Magnetic Field Inclination Angle Research Articles

Effect of uniform inclined magnetic field on mixed convection in a lid-driven cavity having a horizontal porous layer saturated with a ferrofluid

MHD mixed convection in a lid-driven cavity with partially filled with a porous medium saturated with a ferrofluid has been analyzed numerically. The domain of interest consists of a bottom porous layer and a nanofluid layer over the porous one with a heated motionless bottom wall and cooled upper moved wall. The governing partial differential equations formulated on the basis of a single-phase model for nanofluid, Brinkman-extended Darcy model for porous layer and Boussinesq approximation for buoyancy force have been solved by finite difference method of the second-order accuracy. Analysis has been carried out for a wide range of Hartmann number, magnetic field inclination angle, Darcy number, porous layer height, and nanoparticles volume fraction. It has been revealed that average Nusselt number is a non-monotonic function of Darcy number and porous layer height, while a growth of Hartmann number illustrates the heat transfer rate reduction.

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

ABSTRACTThis paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.

Analysis of magnetohydrodynamic natural convection in closed cavities through integral transforms

A hybrid numerical-analytical solution is proposed to analyze MHD (magnetohydrodynamic) natural convection of an electrically-conducting fluid within a square cavity, differentially heated at the sidewalls and subjected to an inclined external magnetic field. The first goal is to expand the spectrum of application of the so called Generalized Integral Transform Technique (GITT), dealing with a multiphysics formulation, while further demonstrating the relative merits of the proposed eigenfunction expansion approach in handling highly nonlinear and coupled systems of partial differential equations. The second goal is to provide a set of benchmark results in this important application for quantities of practical interest in determining the heat transfer rates, such as the average Nusselt number. The two-dimensional steady state equations are written in dimensionless form using the streamfunction-only formulation and are subsequently solved with the GITT approach, under automatic relative error control. Critical comparisons are performed against previous work reported in the literature, both computational and experimental, together with the corresponding physical interpretations, for different values of the governing parameters, such as Grashof number, Hartmann number, Prandtl number, and magnetic field inclination angle.

A Magnetic Map Leads Juvenile European Eels to the Gulf Stream

Migration allows animals to track the environmental conditions that maximize growth, survival, and reproduction [1-3]. Improved understanding of themechanisms underlying migrations allows for improved management of species and ecosystems [1-4]. For centuries, the catadromous European eel (Anguilla anguilla) has provided one of Europe's most important fisheries and has sparked considerable scientific inquiry, most recently owing to the dramatic collapse of juvenile recruitment [5]. Larval eels are transported by ocean currents associated with the Gulf Stream System from Sargasso Sea breeding grounds to coastal and freshwater habitats from North Africa to Scandinavia [6, 7]. After a decade or more, maturing adults migrate back to the Sargasso Sea, spawn, and die [8]. However, the migratory mechanisms that bring juvenile eels to Europe and return adults to the Sargasso Sea remain equivocal [9, 10]. Here, we used a "magnetic displacement" experiment [11, 12] to show that theorientation of juvenile eels varies in response to subtle differences in magnetic field intensity and inclination angle along their marine migration route. Simulations using an ocean circulation model revealed that even weakly swimming in the experimentally observed directions at the locations corresponding to the magnetic displacements would increase entrainment of juvenile eels into the Gulf Stream System. These findings provide new insight into the migration ecology and recruitment dynamics of eels and suggest that an adaptive magnetic map, tuned to large-scale features of ocean circulation, facilitates the vast oceanic migrations of the Anguilla genus [7, 13, 14].

Analysis of natural convective heat transport in homocentric annuli containing nanofluids with an oriented magnetic field using nonhomogeneous dynamic model

