Advanced Transport Phenomena: Fluid Mechanics and Convective by L. Gary Leal

By L. Gary Leal

Complicated shipping Phenomena is perfect as a graduate textbook. It encompasses a unique dialogue of contemporary analytic equipment for the answer of fluid mechanics and warmth and mass move difficulties, targeting approximations in accordance with scaling and asymptotic tools, starting with the derivation of easy equations and boundary stipulations and concluding with linear balance conception. additionally lined are unidirectional flows, lubrication and thin-film conception, creeping flows, boundary layer concept, 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 ideas 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 designated suggestions of differential equations. The ebook additionally makes a speciality of the strategies of consultant difficulties. This displays the book's objective of educating readers to consider 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)

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At the same time, if the probe were sufficiently small compared with the dimensions of the flow domain, we would say that the velocity was measured “at a point,” in spite of the fact that the measured quantity was an average value from the molecular point of view. 2 It is important to remark that we shall never actually calculate macroscopic variables as averages of molecular variables. The purpose of introducing an explicit connection between the macroscopic and molecular (or microscopic) variables is that the conditions for w to define a meaningful macroscopic (or continuum) point variable provide sufficient conditions 14 10:7 P1: JzG 0521849101c02 CUFX064/Leal Printer: cupusbw 0 521 84910 1 April 23, 2007 A.

This problem is also an important contrast with the first two examples because it is a case in which the flow can actually be stabilized by viscous effects. We first consider the classic case of an inviscid fluid, which leads to the well-known criteria of Rayleigh for the stability of an inviscid fluid. We then analyze the role of viscosity for the case of a narrow gap in which analytic results can be obtained. We show that the flow is stabilized by viscous diffusion effects up to a critical value of the Reynolds number for the problem (here known as the Taylor number).

V Dt (2–19) The left-hand side of (2–19) is sometimes referred to as the rate of expansion or the rate of dilation of the fluid and provides a clear physical interpretation of the quantity ∇ · u(or div u). The forms of the continuity equation (2–18) or (2–19) also lead directly to a simpler statement of the mass conservation principle that applies if it can be assumed that the density is constant, so that Dρ/Dt = 0. , is approximated as) incompressible. In general, the density is related to the temperature and pressure by means of an equation of state, ρ = ρ( p, T ).

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