Download PDF by Heinz W. Engl, Ewald Lindner (auth.), a. Univ. Prof.: Case Studies in Industrial Mathematics

By Heinz W. Engl, Ewald Lindner (auth.), a. Univ. Prof. Dipl.-Ing., Dr. Heinz W. Engl, o. Univ. Prof. Dr. Hansjörg Wacker, Dipl.-Ing. Dr. Walter Zulehner (eds.)

ISBN-10: 3663120635

ISBN-13: 9783663120636

ISBN-10: 3663120643

ISBN-13: 9783663120643

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9) Clu (-~ t) =0 Clx 2' ( 2. 1 0) u (x, 0) = f(x) for tE[O,T] dJ for xE [o, 2 ( 2 . 11 ) u ( s ( t) , t) =u 1 for tE[O,TE]. 5) g v : heat transfer function [W/m 2 K], see below; v: casting speed uw : temperature of the water used in spray cooling times when the strand leaves the secondary cooling zone and is completely solid, respectively; these times depend upon v T: max{Tc,TE} ua·.

For bodies of revolution, the problem is two-dimensional if cylindrical coordinates are introduced. In Section 4 the numerical method, a finite element technique, is presented and results of a convergence analysis are reported. The paper concludes with some numerical experiments. 2 The physic~l model The motion of a solid through a liquid is a classic problem in fluid dynamics. This section mainly follows the presentation by Lamb [1]. 1 The equations of motion for the rigid body At each time t the rigid body is represented by a subset G2 (t) of m3, the three-dimensional Euclidean space.

6) div v with p1 0 the constant density of the liquid, v = (v 1 ,v 2 ,v 3 ) the velocity field of the liquid. 6) the conservation of mass. e. a function ¢ exists in G such that 27 (2. 7) lead to the Laplacian equation for cf>: ( 2. 9) lief> = in G 0 On the interface aG 2 the normal velocities of rigid body and liquid have to coincide and, on the fixed wall aG 1 , the normal velocity of the liquid must vanish. 9) for the liquid. 4). Transformation to the body system For technical reasons the whole problem is expressed in terms of the coordinate system fixed in the rigid body.

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Case Studies in Industrial Mathematics by Heinz W. Engl, Ewald Lindner (auth.), a. Univ. Prof. Dipl.-Ing., Dr. Heinz W. Engl, o. Univ. Prof. Dr. Hansjörg Wacker, Dipl.-Ing. Dr. Walter Zulehner (eds.)

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