By L. Gary Leal
Complex delivery Phenomena is perfect as a graduate textbook. It encompasses a certain dialogue of contemporary analytic tools 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 easy equations and boundary stipulations and concluding with linear balance thought. additionally lined are unidirectional flows, lubrication and thin-film idea, creeping flows, boundary layer concept, and convective warmth and mass delivery at low and high Reynolds numbers. The emphasis is on uncomplicated physics, scaling and nondimensionalization, and approximations that may be used to acquire ideas 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 details as attainable in need of acquiring designated recommendations of differential equations. The ebook additionally specializes in the suggestions 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)
An arbitrarily chosen material control volume shown at some initial moment t = 0 and at a later time t, after which it has translated and distorted in shape because each point on its surface moves with the local fluid velocity u. Equation (2–6) represents a statement of mass conservation for this material volume. within the material volume is constant, independent of time. This may be expressed in the mathematical statement D Dt ρd V = 0. (2–6) Vm (t) Here, the symbol D/Dt stands for the convected or material time derivative, which we shall subsequently discuss in some detail.
We emphasize that the split of heat transfer into a convective contribution associated with u, plus an additional molecular contribution, is due to the continuum description of the system. It is conventional to call the diffusive flux of heat “conduction” rather than diffusion, but this is only semantics and does not change the basic diffusive nature of the transport mechanism. Obviously, the sum of the convective and molecular heat flux contributions in the continuum description must be identical to the total flux of heat due to molecular motions if the continuum description of the system is to have any value.
On average there is a net flux of black balls across S into the white region and vice versa. In a macroscopic theory designed to describe the transport of white and black fluid, this net flux would appear as a surface contribution and will be described in the theory as a diffusive flux. The presence of this flux would gradually smear the initial step change in color until eventually the average color on both sides of S would be the same mixture of white and black. tangent to the macroscopic velocity u so that u · n = 0 at each point on the surface S.