In this paper, the time-dependent natural convective heat transport in homocentric annuli containing nanofluids accompanying an oriented magnetic field using a nonhomogeneous dynamic mathematical model is numerically investigated. The analysis is carried out for four different shapes of inner walls such as triangular, square, elliptical and cylindrical. The outermost cylindrical boundary of the annulus is regarded at an unvarying low temperature and undifferentiated thermal condition on the inner surface of the annulus is considered. A finite element method is implemented for finding the solutions to the nanofluid equations of the problem. The magnetite iron oxide–kerosene nanofluid has been taken to gain insight into the thermal fields and concentration levels in terms of isotherms and isoconcentrations, respectively. The local Nusselt number distributions along the interior and exterior boundaries have been displayed for various flow parameters of the problem. To find the best performer, the average Nusselt number enhancements are demonstrated varying four different shapes of inner wall for ten sorts of nanofluids compared to that of base fluids. Results show that the dispersion of local Nusselt number decreases with the increase in the nanoparticle diameter and Hartmann number, whereas it enhances with the increase in the measure of nanoparticle by volume, magnetic field inclination angle and Rayleigh number. It is also found that the inner shape of the annulus significantly affects the thermal flow as well as the Nusselt number.

Effects of the divertor tile geometries and magnetic field angles on the heat fluxes to the surface

A two dimension-in-space and three dimension-in-velocity (2d3v) Particle-In-Cell (PIC) code is applied to investigate the plasma behaviors at the divertor gaps region in this work. Electron and D+ ion fluxes to the tile surface in the poloidal and toroidal gaps for different shaped edges are compared to demonstrate the optimized tile geometry. For poloidal gap, shaped edge in the shadowing side makes more ions penetrate into the gap, while shaped edge in the wetted side can mitigate the peak flux value. For toroidal gap, most ions entering the gap impinge on the side tile mainly due to the E×B drift, and shaped wetted edges also can mitigate the peak heat fluxes. In addition, effects of magnetic field inclination angle from toroidal direction on the plasma behaviors are simulated for poloidal and toroidal gaps, respectively. It is found that the magnetic field angles don’t influence the plasma behaviors in poloidal gap; while significant changes have been observed in the toroidal gap.

Natural convection heat transfer combined with melting process in a cubical cavity under the effects of uniform inclined magnetic field and local heat source

Natural convective heat transfer combined with melting in a cubical cavity filled with a pure gallium under the effects of inclined uniform magnetic field and local heater has been studied numerically. The domain of interest is an enclosure bounded by two isothermal opposite vertical surfaces of low constant temperature and adiabatic other walls. A heat source of constant temperature is located on the bottom wall. An inclined uniform magnetic field affects the melting process inside the cavity. The governing equations formulated in dimensionless vector potential functions, vorticity vector and temperature with corresponding initial and boundary conditions have been solved using implicit finite difference method of the second-order accuracy. The effects of the Hartmann number, magnetic field inclination angle and dimensionless time on streamlines, isotherms, profiles of temperature and velocity as well as mean Nusselt number at the heat source surface have been analyzed. The obtained results revealed that a growth of magnetic field intensity reflects the convective flow suppression and heat transfer rate reduction. High values of Hartmann number homogenize the liquid flow and heat transfer inside the melting zone.

ON HELIUM MIXING IN QUASI-GLOBAL SIMULATIONS OF THE INTRACLUSTER MEDIUM

ABSTRACT The assumption of a spatially uniform helium distribution in the intracluster medium (ICM) can lead to biases in the estimates of key cluster parameters if composition gradients are present. The helium concentration profile in galaxy clusters is unfortunately not directly observable. Current models addressing the putative sedimentation are one-dimensional and parametrize the presence of magnetic fields in a crude way, ignoring the weakly collisional, magnetized nature of the medium. When these effects are considered, a wide variety of instabilities can play an important role in the plasma dynamics. In a series of recent papers, we have developed the local, linear theory of these instabilities and addressed their nonlinear development with a modified version of Athena. Here, we extend our study by developing a quasi-global approach that we use to simulate the mixing of helium as induced by generalizations of the heat-flux-driven buoyancy instability (HBI) and the magnetothermal instability, which feed off thermal and composition gradients. In the inner region of the ICM, mixing can occur over a few gigayears, after which the average magnetic field inclination angle is ∼30°–50°, resulting in an averaged Spitzer parameter higher by about 20% than the value obtained in homogeneous simulations. In the cluster outskirts the instabilities are rather inefficient, due to the shallow gradients. This suggests that composition gradients in cluster cores might be shallower than one-dimensional models predict. More quantitative statements demand more refined models that can incorporate the physics driving the sedimentation process and simultaneously account for the weakly collisional nature of the plasma.

