Natural convection flow under a magnetic field in an inclined square enclosure differentialy heated on adjacent walls

Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined square enclosure differentially heated along the bottom and left vertical walls while the other walls are kept isothermal was considered. The governing equations were solved numerically for the stream function, vorticity and temperature ratio using the differential quadrature method for various Grashof and Hartmann numbers, inclination angle of the enclosure and direction of the magnetic field. The orientation of the enclosure changes the temperature gradient inside and has a significant effect on the flow pattern. Magnetic field suppresses the convective flow and its direction also influences the flow pattern, causing the appearance of inner loops and multiple eddies. The surface heat flux along the bottom wall is slightly increased by clockwise inclination and reduced by half by the counterclockwise inclination. The surface heat flux along the upper portion of the left side wall is reversed by the rise of warmer fluids due to the convection currents for no inclination and clockwise inclination of the enclosure.     

An experimental research on surface oscillation of buoyant-thermocapillary convection in open cylindrical annuli

An experiment is carried out on the surface oscillation of buoyant-thermocapillary convection in an open cylindrical annulus. When the radial temperature difference AT reaches a critical value △Tc, a regular oscillation appears and soon disappears on the open surface, which varies when the liquid layer＇s thickness h and temperature difference △T are varied. With growth of △T, dominant frequency of the visible oscillation will grow too but is found within certain frequencies. Driving forces, buoyance and thermocapillarity, are responsible for this phenomanon and the ＂balance＂ point is considered to exist when h is between 4.5-5.0 mm. Surface oscillation region is also found restricted within a narrow gap when Bo is smaller than 3.7.     

Hydromagnetic convection in a rotating annulus with an azimuthal magnetic field

The problem of convection induced by radial buoyancy in an electrically conducting fluid contained by a rotating cylindrical annulus (angular frequency, ) in the presence of a homogeneous magnetic field (B) in the azimuthal direction is considered. The small gap approximation is used together with rigid cylindrical boundaries. The onset of convection occurs in the form of axial, axisymmetric or oblique rolls. The angle between the roll axis and the axis of rotation depends of the ratio between the Chandrasekhar number, QB², and the Coriolis number, . Fully three-dimensional numerical simulations as well as Galerkin representations for roll patterns including the subsequent stability analysis are used in the theoretical investigation. At finite amplitudes, secondary transitions to 3D-hexarolls and to spatio-temporal chaos are found. Overlapping regions of pattern stability exist such that the asymptotically realized state may depend on the initial conditions. PACS 47.27.-i, 47.65.+a     

Effect of a rotating magnetic field on convection in a horizontal fluid layer

The stability of mechanical equilibrium of a horizontal layer of conducting fluid in the presence of a magnetic field rotating in a horizontal plane is considered. Both finite field rotation frequencies and the limiting case of high frequencies are investigated. It is shown that the magnetic field stabilizes the equilibrium. The dependence of the critical perturbation wavelength on the field strength is non-monotonic, and with increase in the magnetic field strength the mode of most dangerous perturbations changes from long-to short-wave type. Nonlinear three-dimensional convection regimes are calculated numerically. It is found that at finite supercriticalities and a sufficiently strong magnetic field the rolls and the hexagonal cells may be stable simultaneously.     

Effects of magnetic field on nanofluid forced convection in a partially heated microchannel

This paper numerically examines the laminar forced convection of a water–Al₂O₃ nanofluid flowing through a horizontal microchannel. The middle section of the microchannel is heated with a constant and uniform heat flux. The middle section is also influenced by a transverse magnetic field with a uniform strength. The effects of pertinent parameters such as the Reynolds number (0≤Re≤1000), the solid volume fraction (0≤?≤0.04) and the Hartmann number (0≤Ha≤100) on the flow and temperature fields and the heat transfer performance of the microchannel are examined against numerical predictions. The results show that the microchannel performs better heat transfers at higher values of the Reynolds and Hartmann numbers. For all values of the Reynolds and Hartmann numbers considered in this study, the average Nusselt number on the middle section surface of the microchannel increases as the solid volume fraction increases. The rate of this increase is considerably more at higher values of the Reynolds number and at lower values of the Hartmann number.     

