Coefficient thermal diffusivity

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).

Coefficient of heat transfer Diffusion coefficient Flux of a quantity x Heat flow rate Kinematic viscosity Mass flow rate Mass-transfer coefficient Thermal conductivity Thermal diffusion coefficient Thermal diffusivity Viscosity Volume flow rate... 

The dimensionless retention parameter X of all FFF techniques, if operated on an absolute basis, is a function of the molecular characteristics of the compounds separated. These include the size of macromolecules and particles, molar mass, diffusion coefficient, thermal diffusion coefficient, electrophoretic mobility, electrical charge, and density (see Table 1, Sect. 1.4.1.) reflecting the wide variablity of the applicable forces [77]. For detailed theoretical descriptions see Sects. 1.4.1. and 2. For the majority of operation modes, X is influenced by the size of the retained macromolecules or particles, and FFF can be used to determine absolute particle sizes and their distributions. For an overview, the accessible quantities for the three main FFF techniques are given (for the analytical expressions see Table l,Sect. 1.4.1) ... 

The retention is related to the size, charge, diffusion coefficient, thermal diffusion factor, and so forth of the separated species in polarization FFF. As concerns the focusing FFF, the retention is usually related with the intensive properties of the fractionated species. Consequently, the FFF can be used to characterize the properties related to the retention. Because the entry Focusing FFF of Particles and Macromolecules is fully devoted to the focusing FFF, only the polarization FFF methods will be described here. 

Transient heat conduction or mass transfer in solids with constant physical properties (diffusion coefficient, thermal diffusivity, thermal conductivity, etc.) is usually represented by a parabolic partial differential equation. For steady state heat or mass transfer in solids, potential distribution in electrochemical cells is usually represented by elliptic partial differential equations. In this chapter, we describe how one can arrive at the analytical solutions for linear parabolic partial differential equations and elliptic partial differential equations in semi-infinite domains using the Laplace transform technique, a similarity solution technique and Maple. In addition, we describe how numerical similarity solutions can be obtained for nonlinear partial differential equations in semi-infinite domains. 

The critical material properties for refractory oxides are dictated by a given application. In some applications, thermal expansion and strength may be most important while in other situations melting temperature and thermal conductivity are important. In general, the most important material properties for refractory oxides include melting temperature, thermal expansion coefficient, thermal diffusivity and conductivity, elastic modulus, and heat capacity. 

It is demonstrated in [8] that the transport coefficients (thermal diffusivity, diffusion coefficient, fluidity, etc.) considered in the Fourier approximation are proportional to the stability coefficients. This makes it possible to determine whether we are dealing with a critical transition or a limited phase transition of the second kind and, in the latter case, which of the parameters are characteristic. In critical transitions, the transport coefficients decrease strongly, whereas in limited transitions of the second kind they tend to infinite values. This criterion shows that phase transitions of the second kind which occur in binary alloys, polymers, ferromagnets, ferroelectrics, liquid crystals, etc., are essentially transcritical transitions, which are sometimes close to the critical conditions because the values of the transport coefficients decrease strongly at the transition point. The occurrence of superfluidity in He H demonstrates that, even in the absence of a coordinate or a derivative which tends to zero, this substance is a superphase in the kinetic sense. 

Table 7.5 Soret Coefficients, Thermal Diffusion Coefficients, and Heats of Transport for Aqueous Ethylene Glycol and Polyethylene Glycol (PEG) Solutions at 25 °C (Chan et al., 2003)...

The retention is related to the size, charge, diffusion coefficient, thermal diffusion factor, and so forth of the separated species in polarization FFF, whereas it is exclusively... 

Continuous models are easy to implement and, therefore, have been widely used to describe the drying of deformable porous media (e.g., see Chapters 3 and 4, Volume 1 of this series). In these models, gel properties are expressed in terms of average parameters (or parameter functions) such as the diffusion coefficient, thermal diffusivity and Young s modulus, and partial differential equations for mass, heat and momentum balances are solved by discretization ( top-down approach). 

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. 

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... 

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

The dimensionless parameter Dpc / is called the Lewis number, which is the ratio of the diffusion coefficient of a gas through the mixture divided by the thermal diffusion coefficient of the gas mixture. 

Whereas the kinematic viscosity fx/p, the thermal diffusivity k/Cpp, and the diffusivity D are physical properties of the system and can therefore be taken as constant provided that physical conditions do not vary appreciably, the eddy coefficients E, Eh, and ED will be affected by the flow pattern and will vary throughout the fluid. Each of the eddy coefficients is proportional to the square of the mixing length. The mixing length will ... 

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