Mass transfer slab equation

If the reactions were not influenced by in-pore diffusion effects, the intrinsic kinetic selectivity would be kjk2(= S). When mass transfer is important, the rate of reaction of both A and X must be calculated with this in mind. From equation 3.9, the rate of reaction for the slab model is ... 

When E, = Ej we see that kjk2 = sA,/sl2 — a ratio independent of temperature. Hence, if the mass-transfer equations are divided they may, for the case E, = E2, be integrated directly and the gradients evaluated at the slab surface, x = L. Thus ... 

Mathematical modeling of mass or heat transfer in solids involves Pick s law of mass transfer or Fourier s law of heat conduction. Engineers are interested in the steady state distribution of heat or concentration across the slab or the material in which the experiment is performed. This steady state process involves solving second order ordinary differential equations subject to boundary conditions at two ends. Whenever the problem requires the specification of boundary conditions at two points, it is often called a two point boundary value problem. Both linear and nonlinear boundary value problems will be discussed in this chapter. We will present analytical solutions for linear boundary value problems and numerical solutions for nonlinear boundary value problems. 

An important application of mass transfer principles deals with the evaporation of a hazardous liquid after an inadvertent spill. Here, the liquid must vaporize and diffuse through the adjacent air. The slab equation (Equation (8.17)), with partial-pressure driving force, may be used ... 

Consider one-dimensional diffusion and zeroth-order chemical reaction in a flat-slab porous wafer-type catalyst. The conditions are approximately isothermal and the inirapellet Damkohler number of reactant A is Aa. intrapellet = VS. The mass transfer equation is solved numerically, not analytically. 

This equation describes many transient heat and mass transfer processes, such as the diffusion of a solute through a slab membrane with constant physical properties. The exact solution, obtained by either the Laplace transform, separation of variables (Chapter 10) or the finite integral transform (Chapter 11), is given as... 

We should expect that the penetration theory result in Equation 9.2-5 and the film theory result in Equation 9.1-3 should bracket all observed mass transfer conditions. After all, the penetration theory is based on transfer into a semi-infinite fluid, and the film theory is based on transfer across a thin film. All of nature should fall between these two limits of semi-infinite slab and thin film. 

The classic description of heat transfer in a combusting composite laminate or plane slab has been provided by Henderson, [1], and this remains the foundation for practically all variations of mass and energy balances attempted since then, (see equation 14.1). The terms of this equation are included in Figure 14.2. to illustrate the locations within the slab where they are relevant. 

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