By Günter Brenn
This e-book presents analytical strategies to a few classical difficulties in shipping procedures, i.e. in fluid mechanics, warmth and mass move. increasing computing strength and extra effective numerical tools have elevated the significance of computational instruments. besides the fact that, the translation of those effects is frequently tricky and the computational effects have to be validated opposed to the analytical effects, making analytical suggestions a priceless commodity. moreover, analytical strategies for delivery strategies offer a miles deeper figuring out of the actual phenomena eager about a given procedure than do corresponding numerical recommendations. even though this e-book basically addresses the desires of researchers and practitioners, it will possibly even be worthwhile for graduate scholars simply coming into the sphere.
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Additional resources for Analytical Solutions for Transport Processes: Fluid Mechanics, Heat and Mass Transfer
Wiley, New York (1987) 2. : Transport Phenomena. Wiley, New York (1960) 3. : Strömungsmechanik Nichtnewtonscher Fluide (Fluid Mechanics of NonNewtonian Liquids, in German). Teubner, Stuttgart (2000) 4. : The dynamics of thin liquid jets in air. J. Fluid Mech. 140, 91–111 (1984) 5. : Phänomenologische Rheologie - Eine Einführung (Phenomenological Rheology—An Introduction, in German). Springer, Berlin, Heidelberg (1994) 6. : Seven common errors in finding exact solutions of nonlinear differential equations.
87) A special case is a linear steady flow field with the fluid motion in the z direction, which is hydraulically developed and therefore does not depend on the z coordinate. The stream function, therefore, cannot depend on that coordinate. The reduced form of Eq. 84) is the statement that d dr 1 d d r r dr dr 1 dψcθ r dr =0. 2 The Equation for the Stream Function in Cylindrical Coordinates 43 The solution is ψcθ = C1 r4 r2 + C2 16 2 ln r − 1 2 + C3 r2 + C4 . 89) Three of the four constants are determined by boundary conditions, while C4 is a free reference value.
We will discuss the stability of two-phase flows with interfaces in Chap. 6. 5 Quasi One-Dimensional Flow in a Boundary Layer Another example for a quasi one-dimensional description of a flow is the integral formulation of the equations of motion in the boundary-layer form. The idea behind this formulation is to integrate the momentum equation in the coordinate direction across the thickness of a boundary layer as in Fig. 9. In steady, two-dimensional flow, then, only the dependency of the flow properties on the spatial coordinate in the downstream direction remains.
Analytical Solutions for Transport Processes: Fluid Mechanics, Heat and Mass Transfer by Günter Brenn