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

By L. Gary Leal

Complicated delivery Phenomena is perfect as a graduate textbook. It encompasses a designated dialogue of contemporary analytic equipment for the answer of fluid mechanics, and warmth and mass move difficulties, targeting approximations established upon scaling and asymptotic tools, starting with the derivation of simple equations and boundary stipulations and concluding with linear balance idea. additionally lined are unidirectional flows, lubrication and thin-film conception, creeping flows, boundary layer idea, and convective warmth and mass shipping at low and high Reynolds numbers. The emphasis is on simple physics, scaling and non-dimensionalization, and approximations that may be used to acquire recommendations 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 in need of acquiring specific recommendations of differential equations. The publication can also be desirous about the recommendations of consultant difficulties. This displays the author's bias towards studying to consider the answer of shipping difficulties.

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We note first that t is not only a function of position and time, t(x, t), as is the case with u, but also of the orientation of the differential surface element through x on which it acts. The reader may well ask how this is known in the absence of a direct molecular derivation of a theoretical expression for t (the latter being outside the realm of continuum mechanics, even if it were possible in principle). The answer is that we can either deduce or derive certain general properties of t, including its orientation dependence, from (2–23) by considering the limit as we decrease the material control volume progressively toward zero while holding the geometry (shape) of Vm constant.

Koseff, B. R. Munson, K. G. Powell, C. R. Robertson, and S. T. Thoroddsen, “Multi-Media Fluid Mechanics,” CD-ROM, (Cambridge University Press, Cambridge, 2004). 7. M. Van Dyke, An Album of Fluid Motion (Parabolic Press, Stanford, CA, 1982). 8. M. Samimy, K. S. Breuer, L. G. Leal, and P. H. Steen, A Gallery of Fluid Motion (Cambridge University Press, Cambridge, 2004). 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).

When we adopt the continuum or macroscopic point of view, however, we effectively split the molecular motion of the material into two parts: a molecular average velocity u ≡ w and local fluctuations relative to this average. Because we define u as an instantaneous spatial average, it is evident that the local net volume flux of fluid across any surface in the fluid will be u · n, where n is the unit normal to the surface. In particular, the local fluctuations in molecular velocity relative to the average value w yield no net flux of mass across any macroscopic surface in the fluid.

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