Solid heat dispersion coefficients

Fluid and solid heat dispersion coefficients. The description of heat transfer follows the same lines, with two main distinctions concerning mostly the processes occurring in... 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

Here, the densities of the gaseous and solid fuels are denoted by pg and ps respectively and their specific heats by cpg and cps. D and A are the dispersion coefficient and the effective heat conductivity of the bed, respectively. The gas velocity in the pores is indicated by ug. The reaction source term is indicated with R, the enthalpy of reaction with AH, and the mass based stoichiometric coefficient with u. In Ref. [12] an asymptotic solution is found for high activation energies. Since this approximation is not always valid we solved the equations numerically without further approximations. Tables 8.1 and 8.2 give details of the model. 

Power or energy dissipated in the aerated suspension has to be large enough (a) to suspend all solid particles and (b) to disperse the gas phase into small enough bubbles. It is essential to determine the power consumption of the stirrer in agitated slurry reactors, as this quantity is required in the prediction of parameters such as gas holdup, gas-liquid interfacial area, and mass- and heat-transfer coefficients. In the absence of gas bubbling, the power number Po, is defined as... 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

The particle convective heat transfer component is usually treated on the basis of the penetration or packet theory originally proposed by Mickley and Fairbanks (1955) assuming that the clusters are formed next to the immersed surface (e.g., Subbarao and Basu, 1986 Basu and Nag, 1987 Zhang et ai, 1987 Liu et ai, 1990). In that case, the clusters of solids and voids or dispersed phase are assumed to come into contact with the heat transfer surface alternatively, and the heat transfer coefficient can be given as follows ... 

The concept of nanofluids to further intensify microreactors has been discussed by Fan et al. [17]. The nano-fluids are suspensions of solid nano-partides with sizes typically of 1-100 nm in traditional liquids such as water, glycol and oils. These solid-liquid composites are very stable and show higher thermal conductivity and higher convective heat transfer performance than traditional liquids. They can thus be used to enhance the heat transfer in nanofluids in compact multifunctional reactors. A nanofluid based on Ti02 material dispersed in ethylene glycol showed an up to 35% increase in the overall heat transfer coefficient and a... 

For sound process design, we need values of numerous design parameters such as fractional phase holdups, pressure drop, dispersion coefficients (the extent of axial mixing) of all the compounds, heat and mass transfer coefficients across a variety of fluid-fluid and fluid-solid interfaces depending on the type of multiphase system, type of reactor, and the rate-controlling steps. To clarify the scope of the case studies selected, their salient features are next listed. 

In the two-medium treatment of the single-phase flow and heat transfer through porous media, no local thermal equilibrium is assumed between the fluid and solid phases, but it is assumed that each phase is continuous and represented with an appropriate effective total thermal conductivity. Then the thermal coupling between the phases is approached either by the examination of the microstructure (for simple geometries) or by empiricism. When empiricism is applied, simple two-equation (or two-medium) models that contain a modeling parameter hsf (called the interfacial convective heat transfer coefficient) are used. As is shown in the following sections, only those empirical treatments that contain not only As/but also the appropriate effective thermal conductivity tensors (for both phases) and the dispersion tensor (in the fluid-phase equation) are expected to give reasonably accurate predictions. 

After the formal derivations, the energy equation for each phase ((T)f and (T) ) can be written in a more compact form by defining the following coefficients. Note that both the hydrodynamic dispersion, that is, the influence of the presence of the matrix on the flow (noslip condition on the solid surface), as well as the interfacial heat transfer need to be included. The total thermal diffusivity tensors Dff, D , D/s, and Dv/ and the interfacial convective heat transfer coefficient hsf are introduced. The total thermal diffusivity tensors include both the effective thermal diffusivity tensor (stagnant) as well as the hydrodynamic dispersion tensor. A total convective velocity v is defined such that the two-medium energy equations become... 

The two equations for the mass and heat balance, Eqs. (4.10.125) and (4.10.126) or the dimensionless forms represented by Eqs. (4.10.127), (4.10.128) and (4.10.130), consider that the flow in a packed bed deviates from the ideal pattern because of radial variations in velocity and mixing effects due to the presence of the packing. To avoid the difficulties involved in a rigorous and complicated hydrodynamic treatment, these mixing effects as well as the (in most cases negligible contributions of) molecular diffusion and heat conduction in the solid and fluid phase are combined by effective dispersion coefficients for mass and heat transport in the radial and axial direction (D x, Drad. rad. and X x)- Thus, the fluxes are expressed by formulas analogous to Pick s law for mass transfer by diffusion and Fourier s law for heat transfer by conduction, and Eqs. (4.10.125) and (4.10.126) superimpose these fluxes upon those resulting from convection. These different dispersion processes can be described as follows (see also the Sections 4.10.6.4 and 4.10.7.3) ... 

When a reaction takes place in a two-phase system, considerable temperature differences between the phases may occur. This is generally so when the continuous phase is a gaSy and the reaction takes place in, or at the surface of, a dispersed liquid or solid phase. In these situations the gas flow will transport most of the heat of reaction. Since heat transfer coefficients in gases are relatively low, large temperature differences between the dispersed phase and the gas will result. When the reaction is exothermic, heat and mass are then transferred in opposite directions, and the temperature of the dispersed phase will become much higher than than in the gas (as in the example of the burning log). When the reaction is endothermic, heat and mass are transported in die same directions, and the temperature of the dispersed phase will be lower than in the gas phase. 

Althou correlations of axial and radial dispersion coefficients for gases throu a fixed bed are available (72.) > corresponding dispersion coefficients for solids are difficialt to estimate. The temperature distributions of solids are indeed affected by these dispersion coefficients as well as other factors s ach as heat transfer coefficients. 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

Palytoxin is a white, amorphous, hydroscopic solid that has not yet been crystallized. It is insoluble in nonpolar solvents such as chlorophorm, ether, and acetone sparingly soluble in methanol and ethanol and soluble in pyridine, dimethyl sulfoxide, and water. The partition coefficient for the distribution of palytoxin between 1-butanol and water is 0.21 at 25°C based on comparison of the absorbance at 263 nm for the two layers. In aqueous solutions, palytoxin foams on agitation, like a steroidal saponin, probably because of its amphipathic nature. The toxin shows no definite melting point and is resistant to heat but chars at 300°C. It is an optically active compound, having a specific rotation of -i-26° 2° in water. The optical rotatory dispersion curve of palytoxin exhibits a positive Cotton effect with [a]25o being -i-700° and [a]2,j being +600° (Moore and Scheuer 1971 Tan and Lau 2000). 

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