Diffusivity thermal

Thermal diffusivity measurements have been reported for fibre reinforced phenol-formaldehyde resins [31], PA 6,6, PP, PMMA [54] and trifluoroethylene nanocomposites [55]. 

Thermal diffusivity is the parameter that determines the temperature distribution through a material in transient conditions, that is, when the material is being heated or cooled. As shown in Equation 2.7, it is a function of the thermal conductivity, 

By combining the Equation 2.2 with Eqnation 2.50, the heat flnx can be rewritten  

thermal diffusivity a is the parameter relating energy flux to energy gradient, whereas thermal conductivity relates the energy flux to the temperature gradient. 

Thermal diffusivity is of little interest in many insulation applications where steady-state conditions exist, such as civil engineering. However, in rubber processing, when temperatures are changing rapidly, it is of more interest than thermal conductivity, as shown in the Equations 2.45 and 2.48 established as a general case, or even as a particular case with the Equations 2.41 and 2.44. 

Methods of measurements have been reviewed in considerable detail, and the RAPRA apparatus has been described [5,14]. 

A laser flash technique has been used to determine the diffusivity of pyroelectric polymers such as polyvinylidene fluoride [83], whereas hot-wire techniques have been used to determine the thermal diffusivity of high-density polyethylene, low-density polyethylene propylene, and polystyrene [83], Dos Santos and coworkers [84] utilized the laser flash technique to study the effect of recycling on the thermal properties of selected polymers. Thermal diffusivity expresses how fast heat propagates across a bulk material, and thermal conductivity determines the woiking temperature levels of a material. Hence, it is possible to assert that those properties are important if a polymer is used as an insulator, and also if it is used in applications in which heat transfer is desirable. Five sets of virgin and recycled commercial polymers widely used in many applications (including food wrapping) were selected for this study. 

Disc-shaped samples (10 mm in diameter, thickness of 0.3-1 mm) were prepared by hot pressing the polymer or powder, or by cutting discs from long cylindrical bars. Measurements were carried out from room tanperature up to 50°C above the polymer crystalline Experimental results showed different behaviors for the thermal diffusivity of recycled polymers when compared with the corresponding virgin material. 

The thermal diffusivity is a property derived from thermal conductivity, specific heat, and density. The relationship is  

The thermal diffusivity is a very useful quantity in transient heat transfer problems, 

The thermal diffusivity can be calculated from the values k, p, and Cp however, in most cases it is measured directly. In fact, the thermal diffusivity can be measured more easily and accurately than the thermal conductivity. If a thick slab of material, initially at T , is suddenly exposed to an elevated temperature Tj at one wall and maintained at this temperature, the temperature distribution can be described by  

Equation 6.100 is a shortened version of the general energy balance equation (Eq. 5.5) valid for simple unidirectional conduction. This is a standard handbook problem the solution is (see [1] of Chapter 5)  

Equation 6.101 describes conductive heating of a semi-infinite slab. It is valid as long as thermal penetration thickness 6( is less than the slab thickness. Essentially all temperature change (99%) takes place within the thermal penetration thickness, which is given by  

A decrease in thermal diffusivity, with increasing temperature, is also observed in semicrystalline thermoplastics. These materials show a minimum at the melting temperature as demonstrated in Fig. 2.18 [24] for a selected number of semi-crystalline thermoplastics. It has also been observed that the thermal diffusivity increases with increasing degree of crystallinity and that it depends on the rate of crystalline growth, hence, on the cooling speed. 

Whereas heat capacity is a measure of energy, thermal diffiisivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to process-ability. In contrast, metals have values hundreds of times larger than those of plastics. 

Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

When a homogeneous material is subjected to a temperature difference, a heat transfer rate or heat flux, i.e., energy per unit surface area and time, occurs and flows from higher-temperature regions to low-temperature regions, as imposed by the second law of thermodynamics. The heat flux is a vector quantity and is proportional to the temperature gradient 

As a general rule, the thermal conductivity of crystalline solids corresponds to the sum of the conduction of heat by free electrons (i.e., Fermi s gas) in the conduction band and to the vibration of the atoms in the crystal lattice (i.e., phonons)  

When a material is submitted to a transient temperature change, the temperature profile inside the material can be obtained using Fourier s second law  

Every body emits electromagnetic radiation, but only hot bodies emit thermal radiation with a wavelength in the infrared region. In all cases the irradiance is given by the Stefan-Boltzmann equation  

9 Temperature and Latent Enthalpies of Fusion, Vaporization, and Sublimation 

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This definition is in terms of a pool of liquid of depth h, where z is distance normal to the surface and ti and k are the liquid viscosity and thermal diffusivity, respectively [58]. (Thermal diffusivity is defined as the coefficient of thermal conductivity divided by density and by heat capacity per unit mass.) The critical Ma value for a system to show Marangoni instability is around 50-100. 

Fig. XVIII-22. Schematic illustration of the steps that may be involved in a surface-mediated reaction initial adsorption, subsequent thermalization, diffusion and surface reaction, and desorption. (From Ref. 199 copyright 1984 by the AAAS.)...

The coefficients, L., are characteristic of the phenomenon of thermal diffusion, i.e. the flow of matter caused by a temperature gradient. In liquids, this is called the Soret effect [12]. A reciprocal effect associated with the coefficient L. is called the Dufour effect [12] and describes heat flow caused by concentration gradients. The... 

Thermal transpiration and thermal diffusion effects have been neglected in developing the dusty gas model, and will be neglected throughout the rest of the text. The physics of these phenomena and the justification for neglecting them are discussed in some detail in Appendix I. 

Thermal diffusion effects will be neglected throughout, so the flux relations are given by equations (3.17) - (3.19), which are repeated here for convenience ... 

Thermal transpiration and thermal diffusion will not be considered here, but it would be incorrect to assume that their influence is negligible, or even small in all circumstances. Recent results of Wong et al. [843 indi cate that they may Influence computed values of the effectiveness factor iby as much as 30. An account of thermal transpiration and thermal diffu-Ision is given in Appendix I. 

When developing the dusty gas model flux relations in Chapter 3, the thermal diffusion contributions to the flux vectors, defined by equations (3.2), were omitted. The effect of retaining these terms is to augment the final flux relations (5.4) by terms proportional to the temperature gradient. Specifically, equations (5.4) are replaced by the following generalization... 

It is also interesting to examine the relative importance of thermal transpiration and thermal diffusion in the two limiting cases. From equations (A. 1.12) and (A. 1.13)... 

Finally, let us return to the question of the practical importance of thermal diffusion and thermal transpiration in modeling reactive catalyst... 

Fig. 4. Thermal diffusivity of silicon-based stmctural ceramics (a) reaction-bonded SiC (b) hot-pressed and sintered SiC (c) hot-pressed (1% MgO,...

Prandt/Number. The Prandtl number, Pr, is the ratio of the kinematic viscosity, V, to the thermal diffusivity, a. 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Gaseous diffusion and thermal diffusion data may be found in References 8 and 9. 

In the oxidation process, a layer of dopant is apphed to the surface of sihcon and patterned sihcon dioxide for subsequent thermal diffusion into the sihcon. The masking property of the Si02 is based on differences in rates of diffusion. Diffusion of dopant into the oxide is much slower than the diffusion into the sihcon. Thus, the dopants reach only the sihcon substrate. Oxide masks are usually 0.5—0.7 p.m thick. 

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