China
Africa
Explore chapters and articles related to this topic
Numerical Methods for the “Parabolized” Navier–Stokes Equations
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
Magnetohydrodynamic (MHD) flows (see Section 5.1.6) have been computed using PNS solvers that incorporate Maxwell’s equations of electromagnetodynamics with the PNS equations. Codes have been developed for both the low and high magnetic Reynolds number regimes. In the low magnetic Reynolds number regime, the electrical conductivity is low, and the induced magnetic field is negligible compared to the applied magnetic field. This greatly reduces the complexity of the governing equations since the MHD effects are modeled by simply adding source terms to the flow equations (Gaitonde and Poggie, 2000). The UPS code has been extended to permit MHD flow calculations in both the high (Kato et al., 2002) and low magnetic Reynolds number regimes (Kato et al., 2003, 2004; Gupta et al., 2007). Fortunately, most aerospace applications occur in the low magnetic Reynolds number regime.
Torque and Braking in a Magnetic Field
Published in Michael P. Perry, Low Frequency Electromagnetic Design, 2019
An important principle in the electromechanical analysis is the equivalence between the solutions of the steady state diffusion equation with ac excitation and the solutions to the rotating cylinder in a dc field. This duality can be qualitatively understood by noting that a rotating field can be created by summing two uniform ac fields, each π/2 out of phase in space and time. The rotating field produces the same current density in the cylinder as if the field were stationary and the cylinder rotating in the opposite direction with the same speed. In analyzing electromechanical problems, it is theoretically possible therefore to utilize only steady state solutions to the diffusion equation as described in Chapters 2 and 3, and then make an appropriate change in the reference frame of the calculation. The “magnetic Reynolds number” is a universal modulus which indicates the effect of dynamics, in either steady state diffusion or uniform mechanical motion in a magnetic field.
Liquid Metals as Heat Transfer Fluids for Science and Technology
Published in Alina Adriana Minea, Advances in New Heat Transfer Fluids, 2017
Alexandru Onea, Sara Perez-Martin, Wadim Jäger, Wolfgang Hering, Robert Stieglitz
The phase shift is a function of the magnetic Reynolds number (Rm) and the dimensionless exiting frequency (Ω). An additional calibration factor (K) is accounting for geometric dependencies. These are the distance between coil arrangement and flow channel (b) and the shift (l) between the emitting and the receiving side: Δϕ=arctan(Ω⋅π−1⋅Rm⋅K1+Ω2⋅(1+π−1⋅Rm⋅K)) The magnetic Reynolds number is the product of the magnetic permeability (μ), the electric conductivity of the fluid (σ), the velocity of the fluid (v), and the hydraulic diameter of the flow channel (d): Rm=μ⋅σ⋅v⋅d The dimensionless exiting frequency (Ω) is calculated according to Ω=2⋅π⋅f⋅LRRR where f is the exiting frequencyLR is the inductivity of the receiving coil(s)RR is the electric resistance of the receiving coil(s)
Biomedical aspects of entropy generation on MHD flow of TiO2-Ag/blood hybrid nanofluid in a porous cylinder
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
N. Shanmugapriyan, Shaik Jakeer
Consider a steady, laminar flow of an incompressible viscous fluid due to continuous stretching of a horizontal cylinder having radius embedded in a porous medium. Let’s suppose that and represent the and radial direction components of velocity, respectively, as illustrated in Figure 1. While creating the flow formulation, consideration is taken to the effects of thermal radiation, uniform heat source/sink and non-Fourier heat flux model. The cylinder stretching with linear velocity and temperature The cylinder is subjected to magnetic field perpendicular to it. In addition, the magnetic field generated is weaker than the magnetic field applied due to the low magnetic Reynolds numbers. A sufficient number of tiny elements are selected and are treated as allowable and continuous ideas in order to define the physical meaning of density and velocity (Ijaz Khan et al. 2020; Awan et al. 2022). Table 1 displays the thermophysical properties and corresponding values of a hybrid nanofluid consisting of TiO2-Ag and a blood-based liquid.
Edge-Based Finite Element Formulation of Magnetohydrodynamics at High Mach Numbers
Published in International Journal of Computational Fluid Dynamics, 2021
Wenbo Zhang, Wagdi G. Habashi, Guido S. Baruzzi, Nizar Ben Salah
The last equation of system (1) is the magnetic induction equation. It consists of a diffusive curl-curl term, a convective curl term and a time term, and it directly links the hydrodynamic velocity to the magnetic field intensity . The Lorentz force appearing on the right-hand side of the momentum equations requires the computation of the electric current density, which can be obtained from Ohm’s law The non-dimensional form of the magnetic induction equation is introduced to highlight the relative weight of the terms composing it. The following non-dimensional variables are first defined The non-dimensional form of the magnetic induction equation is thus The ratio of the convection of the magnetic field to its diffusion is expressed by the non-dimensional magnetic Reynolds number , defined as Within the boundaries of the low-magnetic Reynolds number approximation, the convective effects of the fluid velocity on the magnetic field are negligible, compared to its diffusion. Thus, when , Eq. (4) reduces to a Laplacian-type equation, stating that the magnetic field is diffused in the domain and vanishes as it approaches the external boundary. This implies that the induced magnetic field is negligible, and the total magnetic field can be approximated by the imposed one (Ben Salah, Soulaimani, and Habashi 2001; Baaziz, Ben Salah, and Kaddeche 2014).