Effective heat conductivity

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. 

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). 

Increase in effective heat conductivity of hydride beds... 

Heat conductivity of hydride powders is insignificant, 0.3-lW/(m-K). For improvement of effective heat conductivity of a hydride reactor stuffing in it enter a skeleton from a high-temperature material (copper, aluminium, nickel). The design of such skeleton can be variously. For example, it can be as radial disks (a plate reactor), as a goffered insert (from the punched foil or a grid), the grids braided in a spiral, cellular bodies. 

In case of application of high heat-conducting materials (Am Xh) takes place cffr m(l-s), effa h/s- That is application of the radial copper ribs established, for example, with porosity s=0.9 results in increase in effective heat conductivity in a radial direction (conterminous with a direction of a heat flow) up to values 40 W/(m-K) and during too time heat conductivity in an axial direction remains small ( effa l-lXh). This restriction and also not adaptability to manufacture of a design result in limited use of plate reactors. 

Application of foamy materials provides uniform on directions effective heat conductivity which can be estimated for the idealized three-dimensional structure under the formula ... 

The analysis shows, that for these structures A.ern there is only a function of a material of a skeleton and its porosity and weakly depends on heat conductivity of hydride. At characteristic for designs of reactors of porosity of cellular bodies (nickel, aluminium, copper) 0.9changes over a wide range 3[Pg.390]

The factor of the resulted heat emission of a hydride bed generally is proportional to effective heat conductivity of a bed and inversely proportional to thickness of a bed. The analysis of these equation shows, that factor of a heat transfer less than smaller factor of a heat emission and consequently it is of no used to increase strongly one of them, thus, not changing another. Results of experiments show, that for brazed and diffusion welded connections of the sorber case and heat-conducting insert R=(0.5-1.5) TO 5 (m2 K)/W. At contact of an insert and the case on tight fit R increases in 10-100 times and influence of contact resistance becomes comparable with influence of the resulted heat emission of a hydride bed. 

Porosity, gas permeability, effective heat conductivity of a hydride bed... 

The fact that the effective heat conduction within the catalyst pellet normally is not the crucial process in determining the excess temperature of the catalyst pellet can be illustrated by analyzing the contribution of the interphase temperature gradient to the total excess temperature. To demonstrate this, we first eliminate the common reaction term occurring in the mass and enthalpy balances (eqs 32 and 33) ... 

A special type of fluid-solid catalyzed reaction is obtained when either the reaction rate is so fast that the reactants become completely exhausted at the external catalyst surface (i.e. at very high reaction temperatures) or when the catalyst is nonporous. Then, pore diffusion and effective heat conduction inside the pellet need not be considered. Thus, the problem is reduced to a treatment of the coupled interphase heat and mass transport. 

Table 2. Correlations to calculate the effective heat conductivity in a catalyst bed and heat transfer coefficient to the reactor wall [8, 39],...

For Rep < 100 and 0.05 < rp/r, < 0.2, wall Biot numbers range between 0.8 and 10 [28], so this means that wall effects cannot be neglected a priori [38]. Also this criterion contains procurable parameters. For the wall heat transfer coefficient hw and the effective heat conductivity in the bed Abc(r, the correlations in Table 2, eqs. 44-47 can be used [8, 39]. These variables are assumed to be composed of a static and a dynamic (i.e. dependent on the flow conditions) contribution. Thermal heat conductivities of gases at 1 bar range from 0.01 to 0.5 Js m l K l, depending on the nature of the gas and temperature. 

Where A, is the effective heat conductivity of the catalyst particle and (-AHt) the heat effect of reaction i. The effective conductivity is the quantity which (when multiplied by the gradient of temperature) yields the true rate of energy transport in the porous structure of the solid. 

The important characteristic for HHM efficiency is the alloy output, i.e. the heat capacity related to weight of hydride alloy. The value achieved for today on the average for a cycle makes 40-100 W/kg. At shortening of a cycle this value grows, but up to achievement of competitive (in comparison with other heat machines of similar type) value in 1000 W/kg [8] are necessary for increasing cardinally amount of active hydrogen, to increase effective heat conductivity of a hydride bed and to optimize operation of system a sorber-heat exchanger. Thus duration of a hill cycle is estimated 2-4 minutes. 

Isothermally Operated Reactors. In an isothermal reactor the temperature of the reactant stream is constant in axial direction. Hence this stream does not take up reaction heat (in the case of an exothermic reaction) and all heat generated within the bed must be transported radially to the reactor wall. If the bed radius is too large and the effective heat conductivity of the bed too low, a radial temperature profile will develop with appreciable differences between the centre of the bed and near the wall. The temperature profile will be more pronounced as the radial distances are longer and as fluid velocities are lower, hence, wide and short reactors are likely to suffer most from radial temperature inhomogeneity. 

An effective way to improve the isothermicity of reactors is to dilute the catalyst with inert particles, preferably of a material with a high heat conductivity, such as silicon carbide (heat conductivity in the solid state about 40 times that of porous alumina). In the diluted bed, the heat generated per unit volume of bed will be lowered, and together with an increased effective heat conductivity this will result in a more even radial temperature distribution. 

Figure 13B shows the calculated temperature differences for the same cases as considered before, but with catalyst beds diluted with silicon carbide to one third of the original catalyst concentration. It can be seen that the temperature differences are appreciably smaller than in the undiluted case (note the differences in temperature scale between Figures 13A and 13B). The dilution with good thermally conducting material is particularly effective at the low velocities in short beds because the convective contribution to the effective heat conductivity is then relatively small. It can be inferred that in microflow reactors (D = 1 cm L = 10 cm) and in bench-scale reactors (D = 2 cm L = 1 m) with diluted beds radial temperature differences are less than 1-2 °C for the considered cases, which is quite acceptable. 

Conduction in the washcoat is described with an effective heat conductivity, and diffusion is Fickian with an effective diffusivity. 

Figure 15.18. Effective heat conductivity of polyethylene vs. filler volume fraction. [Data from Privalko V P, Novikov V V, Adv. Polym. Sci., 119, 1995, 31-77.]...

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