Heat Transfer Under Complicating Factors

Mass and Heat Transfer Under Complicating Factors 

In the last two chapters, relatively simple linear problems of mass and heat transfer were discussed. However, no processes of mass transfer complicated by surface (heterogeneous) or volume (homogeneous) chemical reactions with finite rates have been considered so far. Moreover, it was assumed that the basic parameters of the fluid are temperature- and concentration-independent. This assumption permitted the hydrodynamic part of the problem to be solved first and then the linear thermal or diffusion problem to be considered for a known velocity field. 

In this chapter, some problems of mass and heat transfer with various complicating factors are discussed. The effect of surface and volume chemical reactions of any order on the convective mass exchange between particles or drops and a translational or shear flow is investigated. Linear and nonlinear nonstationary problems of mass transfer with volume chemical reaction are studied. Universal formulas are given which can be used for estimating the intensity of the mass transfer process for arbitrary kinetics of the surface or volume reaction and various types of flow. 

A wide class of nonlinear problems of convective mass and heat exchange is considered taking into account the dependence of the transfer coefficients on concentration (temperature). The results are presented in the form of simple unified formulas for the Sherwood number. 

Nonisothermal flows through tubes and channels accompanied by dissipative heating of liquid are studied. Qualitative features of heat transfer in liquids with temperature-dependent viscosity are discussed. Some issues of film condensation are considered. 

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The general problem of diffusion-reaction for the overall effectiveness factor D is rather complicated. However, the physical and chemical rate processes prevailing under practical conditions promote isothermal particles and negligible external mass transfer limitations. In other words, the key transport limitations are external heat transfer and internal mass transfer. External temperature gradients can be significant even when external mass transfer resistances are negligibly small. 

The slurry reactor has two significant advantages it has the highest volumetric capacity, and the best possibilities for heat transfer. It can often be operated under isothermal conditions (see section 8.3). A consequence is that scaling up is not too difficult. The combined effects of mass transfer and chemical reaction were presented in section S.S.2, eqs. (S.61) and (S.62). These can be used to estimate the quantitative effects for first order surface reactions. For other reaction orders, the same principle can be applied, but the calculations become more complicated. In practice, gas/liquid mass transfer is often the limiting factor, that is when a sufficient amount of finely divided catalyst is used. Therefore effective gas dispersion is essential (see section 4.6.4). 

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