Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat transmission.In the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking sheet.This work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission assessment.Employing appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM technique.The impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a graph.Considering various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical form.This leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of interest.Furthermore,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer declined.According to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)profiles.The HAM and the numerical technique(shooting method)were found to be in good agreement.

Simulation of Natural Convection Flow with Magneto-Hydrodynamics in a Wavy Top Enclosure with a Semi-Circular Heater

Natural convection flow in enclosure has different applications such as room ventilation, heat exchangers, the cooling system of a building etc. The Finite-Element method based on the Galerkin weighted residual approach is used to solve two-dimensional governing mass, momentum and energy-equations for natural convection flow in the presence of a magnetic field on a roof top with semi-circular heater. In the enclosure the horizontal lower wall was heated, the vertical two walls were adiabatic, inside the semi-circular heater, the wavy top wall cooled. The parameters Rayleigh number, Hartmann number and Prandtl number are considered. The effects of the Hartmann number and Rayleigh number on the streamlines, isotherms, velocity profiles and average Nusselt number are examined graphically. The local Nusselt number and the average Nusselt number of the heated portion of the enclosure with the semi-circular heater are presented in this paper. Finally, for the validation of the existing work, the current results are compared with published results and the auspicious agreement is achieved.

Influence of Thermophoresis and Brownian Motion of Nanoparticles on Radiative Chemically-Reacting MHD Hiemenz Flow over a Nonlinear Stretching Sheet with Heat Generation

In this study,a radiative MHD stagnation point flow over a nonlinear stretching sheet incorporating thermophoresis and Brownian motion is considered.Using a similarity method to reshape the underlying Partial differential equations into a set of ordinary differential equations(ODEs),the implications of heat generation,and chemical reaction on the flow field are described in detail.Moreover a Homotopy analysis method(HAM)is used to interpret the related mechanisms.It is found that an increase in the magnetic and velocity exponent parameters can damp the fluid velocity,while thermophoresis and Brownian motion promote specific thermal effects.The results also demonstrate that as the Brownian motion parameter is increased,the concentration values become smaller.

垂直上升通道内气泡–液态金属MHD流动与传热的数值研究

在聚变堆的冷却系统中,由于强磁场的影响,液态金属流动受到抑制,通过掺入气泡到液态金属中可减小磁流体力学(Magnetohydrodynamic,MHD)效应,提升传热速率。该文基于VOF多相流模型,在不同的磁场强度(0~1.3 T)和不同的气泡雷诺数(1.3×10^(4)~6.76×10^(4))范围内,对横向磁场作用下垂直上升通道中气泡-液态金属两相流动传热特性进行数值研究。结果表明,无磁场时气体呈柱状流,而在磁场作用下,由于MHD箍缩效应的影响,气柱破裂、分离,形成了气泡流;随着磁场增大,其分离点由入口逐渐向上移动,且气泡运动速度随之增加。与液态金属单相流相比,气泡-液态金属两相流动的平均换热系数随磁场强度和气泡雷诺数增加均呈下降趋势,但因两相流动显著减小由MHD效应引起的压降,从而提升通道内综合换热因子,且在磁场较小时,提升效果更好。

Magneto-Hydrodynamics Flow of Newtonian Fluid over a Suddenly Accelerated Flat Plate

In this paper the laminar flow of Newtonian conducting fluid produced by a moving plate in presence of transverse magnetic field is investigated. The basic equation governing the motion of such flow is expressed in non-dimensional form. Analytic solution of the governing equation is obtained by Laplace transformation. Numerical solution of the dimensionless equation is also obtained with the help of Crank-Nicholson implicit scheme. Velocity profiles of the corresponding problem are shown in the graphs.

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic （MHD） stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

Direct simulation of MHD flows in dual-coolant liquid metal fusion blanket using a consistent and conservative scheme

Direct simulation of 3-D MHD(magnetohydrodynamics) flows in liquid metal fusion blanket with flow channel insert(FCI) has been conducted.Two kinds of pressure equilibrium slot (PES) in FCI,which are used to balance the pressure difference between the inside and outside of FCI,are considered with a slot in Hartmann wall or a slot in side wall,respectively.The velocity and pressure distribution of FCI made of SiC/SiC_f are numerically studied to illustrate the 3-D MHD flow effects,which clearly show that the flows in fusion blanket with FCI are typical three-dimensional issues and the assumption of 2-D fully developed flows is not the real physical problem of the MHD flows in dual-coolant liquid metal fusion blanket.The optimum opening location of PES has been analyzed based on the 3-D pressure and velocity distributions.

MHD flow and heat transfer of micropolar fluid between two porous disks

A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman＇s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.

