By L. Gary Leal
Complex shipping Phenomena is perfect as a graduate textbook. It incorporates a designated dialogue of contemporary analytic equipment for the answer of fluid mechanics and warmth and mass move difficulties, targeting approximations in response to scaling and asymptotic equipment, starting with the derivation of uncomplicated equations and boundary stipulations and concluding with linear balance conception. additionally coated are unidirectional flows, lubrication and thin-film concept, creeping flows, boundary layer thought, and convective warmth and mass shipping at low and high Reynolds numbers. The emphasis is on uncomplicated 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 establishing difficulties and extracting as a lot info as attainable in need of acquiring unique suggestions of differential equations. The e-book additionally makes a speciality of the strategies of consultant difficulties. This displays the book's aim of training readers to contemplate the answer of shipping difficulties.
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Extra resources for Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge Series in Chemical Engineering)
The first problem considered is the classic problem of Rayleigh–Benard convection – namely the instability that is due to buoyancy forces in a quiescent fluid layer that is heated 10 10:7 P1: JZZ 0521849101c01 CUFX064/Leal Printer: cupusbw 0 521 84910 1 April 23, 2007 Notes and References from below. In this case, both viscous diffusion and thermal diffusion play a role in stabilizing the fluid, leading to the concept of a critical Rayleigh number for instability. This is followed by an analysis of the related buoyancy-driven instabilities that can occur in a system in which the density is dependent on two “species” that diffuse at significantly different rates.
To proceed further, we must consider the types of forces that appear on the right-hand side of (2–22). From the purely continuum mechanics viewpoint that we have now adopted, we recognize two kinds of forces acting on the material control volume. First are the body forces, associated with the presence of external fields, that are capable of penetrating to the interior of the fluid and acting equally on all elements (per unit mass). The most familiar body force is gravity, and we will be concerned exclusively with this single type of body force in this book.
In particular, instead of the original choice of V, we could simply choose a new volume element that lies entirely within the region where the integrand is positive (or negative). Evidently, (2–4) is then violated, leading us to conclude that (2–5) must hold everywhere. Although the derivation of the continuity equation by use of a fixed control volume is perfectly satisfactory, it is less obvious how to apply Newton’s laws of mechanics in this framework. The familiar use of these principles from coursework in classical mechanics is that they are applied to describe the motion of a specific “body” subject to various forces or torques.
Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge Series in Chemical Engineering) by L. Gary Leal