By L. Gary Leal
Complicated shipping Phenomena is perfect as a graduate textbook. It includes a special dialogue of recent analytic tools for the answer of fluid mechanics and warmth and mass move difficulties, targeting approximations according to scaling and asymptotic equipment, starting with the derivation of simple equations and boundary stipulations and concluding with linear balance conception. additionally lined are unidirectional flows, lubrication and thin-film conception, creeping flows, boundary layer conception, and convective warmth and mass delivery at low and high Reynolds numbers. The emphasis is on easy physics, scaling and nondimensionalization, and approximations that may be used to procure options which are due both to geometric simplifications, or huge or small values of dimensionless parameters. the writer emphasizes constructing difficulties and extracting as a lot info as attainable wanting acquiring precise ideas of differential equations. The e-book additionally specializes in the options of consultant difficulties. This displays the book's aim of training readers to consider the answer of delivery difficulties.
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Additional info for Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge Series in Chemical Engineering)
The simplest of the various conservation principles to apply is conservation of mass. It is instructive to consider its application relative to two different, but equivalent, descriptions of our fluid system. In both cases, we begin by identifying a specific macroscopic body of fluid that lies within an arbitrarily chosen volume element at some initial instant of time. Because we have adopted the continuum mechanics point of view, this volume element will be large enough that any flux of mass across its surface that is due to random molecular motions can be neglected completely.
9. Introductory note: Most transport and/or fluids problems are not amenable to analysis by classical methods for linear differential equations, either because the equations are nonlinear (or simply too complicated in the case of the thermal energy equation, which is linear in temperature if natural convection effects can be neglected), or because the solution domain is complicated in shape (or in the case of problems involving a fluid interface having a shape that is a priori unknown). Analytic results can then be achieved only by means of approximations.
2–1, this means that there can be no net flux of black or white balls across the surface S due to the macroscopic motion described by u. Clearly, however, the random translational motions of the molecules will lead to a net flux of black balls across this surface from the bottom to the top (Fig. 2–1), and an equal but oppositely directed flux of white balls from top to bottom until finally at some large time the average color on both sides of S will be the same, and the net flux of either black or white balls will be zero.