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

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

Example text

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. [30] 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.

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