Heat transfer intraparticle

In the adiabatic case we set Kc = 0 in equation (7.196). The above equations with Kc = 0 also represent the nonporous catalyst pellet with external mass- and heat-transfer resistances and negligible intraparticle heat-transfer resistance but the parameters have a different physical meaning as explained earlier on p. 552. 

Conductive heat transfer is the dominant mode of intraparticle heat transfer. Under low Reynolds number flow situations, conductive heat transfer is also an important mode for fluid heat transfer. This section analyzes the conductive heat transfer characteristics of a... 

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

Note that in the limit of external diffusion control, the activation energy 0b,—>0, as can be shown when substituting Eq. (7-110) inEq. (7-108). For more details on how to represent the combined effect of external and intraparticle diffusion on effectiveness factor for more complex systems, see Luss, "Diffusion-Rection Interactions in Catalyst Pellets. Heat-Transfer Resistances A similar analysis regarding external and intraparticle heat-transfer limitations leads to temperature... 

A comprehensive model for the steam reformer should be developed. This model should take into consideration the characteristics of the combustion chamber as well as the details of the processes taking place in the catalyst tubes steam reforming reaction, coke formation, reoxidation of Ni and rereduction of NiO, mass and heat transfer between the catalyst pellets and the bulk gas (both external and intraparticle), heat transfer between the catalyst tubes and the combustion chamber. .. etc. 

There are many cases where the external mass transfer resistance can be neglected while the external heat resistance in not negligible. In gas-solid systems, external heat transfer resistances are usually much higher than external mass transfer resistances especially for light components. Also there are cases where the intraparticle resistances are appreciable while the intraparticle heat transfer resistance is negligible due to the high thermal conductivity of the metal or metal oxides forming the bulk of the catalyst pellet. 

The isothermal effectiyeness factor When the heat effects are negligible or the external and intraparticle heat transfer coefficients are very large, the particle is isothermal and hence > =1.0 and therefore the two equations reduce to one which in this case is linear ... 

The importance of the intraparticle heat transfer resistance is evident for particles with relatively short contact time in the bed or for particles with large Biot numbers. Thus, for a shallow spouted bed, the overall heat transfer rate and thermal efficiency are controlled by the intraparticle temperature gradient. This gradient effect is most likely to be important when particles enter the lowest part of the spout and come in contact with the gas at high temperature, while it is negligible when the particles are slowly flowing through the annulus. Thus, in the annulus, unlike the spout, thermal equilibrium between gas and particles can usually be achieved even in a shallow bed, where the particle contact time is relatively short. 

During sterilization by heat there are two steps in the heat transfer process -heat transfer to the particle surface and intraparticle heat transfer. Due to the poor mixing characteristics of solid beds and the fact that intraparticle heat transfer is limited to conduction, it is more problematic to ensure sterility of a solid substrate than it is to ensure sterility of a liquid medium. In unmixed beds it is highly likely that the effectiveness of the sterilization process will vary with position. 

In intraparticle heat transfer, the parameter analogous to the effective diffusivity is the effective thermal conductivity, /Ig. The defining equation for the heat flux is... 

Catalyst particles in three-phase fixed-bed reactors are usually completely filled with liquid. Then intraparticle temperature gradients are negligible due to the low effective diffusivities in the liquid phase, as pointed out by Satterfield [13] and Baldi [92]. However, if the limiting reactant and the solvent are volatile, vapor-phase reaction may occur in the gas-filled pores, causing significant intraparticle temperature gradients [109, 110]. In these conditions, intraparticle heat transfer resistance is necessary to describe the heat transfer. 

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