Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid over a rotating disk by considering Arrhenius energy

This research work explores the effect of hybrid nanoparticles on the flow over a rotating disk by using an activation energy model. Here, we considered molybdenum disulfide and ferro sulfate as nanoparticles suspended in base fluid water. The magnetic field is pragmatic normal to the hybrid nanofluid flow direction. The derived nonlinear ordinary differential equations are nondimensionalized and worked out numerically with the help of Maple software by the RKF-45method. The scientific results for a non-dimensionalized equation are presented for both nanoparticle and hybrid nanoparticle case. Accoutrements of various predominant restrictions on flow and thermal fields are scanned. Computation estimation for friction factor, local Nusselt number and Sherwood number are also executed. Results reveal that the reduction of the heat transfer rate is greater in hybrid nanoparticles when compared to nanoparticles for increasing values of Eckert Number and the thermal field enhances for the enhanced values of volume fraction.     

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.     

Transport phenomena of carbon nanotubes and bioconvection nanoparticles on stagnation point flow in presence of induced magnetic field

This article is a numerical study of stagnation point flow of carbon nanotubes over an elongating sheet in presence of induced magnetic field submerged in bioconvection nanoparticles. Two types of carbon nanotubes are considered i.e. single wall carbon nanotube and multi wall carbon nanotube mixed in based fluid taken to be water as well as kerosene-oil. The emphasis of present study is to examine effect of induced magnetic field on boundary layer flows along with influence of SWCNT and MWCNT. Physical problem is mathematically modeled and simplified by using appropriate similarity transformations. Shooting method with Runge-Kutta of order 5 is employed to compute numerical results for non-dimensional velocity, induced magnetic field and temperature. The effects of pertinent parameters are portrayed through graphs. Numerical values of skinfriction coefficient and Nusselt number are tabulated to study the behaviors at the stretching surface. It is depicted that induced magnetic field is an increasing function of solid nanoparticles volumetric fraction. Moreover, MWCNT contributes in rising induced magnetic field more as compared to SWCNT for both water and kerosene-oil based fluids.     

Induced electric current-based formulation in computations of low magnetic Reynolds number magnetohydrodynamic flows

We use the induced electric current as the main electromagnetic variable to compute low magnetic Reynolds number magnetohydrodynamic (MHD) flows. The equation for the induced electric current is derived by taking the curl of the induction equation and using Ampère’s law. Boundary conditions on the induced electric current are derived at the interface between the liquid and the thin conducting wall by considering the current loop closing in the wall and the adjacent liquid. These boundary conditions at the liquid–solid interface include the Robin boundary condition for the wall-normal component of the current and an additional equation for the wall potential to compute the tangential current component. The suggested formulation (denominated j-formulation) is applied to three common types of MHD wall-bounded flows by implementing the finite-difference technique: (i) high Hartmann number fully developed flows in a rectangular duct with conducting walls; (ii) quasi-two-dimensional duct flow in the entry into a magnet; and (iii) flow past a magnetic obstacle. Comparisons have been performed against the traditional formulation based on the induced magnetic field (B-formulation), demonstrating very good agreement.     

Particle‐in‐cell simulation of the effect of curved magnetic field on wall bombardment and erosion in a hall thruster

A curved, convex towards the channel bottom magnetic field is an important feature of an advanced Hall thruster that allows confining the plasma flow in the channel center, reducing the divergence angle of the ejected ion beam, and improving the discharge performance. In this article, the discharge behaviour of a Hall thruster in magnetic fields with different degrees of curvature is simulated with a particle‐in‐cell numerical method, and the effect of curved magnetic field on the ion bombardment and wall erosion and the associated mechanisms are studied and analysed. The results show that, as the curvature of the magnetic field increases, the propellant ionization becomes more confined at the channel center, the potential drop inside the channel decreases, and the acceleration region shifts outside the channel, which lead to the attenuation of the ion energy bombarding the wall and the deviation of the bombardment angle from the optimal sputtering angle. Conversely, the ion flux bombarding the wall near the channel exit increases. Nevertheless, the bombardment energy and angle are the dominant factors for the wall erosion, and the wall erosion rate clearly decreases with the increasing curvature of the magnetic field. These findings are closely related to the behaviour of electron conduction under a curved magnetic field; the relevant mechanisms are clarified in this article.     

Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.     

Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection

In this communication, an optimization of entropy generation is performed through thermodynamics second law. Tangent hyperbolic nanomaterial model is used which describes the important slip mechanism namely Brownian and thermophoresis diffusions. MHD fluid is considered. The novel binary chemical reaction model is implemented to characterize the impact of activation energy. Nonlinear mixed convection, dissipation and Joule heating are considered. Appropriate similarity transformations are implemented to get the required coupled ODEs system. The obtained system is tackled for series solutions by homotopy method. Graphs are constructed to analyze the impact of different flow parameters on entropy number, nanoparticle volume concentration, temperature and velocity fields. Total entropy generation rate is calculated via various flow variables. It is noticed from obtained results that entropy number depend up thermal irreversibility, viscous dissipation and Joule heating irreversibility and concentration irreversibility. Decreasing behavior of concentration is witnessed for higher estimations of chemical reaction variable. Entropy number is more for higher Hartmann number, Weissenberg number and chemical reaction variable while contrast behavior is noted for Bejan number.     

Orientational transitions in a ferronematic layer with bistable anchoring at the boundary

A possibility of the first-order transition, as well as reentrant transitions, induced by an external magnetic field between the homeotropic phase and the hybrid homeotropically planar phase in a ferronematic liquid crystal (ferronematic) with bistable anchoring at the layer boundary is demonstrated in the framework of a continuum theory. The critical values of the material parameters of the ferronematic, the anchoring energy, the thickness of the layer, and the magnetic field strength, for which this transition is possible, are determined. The cases of positive and negative diamagnetic anisotropy of the ferronematic are considered.     

Importance of Darcy–Forchheimer porous medium in 3D convective flow of carbon nanotubes

This article explores Darcy–Forchheimer 3D flow of water-based carbon nanomaterial (CNTs). A bi-directional linear stretchable surface has been used to create the flow. Flow in porous space is represented by Darcy–Forchheimer expression. Heat transfer mechanism is explored through convective heating. Results for single-wall (SWCNTs) and multi-wall (MWCNTs) carbon nanotubes have been presented and compared. The reduction of partial differential system into nonlinear ordinary differential system is made through suitable variables. Optimal homotopic scheme is used for solutions development of governing flow problem. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Skin friction coefficients and local Nusselt number are analyzed through plots. Our findings show that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Significance of Darcy-Forchheimer Porous Medium in Nanofluid Through Carbon Nanotubes

This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial (CNTs). A bidirectional nonlinear stretchable surface has been utilized to make the flow. Disturbance in permeable space has been represented by Darcy Forchheimer (DF) expression. Heat transfer mechanism is explored through convective heating. Outcomes for SWCNT and MWCNT have been displayed and compared. The reduction of partial differential framework into nonlinear common differential framework is made through reasonable variables. Optimal series scheme is utilized for arrangements advancement of associated flow issue. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Moreover surface drag coefficients and heat transfer rate are analyzed through plots.     

粗糙微通道内液体流动的多尺度耦合模拟

采用分子动力学与有限容积法多尺度耦合算法对粗糙微通道内的液体Poiseuille流动进行了模拟。分析了粗糙元高度、分布以及几何形状对通道内流动速度和边界滑移长度的影响。结果表明：随着粗糙元高度的增加,流动速度和粗糙元间隙底部壁面上滑移长度均减小;粗糙元分布越密或不同几何形状粗糙元所对应的固壁原子数越多,滑移长度越小,但...     

带引流条导电矩形管磁流体湍流大涡数值模拟

为研究引流条对磁流体湍流的影响，采用自主开发的低磁雷诺数流固耦合磁流体相干结构模型大涡模拟求解器，对均匀磁场作用下平行层内带引流条导电矩形管和标准导电矩形管中液态金属湍流进行了数值模拟研究。结果表明，外加垂直流动方向的均匀磁场与流动的导电流体相互作用产生与流动方向相反的洛伦兹力，能够抑制磁流体的湍流脉动，这种抑制作用随着哈特曼数增大而增强。在弱导电率条件下，当Re=16350、Ha=212 时，两种管道中的流动均转换为层流流动状态。管道内壁面摩擦系数随着哈特曼数的增大而增大。引流条能在其近壁局部区域增强横向速度，有效激发湍流，但在弱壁面导电率条件下，带引流条导电矩形管壁面摩擦系数较标准矩形管大。     

Thermal activation of magnetization in Pr_2Fe_(14)B ribbons

The aftereffect field of thermal activation,which corresponds to the fluctuation field of a domain wall,is investigated via specific measurements of the magnetization behavior in Pr2Fe14B nanocrystalline magnets.The thermal activation is a magnetization reversal arising from thermal fluctuation over an energy barrier to an equilibrate state.According to the magnetic viscosity and the field sweep rate dependence of the coercivity,the calculated values of the fluctuation field are lower than the aftereffect field and in a range between those of domain walls and individual grains.Based on these results,we propose that the magnetization reversal occurs in multiple ways involving grain activation and domain wall activation in thermal activation,and the thermal activation decreases the coercivity by~0.2 kOe in the Pr2Fe14B ribbons.     

