitute position isomers. Structural differences of this type determine the gaps between the values of certain thermophysical properties of isomers, such as, for example, the fusion temperature or sublimation enthalpy. The further the temperature falls, the more these differences are accentuated. The representation of the solid-fluid (low temperature) equilibria is consequently more difficult and the model must take into account the existing structural differences. We came across this problem in the compounds such as anthracene, phenanthrene, pyrene, methylated naphthalenes, hexamethylbenzene and triphenylmethane. As it was out of the question to increase the number of groups because... 

Consider a semi-inlinite solid with constant thermophysical properties, no internal heat generation, uniform theimal cnnditinn.s on its exposed surface, and initially a uniform temperature of Tj throughout. Heat tfansfec in this case occurs only in the direction uormal to the surface (the x direction), and thus it is one-dimensional. Differential equations are independent of the boundary or initial conditions, and thus Eq. 4—lOa for one-dimensional transient conduction in Cartesian coordinates applies. The depth of the solid is large (x expressed mathematically as a boundary condition as T x —> , 0 = T,. 

Hydrodynamically fully-developed laminar gaseous flow in a cylindrical microchannel with constant heat flux boundary condition was considered by Ameel et al. [2[. In this work, two simplifications were adopted reducing the applicability of the results. First, the temperature jump boundary condition was actually not directly implemented in these solutions. Second, both the thermal accommodation coefficient and the momentum accommodation coefficient were assumed to be unity. This second assumption, while reasonable for most fluid-solid combinations, produces a solution limited to a specified set of fluid-solid conditions. The fluid was assumed to be incompressible with constant thermophysical properties, the flow was steady and two-dimensional, and viscous heating was not included in the analysis. They used the results from a previous study of the same problem with uniform temperature at the boundary by Barron et al. [6[. Discontinuities in both velocity and temperature at the wall were considered. The fully developed Nusselt number relation was given by... 

In these numerical simulations, the independent variables are (i) wall superheat, (ii) liquid subcooling, (iii) system pressure, (iv) thermophysical properties of test fluid, (v) contact angle, (vi) gravity level, (vii) thermophysical properties of the solid and surface quality (conjugate problem), and (viii) heater geometry. 

J. Sestak, Thermophysical Properties of Solids, Comprehensive Analytical Chemistry, Vol Xll, Part D, (Ed. G. Svehla), Elsevier, Amsterdam, 1984. H. Schmalzried, Chemical Kinetics of Solids, VCH Publishers, New York, 1995. 

J. Sest, Thermophysical Properties of Solids, Comprehensive Analytical Chemistry, Vol. XllD, Elsevier, Amsterdam, 1984. 

Not much is known about the thermophysical properties of liquid metals, especially the transport properties such as chemical and thermal diffusivities. The existing data are sparse and the scatter makes it difficult to make an accurate determination of the temperature dependency of these properties. This situation was the motivation for Froberg s experiment on Space-lab-1 in which he measured the temperature dependence of the self-diffusion of Sn from 240°C to 1250°C. He found that the diffusion coefficients were 30-50% lower than the accepted values and seemed to follow a 7 dependence as opposed to the Arrhenius behavior observed in solid state diffusion. ... 

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