Bird, Stewart Lightfoot

Bird, Stewart and Lightfoot, Transpoii Phenomena, Wiley, 1960. 

General References Bird, Stewart, and Lightfoot, Transpoii Fhenomena,... 

Microscopic Balance Equations Partial differential balance equations express the conservation principles at a point in space. Equations for mass, momentum, totaf energy, and mechanical energy may be found in Whitaker (ibid.). Bird, Stewart, and Lightfoot (Transport Phenomena, Wiley, New York, 1960), and Slattery (Momentum, Heat and Mass Transfer in Continua, 2d ed., Krieger, Huntington, N.Y., 1981), for example. These references also present the equations in other useful coordinate systems besides the cartesian system. The coordinate systems are fixed in inertial reference frames. The two most used equations, for mass and momentum, are presented here. 

The combined diffusivity is, of course, defined as the ratio of the molar flux to the concentration gradient, irrespective of the mechanism of transport. The above equation was derived by separate groups working independently (8-10). It is important to recognize that the molar fluxes (Ni) are defined with respect to a fixed catalyst pellet rather than to a plane of no net transport. Only when there is equimolar counterdiffusion, do the two types of flux definitions become equivalent. For a more detailed discussion of this point, the interested readers should consult Bird, Stewart, and Lightfoot (11). When there is equimolal counterdiffusion NB = —NA and... 

When the mean free path is small compared with pore diameter, the dominating experience of molecules is that of collision with other molecules in the gas phase. In that respect, the situation is much the same as that which exists in the bulk gas. The appropriate diffusion coefficient Dm may be obtained from published experimental values, or calculated from a theoretical expression. For molecular diffusion in a binary gas, the Chapman and Enskog equation may be used, as discussed by Bird, Stewart and Lightfoot(32). This takes the form ... 

Bird Stewart and Lightfoot have published tables which give values of and a. 

The collision integral has been evaluated and tabulated by Chapman and Cowling and Hirschfelder, Curtiss, and Bird. Bird, Stewart, and Lightfoot listed the values published by Hirschfelder et al. (1949), and they also tabulated values of ejj for common gases. Numerous correlations have been proposed for estimating Bjj and Ojj, and Ravindran et al. (1979) reviewed and compared the various methods. 

There are many excellent texts on combustion [153,235,380,412,424,435], all of which discuss fundamental principles but differ in their applications focus. The classic book by Bird, Stewart, and Lightfoot emphasizes the fundamental principles of transport phenomena, including multicomponent and chemically reacting flow [35]. Rosner s book [339] also develops much of the transport theory for chemically reacting flow systems. In materials processing, such as the synthesis of electronic thin films, there are fewer texts that present the details of chemically reacting flow. However, excellent presentation of the fundamentals can be found in book chapters by Kleijn [228] and Jensen [202]. 

This is a linear ordinary-differential-equation boundary-value problem that can be solved analytically (see Bird, Stewart, and Lightfoot, Transport Phenomena, Wiley, 1960). Here, however, proceed directly to numerical finite-difference solution, which can be implemented easily in a spreadsheet. Assuming a cone angle of a = 2° and a rotation rate of 2 = 30 rpm, determine f(0) — v /r. 

There are a number of excellent references on transport properties, for example, by Hirsch-felder, Curtiss, and Bird [178], Bird, Stewart, and Lightfoot [35], and Reid, Prausnitz, and Poling [332], In addition to providing theoretical background, these references also give tabulated values of transport properties of many chemical compounds. The best of source of transport property data is probably the NASA Technical Report by Svehla [389]. 

The last term is the rate of viscous energy dissipation to internal energy, Ev = jv <5 dV, also called the rate of viscous losses. These losses are the origin of frictional pressure drop in fluid flow. Whitaker and Bird, Stewart, and Lightfoot provide expressions for the dissipation function <5 for Newtonian fluids in terms of the local velocity gradients. However, when using macroscopic balance equations the local velocity field within the control volume is usually unknown. For such... 

The engineering science of transport phenomena as formulated by Bird, Stewart, and Lightfoot (1) deals with the transfer of momentum, energy, and mass, and provides the tools for solving problems involving fluid flow, heat transfer, and diffusion. It is founded on the great principles of conservation of mass, momentum (Newton s second law), and energy (the first law of thermodynamics).1 These conservation principles can be expressed in mathematical equations in either macroscopic form or microscopic form. 

There are many standard texts of fluid flow, e.g. Coulson Richardson,1 Kay and Neddermann2 and Massey.3 Perry4,5 is also a useful reference source of methods and data. Schaschke6 presents a large number of useful worked examples in fluid mechanics. In many recent texts, fluid mechanics or momentum transfer has been treated in parallel with the two other transport or transfer processes, heat and mass transfer. The classic text here is Bird, Stewart and Lightfoot.7... 

Several theories have been developed to describe the rate of interphase mass transfer. These include film theory, boundary layer theory, penetration theory, and surface renewal theory. In this chapter we will review the first two, along with an overview of empirical correlations that are used to describe mass transfer. A more thorough overview of mass transfer theories can be found in Bird, Stewart and Lightfoot [48], Clark [49], Logan [50], and Weber and DiGiano [51]. 

Fick s law of diffusion is also used for problems involving liquid and solid diffusion, and the main difficulty is one of determining the value of the diffusion coefficient for the particular liquid or solid. Unfortunately, only approximate theories are available for predicting diffusion coefficients in these systems. Bird, Stewart, and Lightfoot [9] discuss the calculation of diffusion in liquids, and Jost [6] gives a discussion of the various theories which have been employed to predict values of the diffusion coefficient. The reader is referred to these books for more information on diffusion in liquids and solids. 

The problem of mass transport in parts cleaning will be illustrated with the analogy to a water droplet evaporating in the presence of a flowing air stream of uniform velocity. This simple model can be used to show the importance of fluid flow past the part for removal of contaminant material from the surface. The rate of droplet evaporation in a moving air column is shown in Eq. 4 from Bird, Stewart and Lightfoot, (BSL),t 21... 

The mechanical energy balance is not a fundamental principle rather, it is a corollary (Bird 1957 Bird. Stewart, and Lightfoot 2002) of the equation of motion. For constant fluid density, the macroscopic mechanical energy balance takes the form... 

The term Ey is the rate of viscous dissipation of mechanical energy its estimation is described in Bird, Stewart, and Lightfoot (2002). is a reference pressure, in units of M/Lt the resulting SI unit is the Pascal. 

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