By L. Gary Leal
Complicated delivery Phenomena is perfect as a graduate textbook. It includes a targeted dialogue of contemporary analytic equipment for the answer of fluid mechanics and warmth and mass move difficulties, targeting approximations according to scaling and asymptotic tools, starting with the derivation of easy equations and boundary stipulations and concluding with linear balance thought. additionally coated are unidirectional flows, lubrication and thin-film concept, creeping flows, boundary layer conception, and convective warmth and mass delivery at low and high Reynolds numbers. The emphasis is on easy physics, scaling and nondimensionalization, and approximations that may be used to acquire options which are due both to geometric simplifications, or huge or small values of dimensionless parameters. the writer emphasizes developing difficulties and extracting as a lot details as attainable wanting acquiring designated options of differential equations. The ebook additionally specializes in the suggestions of consultant difficulties. This displays the book's aim of training readers to consider the answer of shipping difficulties.
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Extra info for Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge Series in Chemical Engineering)
Expressing this statement in mathematical terms we obtain V ∂ρ dV = − ∂t ρu · nd A, (2–3) A where V denotes the arbitrarily chosen volume element of fixed position and shape and A denotes its (closed) surface. Equation (2–3) is an integral constraint on the velocity and density fields within a given closed volume element of fluid. Because this volume element was chosen arbitrarily, however, an equivalent differential constraint at each point in the fluid can be derived easily. First, the well-known divergence theorem5 is applied to the right-hand side of (2–3), which thus becomes V ∂ρ + ∇ · (ρu) d V = 0.
However, the physical principles are actually quite simple and generally familiar to any student with a physics background in classical mechanics. Indeed, the main problems of fluid mechanics and of convective heat transfer are not in the complexity of the underlying physical principles, but rather in the attempt to understand and describe the fascinating and complicated phenomena that they allow. From a mathematical point of view, the main problem is not the derivation of the governing equations that is presented in this second chapter, but in their solution.
It is this additional transport that is due to fluctuations in the molecular velocity about the continuum 16 10:7 P1: JzG 0521849101c02 CUFX064/Leal Printer: cupusbw 0 521 84910 1 April 23, 2007 A. The Continuum Approximation velocity u that must be incorporated in a continuum description as a local “molecular” surface heat flux contribution. 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.
Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes (Cambridge Series in Chemical Engineering) by L. Gary Leal