Magneto-hydrodynamic flow of squeezed fluid with binary chemical reaction and activation energy

The present exploration is conducted to describe the motion of viscous fluid embedded in squeezed channel under the applied magnetics effects.The processes of heat and mass transport incorporate the temperature-dependent binary chemical reaction with modified Arrhenius theory of activation energy function which is not yet disclosed for squeezing flow mechanism.The flow,heat and mass regime are exposed to be governed via dimensionless,highly non-linear,ordinary differential equations (ODEs) under no-slip walls boundary conditions.A well-tempered analytical convergent procedure is adopted for the solutions of boundary value problem.A detailed study is accounted through graphs in the form of flow velocity field,temperature and fluid concentration distributions for various emerging parameters of enormous interest.Skin-friction,Nusselt and Sherwood numbers have been acquired and disclosed through plots.The results indicate that fluid temperature follows an increasing trend with dominant dimensionless reaction rate σ and activation energy parameter E.However,an increment in σ and E parameters is found to decline in fluid concentration.The current study arises numerous engineering and industrial processes including polymer industry,compression and injection shaping,lubrication system,formation of paper sheets,thin fiber,molding of plastic sheets.In the area of chemical engineering,geothermal engineering,cooling of nuclear reacting,nuclear or chemical system,bimolecular reactions,biochemical process and electrically conducting polymeric flows can be controlled by utilizing magnetic fields.Motivated by such applications,the proposed study has been developed.

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

The present article investigates the dual nature of the solution of the magneto- hydrodynamic （MHD） stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting： method. It is found that the dual solutions of the flow exist for cer- tain values of tile velocity ratio parameter. The special case of the first branch solutions （the classical Newtonian fluid model） is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.

Electrical conductivity effect on MHD mixed convection of nanofluid flow over a backward-facing step

In this study,magneto-hydrodynamics (MHD) mixed convection effects of Al2O3-water nanofluid flow over a backward-facing step were investigated numerically for various electrical conductivity models of nanofluids.A uniform external magnetic field was applied to the flow and strength of magnetic field was varied with different values of dimensionless parameter Hartmann number (Ha=0,10,20,30,40).Three different electrical conductivity models were used to see the effects of MHD nanofluid flow.Besides,five different inclination angles between 0°-90° is used for the external magnetic field.The problem geometry is a backward-facing step which is used in many engineering applications where flow separation and reattachment phenomenon occurs.Mixed type convective heat transfer of backward-facing step was examined with various values of Richardson number (Ri=0.01,0.1,1,10) and four different nanoparticle volume fractions (Ф=0.01,0.015,0.020,0.025) considering different electrical conductivity models.Finite element method via commercial code COMSOL was used for computations.Results indicate that the addition of nanoparticles enhanced heat transfer significantly.Also increasing magnetic field strength and inclination angle increased heat transfer rate.Effects of different electrical conductivity models were also investigated and it was observed that they have significant effects on the fluid flow and heat transfer characteristics in the presence of magnetic field.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Approximate solutions to MHD Falkner-Skan flow over permeable wall

The magnetohydrodynamic （MHD） Falkner-Skan boundary layer flow over a permeable wall in the presence of a transverse magnetic field is examined. The approximate solutions and skin friction coefficients of the MHD boundary layer flow are obtained by using a method that couples the differential transform method （DTM） with the Pade approximation called DTM-Pade. The approximate solutions are expressed in the form of a power series that can be easily computed with an iterative procedure. The approximate solutions are tabulated, plotted for the values of different parameters and compared with the numerical ones obtained by employing the shooting technique. It is found that the approximate solution agrees very well with the numerical solution, showing the reliability and validity of the present work. Moreover, the effects of various physical parameters on the boundary layer flow are presented graphically and discussed.

Thermal Radiation Effects on MHD Boundary Layer Flow over an Exponentially Stretching Surface

The steady two-dimensional laminar boundary layer flow and heat transfer of a viscous incompressible electrically conducting fluid over an exponentially stretching surface in the presence of a uniform magnetic field with thermal radiation are investigated. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity transformation and solved numerically by shooting method. The effects of various parameters such as magnetic parameter, radiation parameter, Prandtl number and Eckert number on local skin-friction coefficient, local Nusselt number, velocity and temperature distributions are computed and represented graphically.

Dual solutions of MHD stagnation point flow and heat transfer over a stretching/shrinking sheet with generalized slip condition

An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.

MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method

The present paper investigates the magnetohydrodynamic（MHD） flow of a viscous fluid towards a nonlinear porous shrinking sheet.The governing equations are simplified by similarity transformations.The reduced problem is then solved by the homotopy analysis method.The pertinent parameters appearing in the problem are discussed graphically and presented in tables.It is found that the shrinking solutions exist in the presence of MHD.It is also observed from the tables that the solutions for f（0） with different values of parameters are convergent.

Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

MHD Effect of Liquid Metal Film Flows as Plasma-Facing Components

Stability of liquid metal film flow under gradient magnetic field is investigated. Three dimensional numerical simulations on magnetohydrodynamics （MHD） effect of free surface film flow were carried out, with emphasis on the film thickness variation and its surface stability. Three different MHD phenomena of film flow were observed in the experiment, namely, retardant, rivulet and flat film flow. From our experiment and numerical simulation it can be concluded that flat film flow is a good choice for plasma-facing components （PFCs）

Exact solutions of MHD second Stokes flow of generalized Burgers fluid

This work concerns with the exact solutions of magnetohydrodynamic（MHD）flow of generalized Burgers fluid describing the second Stokes problem. The modified Darcy law is taken into account. The related velocity distribution and shear stress are expressed as a combination of steady-state and transient solutions computed by means of integral transformations. The effects of various parameters on the flow field are investigated. The MHD flow results in reduction of velocity distribution and associated thickness of the boundary layer.