Natural Convective Heat Transfer Flow of Nanofluids Inside a Quarter-Circular Enclosure Using Nonhomogeneous Dynamic Model

In this paper, we have studied the problem of two-dimensional transient convective flow and heat transfer in nanofluids in a quarter-circular-shaped enclosure using newly proposed nonhomogeneous dynamic mathematical model. The round wall of the enclosure is maintained at constant low temperature and the variable thermal condition on the bottom heated wall is considered, whereas the vertical wall is regarded as adiabatic. The enclosure is permeated by an inclined uniform magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing nondimensional partial differential equations. The result shows that 1- to 10-nm-sized nanoparticles are uniform and stable in the solution. The external magnetic field and its direction control the flow pattern of nanofluid significantly. The average Nusselt number increases significantly, as nanoparticle volume fraction, magnetic field inclination angle and Rayleigh number increase. Average Nusselt number of cobalt–kerosene nanofluid is much higher than other 17 types of nanofluids which are studied in the present analysis. The flow behaviors and the heat transfer rates of 18 types of nanofluids have been presented for the scientific and engineering community to become familiar with such nanofluids and apply them in practical applications.

MHD natural convection in a partially open trapezoidal cavity filled with a nanofluid

A numerical study of natural convection in a partially open trapezoidal cavity filled with a CuO nanofluid under the effect of uniform magnetic field of various orientations has been carried out. Inclined wall of the cavity is heated, horizontal walls are adiabatic while cold nanofluid enters into the cavity from an open boundary. To analyze the effects of magnetic field intensity and its inclination angle with nanoparticles volume fraction, the finite difference method has been utilized to solve the governing equations formulated in dimensionless stream function, vorticity and temperature. Analysis has been conducted in a wide range of governing parameters such as Rayleigh number (Ra=103–105), Prandtl number (Pr=7.0), Hartmann number (Ha=0, 10, 50, 100), inclination angle of magnetic field (α=0–π) and nanoparticles volume fraction (0≤ϕ≤0.04). It has been found that an increase in Hartmann number leads to the heat transfer reduction, while an increase in the nanoparticles volume fraction reflects the heat transfer enhancement.

Non-Lie top tunneling and quantum bilocalization in planar Penning trap

We describe how a top-like quantum Hamiltonian over a non-Lie algebra appears in the model of the planar Penning trap under the breaking of its axial symmetry (inclination of the magnetic field) and tuning parameters (electric voltage, magnetic field strength and inclination angle) at double resonance. For eigenvalues of the quantum non-Lie top, under a specific variation of the voltage on the trap electrode, there exists an avoided crossing effect and a corresponding effect of bilocalization of quantum states on pairs of closed trajectories belonging to common energy levels. This quantum tunneling happens on the symplectic leaves of the symmetry algebra, and hence it generates a tunneling of quantum states of the electron between the 3D-tori in the whole 6D-phase space. We present a geometric formula for the leading term of asymptotics of the tunnel energy-splitting in terms of symplectic area of membranes bounded by invariantly defined instantons.

Magnetic field and internal heat generation effects on the free convection in a rectangular cavity filled with a porous medium saturated with Cu–water nanofluid

The present study investigates the effect of magnetic field and internal heat generation on the free convection flow in a rectangular cavity. Here, the cavity is filled with a porous medium saturated with Cupper Cu–water nanofluid. The governing equations are transformed into dimensionless form in stream function and solved numerically using finite difference method. The computations were carried out for a wide range of the Hartmann number, solid volume fraction and magnetic field parameter. Results have been presented in terms of the isotherms, streamlines, average Nusselt number, velocity and temperature profiles. The obtained results are compared with the previous published work and it showed a good agreement. It is found that the average Nusselt number decreases as the Hartmann number or the solid volume fraction increases, while the opposite behavior occurs with the increase in magnetic field inclination angle. Moreover, the increase in the Hartmann number leads to decrease the maximum value of stream function, while it enhances the maximum temperature.

