Effective terms thermal conductivity

Eqns. (3) - (9) enable the effective radial thermal conductivity (kr>eff), the apparent wall heat transfer coefficient (hw>eff) and the overall heat transfer coefficient (U) to be predicted in terms of the physical properties p, kg and Cp of air, together with measurable parameters such as , 6, dt, kp, dp (A), dp>(v), dp>(V/A), e and T, the mean bed temperature. The predicted and observed values of U are compared in Figure 6. The averaged normalised standard error... 

Some workers have correlated experimental data in terms of k at the arithmetic mean temperature, and some at the temperature of the bulk plasma. Experimental validation of the true effective thermal conductivity is difficult because of the high temperatures, small particle sizes and variations in velocity and temperature in plasma jets. 

The Chemkin package deals with problems that can be stated in terms of equation of state, thermodynamic properties, and chemical kinetics, but it does not consider the effects of fluid transport. Once fluid transport is introduced it is usually necessary to model diffusive fluxes of mass, momentum, and energy, which requires knowledge of transport coefficients such as viscosity, thermal conductivity, species diffusion coefficients, and thermal diffusion coefficients. Therefore, in a software package analogous to Chemkin, we provide the capabilities for evaluating these coefficients. ... 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

Cook has propounded a rather different theory of the nature of the reaction zone. He emphasises that the demonstrable electrical conductivity of the detonation wave is evidence of a high thermal conductivity. Both these effects are ascribed to ionisation of the explosion products. In terms of the reaction zone, this implies a steady pressure with no peaks. 

Effective Thermal Conductivities of Porous Catalysts. The effective thermal conductivity of a porous catalyst plays a key role in determining whether or not appreciable temperature gradients will exist within a given catalyst pellet. By the term effective thermal conductivity , we imply that it is a parameter characteristic of the porous solid structure that is based on the gross geometric area of the pellet perpendicular to the direction of heat transfer. For example, if one considers the radial heat flux in a spherical pellet one can say that... 

This equation may be used as an appropriate form of the law of energy conservation in various pseudo homogeneous models of fixed bed reactors. Radial transport by effective thermal conduction is an essential element of two-dimensional reactor models but, for one-dimensional models, the last term must be replaced by one involving heat losses to the walls. 

No attempt will be made here to extend our results beyond the simple lowest-order limiting laws the often ad hoc modifications of these laws to higher concentrations are discussed in many excellent books,8 11 14 but we shall not try to justify them here. As a matter of fact, for equilibrium as well as for nonequilibrium properties, the rigorous extension of the microscopic calculation beyond the first term seems outside the present power of statistical mechanics, because of the rather formidable mathematical difficulties which arise. The main interests of a microscopic theory lie both in the justification qf the assumptions which are involved in the phenomenological approach and in the possibility of extending the mathematical techniques to other problems where a microscopic approach seems necessary in the particular case of the limiting laws, obvious extensions are in the direction of other transport coefficients of electrolytes (viscosity, thermal conductivity, questions involving polyelectrolytes) and of plasma physics, as well as of quantum phenomena where similar effects may be expected (conductivity of metals and semi-... 

Salamone and Newman (SI) recently studied heat transfer to suspensions of copper, carbon, silica, and chalk in water over the concentration range of 2.75 to 11.0% solids by weight. These authors calculated effective thermal conductivities from the heat transfer data and reached conclusions which not only contradicted Eqs. (35) and (36), but also indicated a large effect of particle size. However, if one compares the conductivities of their suspensions at a constant volume fraction of solids, the assumed importance of particle size is no longer present. It should also be noted that their calculational procedure was a difficult one in that it placed all undefined errors present in the heat transfer data into the thermal conductivity term. For example, six of the seven-... 

It seems to me that we can scarcely progress in our understanding of the structural and kinetic effects of the H-bond without knowing the AG and AH terms involved, so I intend to discuss some methods of determining them. The references will provide simple examples of the methods mentioned. The most significant AG and AH values are those evaluated from equilibrium measurements in the gas phase—either by classical vapour density measurements, the second virial coefficient [1], or from, spectroscopic, specific heat or thermal conductance [2], or ultrasonic absorptions [3]. All these methods essentially measure departures from the ideal gas laws. The second virial coefficient provides a measure of the equilibrium constant for the formation of collision dimers in the vapour as was emphasized by Dr. Rowlinson in the discussion, this factor is particularly significant as only the monomer-dimer interaction contributes to it. 

All of the heat transfer terms considered are summarized in Table 5.5. Except for thermal conductivity of the gas, all the effects contribute only a few percent to the heat transfer. However, if nitrogen were used as the carrier gas, the TC term would be six times lower, and the other terms would be more important... 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

The term thermal properties is open to more than one interpretation. Specific heat, thermal conductivity and diffusivity clearly come under this heading but the term can be taken to also include heat ageing, low temperature tests and fire resistance. However, these are more properly dealt with, as in this volume, under Effect of Temperature. Thermal analysis is a group of techniques in which a property of a sample is monitored against temperature, or time at a temperature, and, therefore, is also generally concerned with measuring the effect of temperature. Nevertheless, for convenience, a brief overview of thermal analysis is given here. 

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