Concept of Effective Thermal Conductivity

From available data it appears that E is only a few kilocalories per mole. The heat of adsorption AH is generally greater than this, particularly for chemisorption, and is always negative. Therefore the observed effect is a decrease in rate of surface diffusion with increase in temperature. 

From the assumptions and approximations presented, it is clear that, surface diffusion js Jiot jvell junderstoad. lt is. hope.d that impro.V d -interpretations of surface migration will permit a more accurate assessment of its effect on global rates of reaction. When we consider the effect of intraparticle resistances in Secs. 11-6 to 11-11 we shall suppose that the used is the most appropriate value and includes, if necessary, a surface contribution. 

The effective thermal conductivities of catalyst pellets are surprisingly low. Therefore significant intrapellet temperature gradients can exist, and the global rate may be influenced by thermal effects. The effective conductivity is the energy transferred per unit of total area of pellet (perpendicular to the direction of heat transfer). The defining equation, analogous to Eq. (11-18) for mass transfer, may be written 

CHAPTER 11 REACnON AND DIFFUSION WITHIN POROUS CATALYSTS 

The theory of heat transfer in porous materials has not been developed 

---

Implicit in this equation is the assumption that because of a large vascular surface area, the blood temperature equilibrates with the tissue temperature. The concept of effective thermal conductivity has been used by several investigators in thermal physiology (Shitzer and Eberhart, 1985). Jain and Wei (1977) also used this concept to describe the drug distribution in tumors. 

Although the heat flow and fluid flow in packed beds are quite complex, the heat transfer characteristics can be described by a simple concept of effective thermal conductivity Ke that is based on the assumption that on a macroscopic scale the bed can be described by a continuum. Effective thermal conductivity is a continuum property that depends on temperature, bed material, and structure. It is usually determined by evaluating the steady-state heat flux between two parallel plates separated by a packed bed. The effective thermal conductivity applies very accurately to steady-state heat transfer and to unsteady-state heat transfer if (t d2p) > 1.94 x 107 s/m2 [27] in other cases, for unsteady state heat transfer the thermal... 

Packed-bed heat transfer can be conveniently expressed by the concept of effective thermal conductivity, which is based on the assumption that on a macroscale the bed can be described by a continuum. In general, the effective thermal conductivity increases with increasing operating pressure. The wall-to-bed heat transfer coefficient increases with decreasing particle diameter. 

In order to further validate the modeling approach, the hot disk method with transient thermal analysis was used to measure the temperature-dependent effective thermal conductivity [21]. This experimental technique is based on the concept of the transient hot strip (THS) technique, first introduced by Gustafsson [22] and currently accepted as one of the most convenient techniques for studying effective thermal conductivity [23, 24]. One advantage is that the apparatus employs a comparatively large specimen that allows analyzing the material in its proper structure rather than a small nonrepresentative coupon. 

A 2.54-cm Styrofoam plastic foam with thermal conductivity of ca 0.03 W/ (m-K) (0.21 (Btu-in.)/(ft-b°F)) is equivalent to 61 cm of gravel. Any synthetic foam having compressive strength sufficiently high and thermal conductivity sufficiently low is effective. However, the resistance of PS-type foams to water, frost damage, and microorganisms in the sod makes them especially desirable. An interesting and important appHcation of this concept was the use of Styrofoam in the constmction of the Alaska pipeline. In this case, the foam was used to protect the permafrost. 

That is, thermal contact resistance is the inverse of thermal contact conductance. Usually, thermal contact conductance is reported in the jiterature, but the concept of thermal contact resistance serves as a better vehicle for explaining the effect of interface on heat transfer. Note that represents thermal contact resistance per unit area. The thermal resistance for the entire interface is obtained by dividing by the apparent interface area/t. 

Dalla Betta et al. first proposed an inert porous layer, or diffusion barrier, to prevent temperature runaway, and loosely interpreted the effect in terms of a reduction in the rate of combustion. A more rigorous interpretation of the effect of an inert porous layer on catalyst temperature was provided by McCarty et al, who also described the desired properties for diffusion layer materials, including a high thermal conductivity and low specific combustion activity. These authors stated that the high washcoat temperatures found in catalytic combustion of natural gas were due to the high diffusivity of methane in air, which causes the diffusion rate to the catalyst surface to match the rate of heat dissipation by conduction to the gas phase. The diffusion barrier decreases the rate of diffusion of methane to the catalyst surface, thus reducing the catalyst temperature. Modeling work by Hayes et al. confirmed those concepts. ... 

Equations 6.100 and 6.102 with ts = te = 1, t = / have been solved for real air in Ref. 16 and in Refs. 51-55, with the latter references utilizing the concept of total properties kT, cpT, Prr. The air properties of Ref. 56 were employed in all the studies except that of Ref. 55, which employed properties evaluated in Refs. 57 and 58, where careful consideration was given to the effect of dominant resonant charge exchange cross sections in establishing the thermal conductivity of ionized nitrogen. 

Insufficient chemical resistance of a blend at times leads to its rejection for use in an aggressive chemical environment, although it possesses an excellent combination of mechanical properties. Thus chemical and solvent effects on polymer blends are important factors that frequently determine blends applicability. Attention has been given to chemical resistance of blends starting from the fundamental concept of the solubility parameters. Apart from the chemical and environmental restrictions, thermal resistance of a polymer blend is often a major criterion for its applicability. Thus, the thermal conductivity, heat capacity and heat deflection temperature of polymeric materials are discussed in separate sections. 

---