MHD free convection in a wavy open porous tall cavity filled with nanofluids under an effect of corner heater

A numerical analysis of MHD natural convection in a wavy open porous tall cavity filled with a Cu–water nanofluid in the presence of an isothermal corner heater has been carried out. The cavity is cooled from the left wavy wall and heated from the right bottom corner while the bottom wall is adiabatic. Uniform magnetic field affects the heat transfer and fluid flow with an inclination angle to the axis x¯. Mathematical model formulated using the single-phase nanofluid approach in dimensionless variables stream function, vorticity and temperature has been solved by finite difference method of the second order accuracy in a wide range of governing parameters: Rayleigh number (Ra=100–1000), Hartmann number (Ha=0–100), inclination angle of the magnetic field (γ=0–π) and solid volume fraction parameter of nanoparticles (φ=0.0–0.05). Main efforts have been focused on the effects of these parameters on the fluid flow and heat transfer inside the cavity. Numerical results have been presented in the form of streamlines, isotherms and average Nusselt numbers. It has been found heat transfer enhancement with Rayleigh number and heat transfer reduction with Hartmann number, while magnetic field inclination angle leads to non-monotonic changes of the heat transfer rate.

Influence of inclined Lorentz force on micropolar fluids in a square cavity with uniform and nonuniform heated thin plate

In the present study, the effect of inclined magnetic field on natural convection of micro-polar fluid in a square cavity with uniform and nonuniform heated thin plate built in centrally is investigated numerically. The vertical walls are cooled while the top and bottom walls are insulated. The thin plate is assumed to be isothermal with a linearly varying temperature. The governing equations were solved by finite volume method using second order central difference scheme and upwind differencing scheme. The numerical investigation is carried out for different governing parameters namely, the Hartmann number, inclination angle of magnetic field, Rayleigh number, vortex viscosity and source non-uniformity parameters. The result shows that the heat transfer rate is decreased when increasing Hartmann number, inclination angle of magnetic field and vortex viscosity parameter. It is found that the non-uniformity parameter affects the fluid flow and temperature distribution especially for the high Rayleigh numbers. Finally, the overall heat transfer rate of micro-polar fluids is found to be smaller than that of Newtonian fluid.

Numerical Approach of Coupling Vibration Magneto-convection In Nanofluid

The objective of our work is to visualize numerically the effect of coupling vibratory excitation and magnetic field on cooling an electronic component or a solar cell (originality of our study) in arid and semi-arid area . A square cavity of side H filled with Al 2 O 3 -water nanofluid where an electronic component is placed on the bottom horizontal wall is maintained at isothermal hot temperature T h . The top horizontal wall is maintained at a cold temperature T c . The vertical walls are adiabatic. The equations describing the natural convection flow in the square cavity consist of mass conservation, momentum and energy. For the physical parameters of Al 2 O 3 -water nanofluid, we use the Brinkman and Wasp model. Transport equations are solved numerically by finite element method. The results are obtained for Rayleigh number Ra= 10 5 , Hartmann numbers between 0 and 100 and vibratory excitation inclination angle between 0° and 90°. The external magnetic field inclination angle varies between 0° and 90° and the Rayleigh number ratio between 0 and 50. Results are presented in the form of heat transfer flux ratio and maximum absolute value of stream function.

Effect of inclined magnetic field on natural convection melting in a square cavity with a local heat source

MHD natural convection melting in a square cavity with a local heater has been analyzed numerically. The domain of interest is an enclosure bounded by isothermal vertical walls of low constant temperature and adiabatic horizontal walls. A heat source of constant temperature is located on the bottom wall. An inclined uniform magnetic field affects the natural convective heat transfer and fluid flow inside the melt. The governing equations formulated in dimensionless stream function, vorticity and temperature with corresponding initial and boundary conditions have been solved using implicit finite difference method of the second-order accuracy. The effects of the Rayleigh number, Stefan number, Hartmann number, magnetic field inclination angle and dimensionless time on streamlines, isotherms and Nusselt number at the heat source surface have been analyzed.

