By Petr A. Nikrityuk
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 manage the warmth, mass and fluid flows in melts and on part switch phenomena throughout the solidification of natural fabrics and binary alloys. despite the fact that, the ebook offers even more than formalisms and algorithms; it additionally stresses the significance of excellent, possible and achievable versions to appreciate advanced structures, and develops those in detail.
Bringing computational fluid dynamics, thermodynamics and electrodynamics jointly, it is a helpful resource for fabrics scientists, PhD scholars, sturdy country physicists, approach engineers and mechanical engineers, in addition to teachers in mechanical engineering.
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Extra resources for Computational Thermo-Fluid Dynamics: In Materials Science and Engineering
94) in the case of incompressible ﬂow (r u D 0) with constant electrical conductivity, Eq. 93) can be simpliﬁed (due to Eq. 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.
123) We deﬁne the boundary conditions from the condition of the vanishing of the electric current on the cylinder surfaces. Using Eqs. 120) we have @φ 1 j rDR0 D 0 , @r @φ 1 j zD0,H0 D B0 ωr . 125) On referring to the work of Marty et al.  the time-averaged electric current density induced by the RMF ﬂows along a meridional perimeter of a cylinder and rotates with angular velocity ω. 2. It can be seen that the azimuthal Lorentz force is axisymmetric, which is induced by the nonaxisymmetric electric current density and the radial magnetic ﬁeld rotating around the axis of a cylinder of angular velocity ω.
The Inﬂuence of the σ s /σ l Ratio on the Lorentz Force The ﬁrst series of numerical simulations are devoted to the study of the Lorentz force induced by an RMF in a cylindrical cavity whose lower part is solidiﬁed. In particular, we study the inﬂuence of the ratio σ s /σ l on the induced Lorentz force. 5 H0 . The planarity of the solid front (see paragraph “General Formulation”) and identical size of the liquid and solid domains signiﬁcantly simpliﬁes the application of the sharp-interface model.