Effective thermal conductivity comparison

By comparison with a fixed-bed gas-liquid reaction, a three-phase fluidized-bed reactor offers the advantage of very high effective thermal conductivity and, therefore, a more uniform temperature distribution in the reactor. Van Driesen and Stewart139 have demonstrated this for large-scale catalytic desulfurization and hydrocracking of heavy petroleum fractions. 

The two-dimensional method has resulted in better agreement than the simplified approach, but the computed conversions are still less than the experimental results. In view of the problems in estimating the radial heat- and mass-transfer rates, and possible uncertainties in kinetic rate data, the comparison is reasonably good. The net effect of allowing for radial heat and mass transfer is to increase the conversion. The computed results are sensitive to rather small variations in the effective thermal conductivities and diffusivities, which emphasizes the need for the best possible information concerning these quantities. 

Figure 1. Comparison of effective thermal conductivities for porous acrylic, polypropylene, wool and cotton.

In the following, after reviewing the requirements for the validity of the assumption of the local thermal equilibrium, the attempt at predicting the effective thermal conductivity is reviewed along with some correlations and comparisons with experimental results... 

FIGURE 9.4 Comparison of several correlations for the effective thermal conductivity with experimental results from several sources. 

U. Hoffmann, G. Emig and H. Hofmann Comparison of different determination methods for effective thermal conductivity of porous catalysts, ACS Symp.Ser. 65(1978)189-200 /23/ R. Broucek, G. Emig and H. Hofmann Rechnergesteuerter Kreislaufreaktor fiir kinetische Untersuchungen,Chem.Ing.Techn. (1984) 236-237... 

The dependence of the local Nusselt number on non-dimensional axial distance is shown in Fig. 4.3a. The dependence of the average Nusselt number on the Reynolds number is presented in Fig. 4.3b. The Nusselt number increased drastically with increasing Re at very low Reynolds numbers, 10 < Re < 100, but this increase became smaller for 100 < Re < 450. Such a behavior was attributed to the effect of axial heat conduction along the tube wall. Figure 4.3c shows the dependence of the relation N /N on the Peclet number Pe, where N- is the power conducted axially in the tube wall, and N is total electrical power supplied to the tube. Comparison between the results presented in Fig. 4.3b and those presented in Fig. 4.3c allows one to conclude that the effect of thermal conduction in the solid wall leads to a decrease in the Nusselt number. This effect decreases with an increase in the... 

De Wasch and Froment (1971) and Hoiberg et. al. (1971) published the first two-dimensional packed bed reactor models that distinguished between conditions in the fluid and on the solid. The basic emphasis of the work by De Wasch and Froment (1971) was the comparison of simple homogeneous and heterogeneous models and the relationships between lumped heat transfer parameters (wall heat transfer coefficient and thermal conductivity) and the effective parameters in the gas and solid phases. Hoiberg et al. (1971)... 

Figure 3.47 shows the evolution of the heating process of the composite block and how it attains a complex steady state structure with the surface zones covered by complicated isothermal curves (see also Fig. 3.46). Secondly, this figure shows how the brick with the higher thermal conductivity is at steady state and remains the hottest during the dynamic evolution. As explained above, this fact is also shown in Fig. 3.46 where all high isothermal curves are placed in the area of the brick with highest thermal conductivity. At the same time an interesting vicinity effect appears because we observe that the brick with the smallest conductivity does not present the lowest temperature in the centre (case of curve G compared with curves A and B). The comparison of curves A and B, where we have X = 0.2, with curves C and D, where X = 0.4, also sustains the observation of the existence of a vicinity effect. In Fig. 3.48, we can also observe the effect of the highest thermal conductivity of one block but not the vicinity effect previously revealed by Figs. 3.46 and 3.47. If we compare the curves of Fig. 3.47 with the curves of Fig. 3.48 we can appreciate that a rapid process evolution takes place between T = 0 and T = 1. Indeed, the heat transfer process starts very quickly but its evolution from a dynamic process to steady state is relatively slow.

The use of local theories, incorporating parameters such as the eddy viscosity Km and eddy thermal conductivity Ke, has given reasonable descriptions of numerous important flow phenomena, notably large scale atmospheric circulations with small variations in topography and slowly varying surface temperatures. The main reason for this success is that the system dynamics are dominated primarily by inertial effects. In these circumstances it is not necessary that the model precisely describe the role of turbulent momentum and heat transport. By comparison, problems concerned with urban meso-meteorology will be much more sensitive to the assumed mode of the turbulent transport mechanism. The main features of interest for mesoscale calculations involve abrupt... 

Thermal Conductivity. The results of the thermal conductivity, k, tests are given in Table VII for four different mixture ratios representing S/A ratios of 1.3 to 10. The data indicate that additional sulfur had little effect on the thermal conductivity, which averaged 11.7 X 10 4 cal-cm/ cm2-sec-°C (3.40 X Btu-in./ft2-hr-°F). A comparison with the value obtained for the A/C system of 15.77 cal-cm/cm2-sec-°C (4.57 Btu-in./ft2-hr-°F) would indicate that the thermal conductivity is about 25% less for S-A—S than for A/C. This is attributed to the higher air void contents in the former which add to the insulative characteristics of the material. 

Park et al (1999) conducted the research project on the prediction of temperature distribution around rock cavern on pilot scale in Korea. They proposed that the specific heat increased 25% and thermal conductivity is decreased 23% that of intact value from comparison of the predicted and measured temperature. They also proposed that change of thermal properties are caused from the effect of groundwater and joint for the reason that discontinuity makes thermal conductivity lower and water content makes thermal conductivity and specific heat higher. 

In view of the complex nature of the mass-transfer process only, an order-of-magnitude calculation was performed, primarily to obtain a value for comparison with the thermal effect described above. The following assumptions are necessary (1) the fluid within the capillary tube and cold volume possess infinite thermal conductivity (2) transition volume effects are neglected and (3) laminar flow prevails in the capillary tube. It then follows that a step temperature rise in the cold volume must result in the transfer of a quantity of mass, AM, across the cold-warm boundary. This mass immediately achieves the warm temperature and must subsequently be transferred throughout the system until pressure equilibrium is again achieved. A description of this transfer may be described in time as... 

Shock tube studies of fast reactions are subject to several commonly recognized physical effects, some advantageous and others not. The spatial gradient in the time origin of a chemical reaction in the postshock volume makes for a reaction zone profile with accountable axial gradients in molecular concentrations, temperature, and flow speed. Fortunately, however, the transport processes of diffusion, thermal conduction, and viscous dissipation are so slow in comparison with the... 

Having established that the thermal conductivity of most metals is affected by the magnetic field, the question is How does the field effect compare to that caused by lot-to-lot composition variations and different thermal histories In most cases, ideal data for making the desired comparisons are not available. But by making use... 

For many applications of filled polymers, knowledge of properties such as permeability, thermal and electrical conductivities, coefficients of thermal expansion, and density is important. In comparison with the effects of fillers on mechanical behavior, much less attention has been given to such properties of polymeric composites. Fortunately, the laws of transport phenomena for electrical and thermal conductivity, magnetic permeability, and dielectric constants often are similar in form, so that with appropriate changes in nomenclature and allowance for intrinsic differences in detail, a general solution can often be used as a basis for characterizing several types of transport behavior. Useful treatments also exist for density and thermal expansion. 

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