Natural convection in a flexible sided triangular cavity with internal heat generation under the effect of inclined magnetic field

In this numerical study, magnetohydrodynamics natural convection in a flexible sided triangular cavity with internal heat generation is investigated. The inclined wall of the cavity is cooled and flexible while the left vertical wall is partially heated. Galerkin weighted residual finite element method is used to solve the governing equations. The effects of pertinent parameters such as external Rayleigh number (between 104 and 106), internal Rayleigh number (between 104 and 107), elastic modulus of flexible wall (between 500 and 105), Hartmann number (between 0 and 40) and inclination angle of the magnetic field (between 0° and 90°) on the fluid flow and heat transfer characteristics were numerically investigated. It was observed local and averaged Nusselt number enhance with external Rayleigh number but in the vicinity of the upper location of the heater local heat transfer deteriorates due to the inclined wall deformation with increasing external Rayleigh number. Heat transfer reduces with internal Rayleigh number and Hartmann number. Averaged heat transfer decreases 13.25% when internal Rayleigh number is increased from 104 to 107 and decreases 40.56% when Hartmann number is increased from 0 to 10. The reduction in the convection with magnetic field is effective for higher values of external Rayleigh numbers and averaged heat transfer increases with magnetic field inclination angle.

Magnetic field effect on natural convection and entropy generation in a half-moon shaped cavity with semi-circular bottom heater having different ferrofluid inside

In this study magneto-hydrodynamic convection in a half-moon shaped cavity filled with ferrofluid has been analyzed numerically. The cavity has two semi-circular bottom heaters and effect of the distance between these two heaters (λ=0.1,0.4) has been thoroughly investigated. Numerical simulation has been carried out for a wide range of Rayleigh number (Ra=103∼107), Hartmann number (Ha=0∼100) and inclination angle of magnetic field (γ=0°∼90°) to understand the flow field, thermal field and entropy generation respectively. Cobalt-kerosene and Fe3O4 -water ferrofluids are used for the present investigation and considered as a single phase fluid. Galerkin weighted residual method of finite element analysis has been used for numerical solution. The code validation and grid independency test have been carried out to justify the numerical accuracy. It has been observed that increment of magnetic field reduces the heat transfer rate, whereas increment of heater distance augments the heat transfer rate significantly. Results are discussed on the basis of Nusselt number (Nu), Bejan number (Be) and shown by contours and 3D plots. It has also been found that λ=0.4 always shows better heat transfer rate and entropy optimization.

Plasma-facing surface estimation in the presence of oblique magnetic field

Useful analytical approximation formulas for the sheath electric potential profile in the presence of secondary electron emission in oblique magnetic field is suggested.The potential distributions calculated with the proposed model are in good agreement with the respective simulations perfomed with a combined PIC and Monte Carlo code ELECTRAN. The influence of the magnetic field inclination angle on the angular and energy distributions of ions incident on plasma-facing components (PFC) and thus on the effective sputtering yield is analyzed.

MHD mixed convection and entropy generation of nanofluid filled lid driven cavity under the influence of inclined magnetic fields imposed to its upper and lower diagonal triangular domains

In this study, mixed convection of CuO–water nanofluid filled lid driven cavity having its upper and lower triangular domains under the influence of inclined magnetic fields is numerically investigated. The top horizontal wall of the cavity is moving with constant speed of uw with +x direction while no-slip boundary conditions are imposed on the other walls of the cavity. The top wall of the cavity is maintained at constant cold temperature of Tc while the bottom wall is at hot temperature of Th and on the other walls of the cavity are assumed to be adiabatic. The governing equations are solved by using Galerkin weighted residual finite element formulation. Entropy generation is produced by using formulation and integrated with calculated velocities and temperatures. The numerical investigation is performed for a range of parameters: Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), inclination angle of magnetic field (between 0° and 90°) and solid volume fraction of the nanofluid (between 0 and 0.05). Different combinations of Hartmann numbers and inclination angles of the magnetic fields are imposed in the upper and lower triangular domains of the square cavity. It is observed that the local and averaged heat transfer deteriorates when the Richardson number, Hartmann number of the triangular domains increase. When the Hartmann number and magnetic angle of the upper triangle are increased, more deterioration of the averaged transfer is obtained when compared to lower triangular domain. Local and averaged heat transfer increase as the solid volume fraction of the nanoparticles increases and adding nanoparticles is more effective for the local enhancement of the heat transfer when the heat transfer rate is high and convection is not damped with lowering the Hartmann number. Second law analysis of the system for different combinations of flow parameters is also performed.