By L. Gary Leal
Complex shipping Phenomena is perfect as a graduate textbook. It includes a distinctive dialogue of recent 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 uncomplicated equations and boundary stipulations and concluding with linear balance thought. additionally coated are unidirectional flows, lubrication and thin-film concept, creeping flows, boundary layer thought, and convective warmth and mass delivery at low and high Reynolds numbers. The emphasis is on easy physics, scaling and non-dimensionalization, and approximations that may be used to procure 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 wanting acquiring exact strategies of differential equations. The e-book is additionally occupied with the ideas of consultant difficulties. This displays the author's bias towards studying to contemplate the answer of shipping difficulties.
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Extra info for Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes
Vm (t) (2–11) To the quantity on the right-hand side of (2–11), we now add and subtract the term Vm (t) B(t + δt)d V : D Dt Bd V = lim Vm (t) δt→0 + 22 1 δt 1 δt B(t + δt)d V − Vm (t+δt) B(t + δt)d V − Vm (t) B(t + δt)d V Vm (t) B(t)d V Vm (t) . (2–12) 10:7 P1: JzG 0521849101c02 CUFX064/Leal Printer: cupusbw 0 521 84910 1 April 23, 2007 B. Conservation of Mass – The Continuity Equation The second term is just lim δt→0 Vm (t) B(t + δt) − B(t) dV ≡ δt Vm (t) ∂B d V. ∂t (2–13) The first term is simply rewritten as lim δt→0 1 δt B(t + δt)d V , (2–14) Vm (t+δt)−Vm (t) which shows that it is the integral of B(t) over the differential volume element Vm (t + δt) − Vm (t).
This section is perhaps the most important one in the chapter from a pedagogical point of view, because it challenges most of the simplistic ideas that students may have from undergraduate transport courses, and forces them to see that boundary layers are applicable to a very broad class of problems. For example, the question of a boundary layer on a bubble forces students to reconsider the simplistic (and often incorrect) idea that a boundary layer exists because of the no-slip condition. Chapter 11: Heat and Mass Transfer at Large Reynolds Number In this chapter, we return to forced convection heat and mass transfer problems when the Reynolds number is large enough that the velocity field takes the boundary-layer form.
On the other hand, the coefficient b depends on the maginitude of the Prandtl (or Schmidt) number and also changes depending on whether the boundary is a no-slip surface or a fluid interface. For example, for a no-slip surface, b = 1/2 in the limit Pr (or Sc) → 0 but b = 1/3 for Pr (or Sc) → ∞. By now, students can easily analyze and understand qualitatively the reasons for these changes, as well as the effect of changes in the fluid mechanics or thermal boundary conditions. The coefficient c is an order 1 number that depends on the geometry, but we show that 9 10:7 P1: JZZ 0521849101c01 CUFX064/Leal Printer: cupusbw 0 521 84910 1 April 23, 2007 A Preview very general solutions for “arbitrary” body shapes can be obtained by means of similarity transformations.