Significance of Darcy-Forchheimer Porous Medium in Nanofluid Through Carbon Nanotubes

This article manages Darcy-Forchheimer 3D flow of water based carbon nanomaterial (CNTs). A bidirectional nonlinear stretchable surface has been utilized to make the flow. Disturbance in permeable space has been represented by Darcy Forchheimer (DF) expression. Heat transfer mechanism is explored through convective heating.Outcomes for SWCNT and MWCNT have been displayed and compared. The reduction of partial differential framework into nonlinear common differential framework is made through reasonable variables. Optimal series scheme is utilized for arrangements advancement of associated flow issue. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Moreover surface drag coefficients and heat transfer rate are analyzed through plots.     

Cholesteric–nematic transitions induced by a shear flow and a magnetic field

The untwisting of the helical structure of a cholesteric liquid crystal under the action of a magnetic field and a shear flow has been studied theoretically. Both factors can induce the cholesteric–nematic transition independently; however, the difference in the orienting actions of the magnetic field and the shear flow leads to competition between magnetic and hydrodynamic mechanisms of influence on the cholesteric liquid crystal. We have analyzed different orientations of the magnetic field relative to the direction of the flow in the shear plane. In a number of limiting cases, the analytic dependences are obtained for the pitch of the cholesteric helix deformed by the shear flow. The phase diagrams of the cholesteric–nematic transitions and the pitch of the cholesteric helix are calculated for different values of the magnetic field strength and the angle of orientation, the flow velocity gradient, and the reactive parameter. It is shown that the magnetic field stabilizes the orientation of the director in the shear flow and expands the boundaries of orientability of cholesterics. It has been established that the shear flow shifts the critical magnetic field strength of the transition. It is shown that a sequence of reentrant orientational cholesteric–nematic–cholesteric transitions can be induced by rotating the magnetic field in certain intervals of its strength and shear flow velocity gradients.     

基于微通道液氮换热的脉冲磁体快速冷却方法研究北大核心CSCD

影响脉冲磁体重频运行能力的关键因素是磁体的冷却速度。提出了一种脉冲磁体快速冷却方法:在磁体导体内开微小通道,在通道内注入液氮,通过增大导体与液氮之间的直接接触面积(换热面积)、液氮单相流动换热、液氮流动沸腾换热这三个途径来大幅提高导体的冷却速度,与此同时尽可能减小对脉冲磁体性能(磁场强度、脉宽和内直径)的影响。阐述了基于微通道内液氮流动、沸腾换热的脉冲磁体快速冷却方法的原理,开展了数值模拟和验证性试验,结果表明,对于25 T的20 mm口径脉冲磁体,采用快速冷却方法,30 s即可冷却至初始温度,为磁体仅浸泡在液氮中的冷却时间(600 s)的5%,冷却速度提高了19倍。     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Magnetic field-induced orientational phases of ferronematics in shear flow

We examine the effect of shear flow on the orientational phase transitions induced by a magnetic field in ferronematic liquid crystals. Continuum approach based on the generalized Leslie–Ericksen theory is used to describe the dynamics of ferronematic liquid crystals. We consider three orientations of the magnetic field in a plane of shear flow. Stationary solutions for the director and the magnetization are obtained as functions of the magnetic field strength for different values of material parameters. Our results show that shear flow can lead to the shift of the field thresholds or to a “smoothing” of the magnetic field-induced transitions in ferronematics. In the limiting case of pure nematic liquid crystals, we revealed threshold effects, which are unstipulated by the orientational elasticity of a liquid crystal, in contrast to the conventional Fréedericksz transition.     

Effect of couple stresses on transient MHD poiseuille flow

The unsteady laminar flow of an electrically conducting viscous fluid between parallel insulating plates subject to a transverse magnetic field is considered. The plates are fixed and flow is due to a constant pressure gradient. The induced field is taken into account. The fluid is incompressible and of couple stress type. The defining equations are coupled and numerical solutions for different values of couple stress parameter are obtained. The velocity and induced magnetic field profiles are sketched as functions of time, Hartmann number, and magnetic Prandtl number. The velocity decreases with increase in couple stress parameter.