By Petr A. Nikrityuk

ISBN-10: 3527331018

ISBN-13: 9783527331017

ISBN-10: 3527636072

ISBN-13: 9783527636075

Combining formerly unconnected computational tools, this monograph discusses the newest uncomplicated schemes and algorithms for the answer of fluid, warmth and mass move difficulties coupled with electrodynamics. It provides the required mathematical historical past of computational thermo-fluid dynamics, the numerical implementation and the appliance to real-world difficulties. specific emphasis is put all through at the use of electromagnetic fields to regulate the warmth, mass and fluid flows in melts and on section swap phenomena throughout the solidification of natural fabrics and binary alloys. in spite of the fact that, the publication offers even more than formalisms and algorithms; it additionally stresses the significance of excellent, possible and potential versions to appreciate complicated structures, and develops those in detail.

Bringing computational fluid dynamics, thermodynamics and electrodynamics jointly, it is a helpful resource for fabrics scientists, PhD scholars, reliable country physicists, method engineers and mechanical engineers, in addition to teachers in mechanical engineering.

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**Example text**

85)) to the so-called induction equation for incompressible ﬂuids: 1 @B C (u r) B D ∆ 2 B C (B r) u . 95) Note that since B is solenoidal, r (r B) D r 2 B. The induction equation describes the temporal evolution of the magnetic ﬁeld due to advection (u r) B, diffusion ∆ 2 B, and the ﬁeld intensity source (B r) u generated by mechanical stretching of the ﬁeld lines by the velocity ﬁeld. The quantity (µ 0 σ) 1 D η is deﬁned as a magnetic diffusivity by analogy to other diffusive processes such as heat conduction.

91)), combining which produces the electric potential equation for a static ﬁeld: r (σr φ) D r [σ (u B 0 )] . 100) i where σ i and ε i are the electric conductivity and volume fraction of phase i, respectively. We note here that in several engineering applications such as arc plasma, arc welding technologies, or any technologies dealing with an electrical current passing through a liquid metal it is necessary to calculate the magnetic ﬁeld B j induced by the electrical current. In the case of low-Re m approximation the equations that are needed to calculate the induced magnetic ﬁeld can be derived from the Biot– Savart law (see Eq.

1 Maxwell Equations The basic equations of electromagnetism are the so-called Maxwell equations plus Ohm’s law with the charge conservation equation. 85) where e is the charge density and ε 0 and µ 0 are the permittivity and the permeability of free space, respectively. 3 Conservation Equations in Electromagnetics Ohm’s equation is an empirical law that relates the electric current density j in a conducting moving medium to the electric ﬁeld E: j D σ (E C u B) . 86) The charge conservation equation takes the following form: @ e .

### Computational Thermo-Fluid Dynamics: In Materials Science and Engineering by Petr A. Nikrityuk

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