Interphase heat transfer

These equations allow for interphase heat transfer with hi as the heat transfer coefficient. As written, they envision heat transfer to the environment to occur only through the liquid phase since it is normally the continuous phase. 

Regarding mass transfer, the slowest step is normally pore diffusion rather than external mass transfer, whilst for heat transfer the slowest step is the interphase heat transfer between the particle and the fluid phase rather than the internal heat transfer in the solid particle. 

The Biot number Bib for heat transport. Analogous to Bim, this is defined as the ration of the internal to external heat transfer resistance (intraparticle heat conduction versus interphase heat transfer). 

Film and Pore Diffusion Together with Interphase Heat Transfer... 

Figure 10. Effectiveness factor ij as a function of the Weisz modulus ji. Combined influence of intraparticle and interphase mass transfer and interphase heat transfer on the effective reaction rate (first order, irreversible reaction in a sphere, Biot number Bim = 100, Arrhenius number y — 20, modified Prater number ( as a parameter).

In reality, the Biot number for mass transport in most cases is considerably higher than the Biot number for heat transport, i.e. the ratio r is frequently larger than 40-50 [19]. This means that the catalyst pellet can usually be treated as isothermal, at a temperature level which is controlled by the interphase heat transfer resistance. However, this leads to a reduction of the general problem to the case which has already been treated in the previous section. 

Criteria have also been developed for evaluating the importance of intraphase and interphase heat transfer on a catalytic reaction. The Anderson criterion for estimating the significance of intraphase temperature gradients is [J. B. Anderson, Chem. Eng. Sci., 18 (1963) 147] ... 

Gillespie, B.M. Crandall, E.D. Carberry, J.J. Local and average interphase heat transfer coefficients in a randomly packed bed of spheres. Amer. Inst. Chem. Eng. J. 14 (1968) 483-490... 

Gas-solid (catalytic) reactions. Mass transfer is likely to be more important within the pellet than in the external film, and heat transfer more important in the film than within the pellet. In other words, intraphase mass transfer and interphase heat transfer would normally be the dominant transport processes. Thus the pellet can reasonably be assumed to be isothermal. 

Meltser, V.L. and Pisarik, N.K. 1980. Interphase heat transfer in impinging single and two-phase streams. Proceedings of the XI All Russian Conference on Heat and Mass Transfer, 6(1) 132-135 (in Russian). 

Damkohler jiej, fiscal heat liberated/inter-phase heat transfer coefficient R/ h Tj et a = area/vol. of catalyst h = interphase heat transfer coefficient R = ideal gas constant... 

Superheated steam has heat transfer properties superior to air at the same temperature. Since there is no resistance to diffusion of the evaporated water in its own vapor, the drying rate in the constant rate period is dependent only on the heat transfer rate. The convective heat transfer coefficient (h) between steam and the solid material surface can be estimated using standard correlations for interphase heat transfer. Neglecting sensible heat effects, heat losses, and other modes of heat transfer, the rate at which surface moisture evaporates into steam is given simply by... 

For many chemical reactions we will also have to consider the effects of physical transport phenomena. This is the case when mixing rates are relevant, or when we have heterogeneous reactions (with two or more phases). For such situations it is better to skip Chapter 3 and move on to Chapter 4, where the problems of physical contacting of reactants (such as mixing and mass transfer between two phases) are discussed, as well as interphase heat transfer. For many chemical reactions the way of contacting the reactants will determine the reactor configuration, or indeed the type of reactor we will have to use. 

The parameter Qi is the interphase heat transfer term expressed as... 

Borowiec et al. (XL) presented a steady state model for a counterCTjrrent moving-bed gasifier by considering the effect of interphase heat transfer coefficient on temperature and composition profiles, and on the location of the combustion zone. 

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