Flow and heat transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet subject to a transverse magnetic field

An analysis is performed for flow and heat transfer of a steady laminar boundary layer flow of an electrically conducting fluid of second grade in a porous medium subject to a transverse uniform magnetic field past a semi-infinite stretching sheet with power-law surface temperature or power-law surface heat flux. The effects of viscous dissipation, internal heat generation of absorption and work done due to deformation are considered in the energy equation. The variations of surface temperature gradient for the prescribed surface temperature case (PST) and surface temperature for the prescribed heat flux case (PHF) with various parameters are tabulated. The asymptotic expansions of the solutions for large Prandtl number are also given for the two heating conditions. It is shown that, when the Eckert number is large enough, the heat flow may transfer from the fluid to the wall rather than from the wall to the fluid when Eckert number is small. A physical explanation is given for this phenomenon.     

Steady and transient free convection of an electrically conducting fluid from a vertical plate in the presence of a magnetic field

Summary An analysis is made for the laminar free convection and heat transfer of a viscous electrically conducting fluid from a hot vertical plate in the case when the induced field is negligible compared to the imposed magnetic field. It is found that similar solutions for velocity and temperature exist when the imposed magnetic field (acting perpendicular to the plate) varies inversely as the fourth root of the distance from the lowest end of the plate. Explicit expressions for velocity, temperature, boundary layer thickness and Nusselt number are obtained and the effect of a magnetic field on them is studied. It is found that the effect of the magnetic field is to decrease the rate of heat transfer from the wall. In the second part, the method of characteristics is employed to obtain solutions of the time-dependent hydromagnetic free convection equations (hyperbolic) of momentum and energy put into integral form. The results yield the time required for the steady flow to be established, and the effect of the magnetic field on this time is studied.     

Effect of induced magnetic field on natural convection in vertical concentric annuli

In the present paper,we have considered the steady fully developed laminar natural convective flow in open ended vertical concentric annuli in the presence of a radial magnetic field.The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account.The transport equations concerned with the considered model are first recast in the non-dimensional form and then unified analytical solutions for the velocity,induced magnetic field and temperature field are obtained for the cases of isothermal and constant heat flux on the inner cylinder of concentric annuli.The effects of the various physical parameters appearing into the model are demonstrated through graphs and tables.It is found that the magnitude of maximum value of the fluid velocity as well as induced magnetic field is greater in the case of isothermal condition compared with the constant heat flux case when the gap between the cylinders is less or equal to 1.70 times the radius of inner cylinder,while reverse trend occurs when the gap between the cylinders is greater than 1.71 times the radius of inner cylinder.These fields are almost the same when the gap between the cylinders is equal to 1.71 times the radius of inner cylinder for both the cases.It is also found that as the Hartmann number increases,there is a flattening tendency for both the velocity and the induced magnetic field.The influence of the induced magnetic field is to increase the velocity profiles.     

On the suppression of the vorticity in an electrically conducting fluid by means of an applied magnetic field

Summary The aim of this work is to investigate the effects of the application of a transverse magnetic on a fluid capable to support electrical current. It has been supposed that the flow could be represented by the vorticity model of Stuart.It turns out that, when a suitable magnetic parameter exceeds a peculiar value, the vorticity tends to decay in the long run; at the same time the inflexions in the velocity profiles tend to disappear, becoming smoother and smoother. Consequently the majority of the velocity gradient inclines to be transferred to the wall.Finally this work analyzes the thin boundary layer originated near the wall because of the smoothing of the velocity profiles.

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Sommario Scopo di questo lavoro è lo studio degli effetti dell'applicazione di un campo magnetico trasversale su di una corrente di fluido conduttore di elettricità che segue nel suo moto il modello di vorticità di Stuart. Si trova che, per valori sufficientemente grandi di un opportuno parametro magnetico, la vorticità tende a spegnersi nel tempo e i flessi nei profili di velocità tendono a smorzarsi, comportando un progressivo appiattimento nella forma di questi, con conseguente trasferimento a parete della maggior parte del gradiente di velocità.Viene inoltre studiato lo strato limite viscoso di limitato spessore che si forma a parete come conseguenza dell'appiattimento dei profili di velocità.

