Temperature effects thermal conductivity

The nondimensional parameter /) (positive for exothermic reactions) is a measure of nonisothermal effects and is called the heat generation function. It represents the ratio between the rate of heat generation due to the chemical reaction and the heat flow by thermal conduction. Nonisothermal effects may become important for increasing values of /3, while the limit (3 - 0 represents an isothermal pellet. Table 9.1 shows the values of [3 and some other parameters for exothermic catalytic reactions. For any interior points within the pore where the reactant is largely consumed, the maximum temperature difference for an exothermic reaction becomes... 

Li, J., L. J. Porter, and S. Yip, Atomistic Modeling of Finite-temperature Properties of Crystalline B-SiC. II.Thermal Conductivity and Effects of Point Defects. Journal of Nuclear Materials, 1998. 255 p. 139-152. 

In an experimental apparatus utilizing constant (and known) drying conditions, change in weight of the two-layer slab as well as the temperature of the evaporation front must be measured as functions of time. Appropriate plots of Equations 2.33 and 2.36 using this data yield the effective and thermal conductivity of the dry layer. An example of the determination of the thermal conductivity and effective dif-fusivity coefficients of dry layers follows. 

Here, p is the density, k is the thermal conductivity, Pi is the fluid dynamic viscosity, p is the pressure, T is the temperature, u is the velocity vector, Cp is the specific heat capacity, d> is the viscous dissipation, and the subscripts f and s represent fluid and solid, respectively. For nanofluids, the corresponding effective thermal conductivities and effective fluid dynamic viscosities will be introduced. 

HEAT EXCHANGERS [see also HEAT TRANSFER. THERMAL CONDUCTIVITY] The Effect of Some Variables in Low Temperature Processes (1) 342 Freeze-out Purification of Gases in Heat Exchangers (2) 45... 

A typical, unsealed plot of versus the nonisothermal Thiele modulus is shown in Figure 9.10. Two additional parameters that contain the thermal factors make their appearance here the Arrhenius number EJRT which contains the important activation energy E and the dimensionless parameter P, which reflects the effect due to the heat of reaction and the transport resistances. For p = 0 (i.e., for a vanishing heat of reaction or infinite thermal conductivity), the effectiveness factor reduces to that of the isothermal case. P > 0 denotes an exothermic reaction, and here the rise in temperature in the interior of the pellet is seen to have a significant impact on E which may rise above unity and reach values as high as 100. This means that the overall reaction rate in the pellet is up to 100 times faster than would be the case at the prevailing surface conditions. This is due to the strong exponential dependence of reaction rate on temperature, as expressed by the Arrhenius relation... 

When an atom or molecule receives sufficient thermal energy to escape from a Hquid surface, it carries with it the heat of vaporization at the temperature at which evaporation took place. Condensation (return to the Hquid state accompanied by the release of the latent heat of vaporization) occurs upon contact with any surface that is at a temperature below the evaporation temperature. Condensation occurs preferentially at all poiats that are at temperatures below that of the evaporator, and the temperatures of the condenser areas iacrease until they approach the evaporator temperature. There is a tendency for isothermal operation and a high effective thermal conductance. The steam-heating system for a building is an example of this widely employed process. 

The heat pipe has properties of iaterest to equipmeat desigaers. Oae is the teadeacy to assume a aeady isothermal coaditioa while carrying useful quantities of thermal power. A typical heat pipe may require as Htfle as one thousandth the temperature differential needed by a copper rod to transfer a given amount of power between two poiats. Eor example, whea a heat pipe and a copper rod of the same diameter and length are heated to the same iaput temperature (ca 750°C) and allowed to dissipate the power ia the air by radiatioa and natural convection, the temperature differential along the rod is 27°C and the power flow is 75 W. The heat pipe temperature differential was less than 1°C the power was 300 W. That is, the ratio of effective thermal conductance is ca 1200 1. 

Thickness. The traditional definition of thermal conductivity as an intrinsic property of a material where conduction is the only mode of heat transmission is not appHcable to low density materials. Although radiation between parallel surfaces is independent of distance, the measurement of X where radiation is significant requires the introduction of an additional variable, thickness. The thickness effect is observed in materials of low density at ambient temperatures and in materials of higher density at elevated temperatures. It depends on the radiation permeance of the materials, which in turn is influenced by the absorption coefficient and the density. For a cellular plastic material having a density on the order of 10 kg/m, the difference between a 25 and 100 mm thick specimen ranges from 12—15%. This reduces to less than 4% for a density of 48 kg/m. References 23—27 discuss the issue of thickness in more detail. 

Phonon transport is the main conduction mechanism below 300°C. Compositional effects are significant because the mean free phonon path is limited by the random glass stmcture. Estimates of the mean free phonon path in vitreous siUca, made using elastic wave velocity, heat capacity, and thermal conductivity data, generate a value of 520 pm, which is on the order of the dimensions of the SiO tetrahedron (151). Radiative conduction mechanisms can be significant at higher temperatures. 

Foam Insulation Since foams are not homogeneous materials, their apparent thermal conductivity is dependent upon the bulk density of tne insulation, the gas used to foam the insulation, and the mean temperature of the insulation. Heat conduction through a foam is determined by convection and radiation within the cells and by conduction in the solid structure. Evacuation of a foam is effective in reducing its thermal conductivity, indicating a partially open cellular structure, but the resulting values are stiU considerably higher than either multilayer or evacuated powder insulations. 

That some enhancement of local temperature is required for explosive initiation on the time scale of shock-wave compression is obvious. Micromechanical considerations are important in establishing detailed cause-effect relationships. Johnson [51] gives an analysis of how thermal conduction and pressure variation also contribute to thermal explosion times. 

Recently, Dinwiddie et al. [14] reported the effects of short-time, high-temperatme exposures on the temperature dependence of the thermal conductivity of CBCF. Samples were exposed to temperatures ranging from 2673 to 3273 K, for periods of 10, 15, and 20 seconds, to examine the time dependent effects of graphitization on thermal conductivity measured over the temperature range from 673 to 2373 K. Typical experimental data are shown in Figs. 7 and 8 for exposure times of 10 and 20 seconds, respectively. The thermal conductivity was observed to increase with both heat treatment temperature and exposure time. 

Figures 7 and 8 show thermal conductivity data for CBCF after exposure to temperatures of 2673, 2873, 3073, and 3273 K, for 5.7 and 15 7 seconds, respectively. The symbols in the Figs. 7 and 8 represent measured thermal conductivity values, and the solid lines are the predicted behavior from Eqs. (5) through (8) The model clearly accounts for the effects of measurement temperature, exposure tune, and exposure temperature The fit to the data is good (typically within 10%). However, the fit to the as fabricated CBCF data (Fig 6) was less good (-20%), although the scatter in the data was larger because of the much lower heat treatment temperature (1873 K) in that case.

Dinwiddie, R.B., Nelson, G.E., and Weaver, C.E., The effect of sub-minute high temperature heat treatments on the thermal conductivity of carbon-bonded carbon fiber (CBCF) insulation. In Proc. Thermal Conductivity 23, ed. K.E. Wilkes, R.B. Dinwiddie and R.S. Graves, Technomic Pub. Co., Inc., Lancaster, PA, 1996, pp. 466 477. 

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