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Direct numerical simulations are carried out to study the flow structure and transport properties in turbulent Rayleigh–Bénard convection in a vertical cylindrical cell of aspect ratio one with an imposed axial magnetic field. Flows at the Prandtl number$0.025$and Rayleigh and Hartmann numbers up to$10^{9}$and$1400$, respectively, are considered. The results are consistent with those of earlier experimental and numerical data. As anticipated, the heat transfer rate and kinetic energy are suppressed by a strong magnetic field. At the same time, their growth with Rayleigh number is found to be faster in flows at high Hartmann numbers. This behaviour is attributed to the newly discovered flow regime characterized by prominent quasi-two-dimensional structures reminiscent of vortex sheets observed earlier in simulations of magnetohydrodynamic turbulence. Rotating wall modes similar to those in Rayleigh–Bénard convection with rotation are found in flows near the Chandrasekhar linear stability limit. A detailed analysis of the spatial structure of the flows and its effect on global transport properties is reported.

We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with a transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The problem is discretized by a double expansion in Chebyshev polynomials in the cross-stream coordinates. The linear eigenvalue problem for the critical Reynolds number depends on the streamwise wavenumber, Hartmann number and the aspect ratio. We consider the limits of small and large aspect ratios in order to compare with stability models based on one-dimensional base flows. For large aspect ratios, we find good numerical agreement with results based on the quasi-two-dimensional approximation. The lift-up mechanism dominates in the limit of a zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann numbers in the duct. As the aspect ratio is reduced away from unity, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations imposed on the plane Poiseuille base flow. We also examine different possible symmetries of eigenmodes as well as the purely hydrodynamic case in the duct geometry.

We derive a mathematical model for steady, unidirectional, thermoelectric magnetohydrodynamic (TEMHD) flow of liquid lithium along a solid metal trench, subject to an imposed heat flux. We use a finite-element method implemented in COMSOL Multiphysics to solve the problem numerically, demonstrating how the fluid velocity, induced magnetic field and temperature change depending on the key physical and geometrical parameters. The observed flow structures are elucidated by using the method of matched asymptotic expansions to obtain approximate solutions in the limit where the Hartmann number is large and the trench walls are thin.

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of a very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.

A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from the instability of the jet. The flow structure and fluctuation properties are largely determined by the value of the Stuart number ${{N}}$. At moderate ${{N}}$, the mean velocity profile retains a central jet with three-dimensional perturbations increasingly suppressed by the magnetic field as ${{N}}$ grows. At higher values of ${{N}}$, the flow becomes quasi-two-dimensional and acquires the form of an asymmetric macrovortex, with high-amplitude velocity fluctuations reemerging.

Pumping fluid is one of the crucial parts of any microfluidic system. Using electric and magnetic fields as a substitute for moving parts can have many advantages. In this study hydrodynamic and heat transfer characteristics of electroosmotic flow under influence of lateral electric and transverse magnetic field, are studied numerically. Results indicate that the dimensionless parameters such as Hartmann number, intensity of the lateral electric field, pressure gradient parameter and aspect ratio have an important role in controlling flow. It can be implied that the enhancement of pressure gradient leads to the decrease of critical Hartmann number, and this dependency can be reduced from 44% to 1% for S = 0.5 to S = 50 in two pressure gradients of Q = 1 and Q = 20. In addition, the reduction of aspect ratio of microchannel section leads to the increment of critical Hartmann number in a specified lateral electric field. At the end, thermal analysis is being done by consideration of the effects of magnetic and electric fields on the Nusselt number.

Porosity plays a significant role in controlling the wake dynamics behind a porous object. A porous object allows fluid to flow through it partially, which causes a reduction in the size of the wake behind the body. The wake dynamics can also be controlled by imposing an external magnetic field on an electrically conducting fluid. Keeping in view the above facts, numerical computations are performed to explore the coupled effect of the porosity and the magnetic field on the wake dynamics around a porous square cylinder. The cylinder is placed in a two-dimensional unconfined domain having a fictitious blockage ratio of 0.025. The Reynolds number is kept in the range 10–40 with Darcy number 10 −6 –10 −2 and Hartmann number 0–8. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. The critical magnetic parameter for the complete suppression of the wake behind the cylinder for the given range of Darcy and Reynolds numbers is computed. The results show that the critical Hartmann number increases with the Reynolds number, whereas it decreases with the Darcy number. Another interesting finding is the estimation of the critical Hartmann number for the detachment of the recirculation region from the rear surface of the cylinder. The detachment Hartmann number increases with an increase in the Reynolds number and a decrease in the Darcy number .

A stabilized element-free Galerkin (EFG) method is proposed in this paper for numerical analysis of the generalized steady MHD duct flow problems at arbitrary and high Hartmann numbers up to 1016. Computational formulas of the EFG method for MHD duct flows are derived by using Nitsche’s technique to facilitate the implementation of Dirichlet boundary conditions. The reproducing kernel gradient smoothing integration technique is incorporated into the EFG method to accelerate the solution procedure impaired by Gauss quadrature rules. A stabilized Nitsche-type EFG weak formulation of MHD duct flows is devised to enhance the performance damaged by high Hartmann numbers. Several benchmark MHD duct flow problems are solved to testify the stability and the accuracy of the present EFG method. Numerical results show that the range of the Hartmann number Ha in the present EFG method is 1≤Ha≤1016, which is much larger than that in existing numerical methods.

This examination is passed on to decide the properties of three-dimensional flow of H 2 O/NaC 6 H 9 O 7 base liquid with F e 3 O 4 /Al 2 O 3 nanoparticles confined by a Riga plate. Mathematical model is detailed as PDEs and afterward transmuted into ODEs with the assistance of similarity transformations. The subsequent system is numerically dealt with the aid of the Runge-Kutta procedure bolstered by shooting technique. Highlights of the flow field and thermal field are exemplified quantitatively through plots. Results for the local skin friction coefficient and local Nusselt number are registered and examined tabularly. It is induced that the modified Hartmann number and stretching ratio parameter ameliorate the velocity profile. Additionally, it is likewise explained that H 2 O − Al 2 O 3 nanofluid has high skin friction values and the rate of heat transfer of NaC 6 H 9 O 7 − Al 2 O 3 nanofluid is more desirable.

In this study, the electrically conducting fluid flow inside a channel with local symmetric constrictions, in the presence of a uniform transverse magnetic field is investigated using Lattice Boltzmann Method (LBM). To simulate Magnetohydrodynamics (MHD) flow, the extended model of D2Q9 for MHD has been used. In this model, the magnetic induction equation is solved in a similar manner to hydrodynamic flow field which is easy for programming. This extended model has a capability of simultaneously solving both magnetic and hydrodynamic fields; so that, it is possible to simulate MHD flow for various magnetic Reynolds number (Rem). Moreover, the effects of Rem on the flow characteristics are investigated. It is observed that, an increase in Rem, while keeping the Hartman number (Ha) constant, can control the separation zone; furthermore, comparing to increasing Ha, it doesn't result in a significant pressure drop along the channel.