     

Numerical study on magneto-convection of cold water in an open cavity with variable fluid properties

The aim of the present study is to understand the problem of buoyancy and thermocapillary induced convection of cold water near its density maximum in an open cavity with temperature dependent properties in the presence of uniform external magnetic field. The governing equations are solved by the finite volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, Rayleigh, Hartmann and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. Convection heat transfer is enhanced by thermocapillary force when buoyancy force is weakened.     

Effect of non-uniform temperature gradient and magnetic field on onset of Marangoni convection heated from below by a constant heat flux

This paper investigates the effect of non-uniform temperature gradient and magnetic field on Marangoni convection in a horizontal fluid layer heated from below and cooled from above with a constant heat flux. A linear stability analysis is performed. The influence of various parameters on the convection onset is analyzed. Six non-uniform basic temperature profiles are considered, and some general conclusions about their desta- bilizing effects are presented.     

Effect of a longitudinal magnetic field on the flow of an electrically conducting fluid in a circular tube with a sharp narrowing at the entrance

The procedure described in [1] is used to study the effect of entry conditions to the test section on the nature of the flow of an electrically conducting fluid in a circular tube in a longitudinal magnetic field.

     

Effect of thermophoretic particle deposition in non-Newtonian free convection flow over a vertical plate with magnetic field effect

The present contribution deals with the effects of thermophoretic particle deposition on the free convective flow over a vertical flat plate embedded in a non-Newtonian fluid-saturated porous medium in the presence of a magnetic field. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an efficient implicit finite-difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.     

Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel

The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Unsteady stagnation-point flow of a Newtonian fluid in the presence of a magnetic field

The unsteady stagnation-point flow of a viscous fluid impinging on an infinite plate in the presence of a transverse magnetic field is examined and solutions are obtained. It is assumed that the infinite plate at y=0 is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained for various values of the Hartmann's number.     

The effect of the couple stress parameter and Prandtl number on the transient natural convection flow over a vertical cylinder

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nus- selt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.     

An experimental study of the effect of wall temperature nonuniformity on natural convection in an enclosure heated from the side

An experimental study of natural convection in a parallelepipedal enclosure induced by a single vertical wall is described. The upper half of this wall was warm and the lower half cold. The other enclosure walls were insulated. The temperature and flow measurements were performed in the high Rayleigh number regime (10¹⁰<Ra<5×10¹⁰) by using water as the working fluid. The Rayleigh number was based on the enclosure height and the temperature difference between the warm and the cold part of the driving wall. The flow field featured two flat cells, one filled with warm fluid along the top horizontal wall, and the other filled with cold fluid along the bottom horizontal wall. Each of these cells was surrounded by an additional cell as tall as half the enclosure height. The above flow structure prohibited extensive thermal contact between warm and cold fluid, thus limiting the role of convection on the heat transfer process in the cavity. The findings of this study differ significantly from the findings of previous studies based on the ‘classical’ enclosure model possessing two isothermal vertical walls, the one warm and the other cold, and support the view that the use of ‘more realistic‘ temperature boundary conditions in enclosure natural convection needs careful examination.     

Thermal convection in a cylindrical annulus under a combined effect of the radial and vertical gravity

The stability of the flow of a dielectric fluid confined in a cylindrical annulus submitted to a radial temperature gradient and a radial electric field is investigated theoretically and experimentally. The radial temperature gradient induces a vertical Archimedean buoyancy and a radial dielectrophoretic buoyancy. These two forces intervene simultaneously in the destabilization of the flow, leading to the occurrence of four types of modes depending on the relative intensity of these two buoyancies and on the fluid's properties: hydrodynamic and thermal modes that are axisymmetric and oscillatory, stationary columnar modes and electric modes which are stationary and non-axisymmetric modes. Experiments performed in a parabolic flight show the existence of non-axisymmetric modes that should be either columnar or helicoidal vortices.