Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

Hydromagnetic flow near an accelerated plate in the presence of a magnetic field

Summary Hydromagnetic flow of a viscous incompressible fluid due to uniformly accelerated motion of an infinite flat plate in the presence of a magnetic field fixed relative to the plate, is discussed. It is assumed that the induced magnetic field is negligible compared to the imposed magnetic field. It is observed under these conditions that the velocity at any point and at any instant decreases when the strength of the magnetic field is increased.     

Effect of magnetic field on thermal instability in mixed convection flow over a rotating boundary layer

Effect of magnetic field on the formation of longitudinal vortices in mixed convection flow over a rotating heated flat plate is presented. The onset position is characterized by the Grashof number, the rotational number, the Prandtl number, the Eckert number, the magnetic field parameter, and the wave number. Negative rotation (clockwise) and external magnetic field stabilize the boundary layer flow. On the contrary, positive rotation (anti-clockwise), the Eckert number, and the Prandtl number destabilize the flow. The numerical data show agreement with the experimental data with the case of zero Hartmann number in the literature.     

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.     

Thermal instability in natural convection flow over a boundary layer subject to external electrical and magnetic fields

This paper presents a numerical study of external electrical and magnetic effects on the formation of longitudinal vortices in natural convection flow over a heated horizontal plate. The criterion on the position marking on the onset of longitudinal vortices is defined in the present paper. The onset position characterized by the Grashof number depends on the Prandtl number, the wave number, the electric field parameter, and the magnetic field parameter. The flow is found more stable as the value of the magnetic field parameter increases. Moreover, the stabilizing effect is also found on the flow when the positive electric field parameter Ec is applied. The results of the present numerical prediction show reasonable agreement with the experimental data with zero magnetic field and electric field parameters in literature.     

聚变堆相关的液态金属膜流初步实验研究

在磁约束核聚变堆的面对等离子部件设计中,液态金属锂膜流因具有带走杂质、保护面对等离子固壁等优点而被认为是优选方案之一. 然而,如何克服聚变堆中强磁场环境下产生的磁流体力学效应并形成大面积均匀铺展锂膜流动是目前亟需解决的问题.本文通过搭建室温液 态镓铟锡回路和高温液态锂回路,开展了两种不同特性的液态金属膜流实验, 并采用传统可视化方法获得了展向磁场存在时镓铟锡和锂在导电底板形成的液膜流动表面特征.实验结果 表明: 无磁场时,两种液态金属膜流流动表面波动特性与常规流体膜流均一致, 即随着流动雷诺数的增加表面波动变得更为混乱; 而展向磁场存在时,镓铟锡膜流表面波动变得更为规则, 且沿着磁场方向平行排列,表现为拟二维波动的特征; 而锂膜流却产生了明显的磁流体 力学阻力效应,表现为在流动方向局部产生锂滞留现象, 且滞留点随雷诺数增大向下游移动. 最后通过膜流受力分析,进一步阐述了锂膜流受到比镓铟锡膜流更为严重磁流体力学效应影响的原因.      

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.     

Finite deformation theory for soft ferromagnetic elastic solids

A general theory of finite deformation of soft ferromagnetic elastic solids is formulated following the linear theory developed earlier by Pao and Yeh. The constitutive equations, field equations, and the boundary conditions of this theory are applied to analyse the buckling of a plate under the action of a uniform magnetic field. A nontrivial equilibrium configuration for the deformed plate is shown to exist, and the critical value of the externally applied magnetic induction at which the plate buckles is determined. It is demonstrated that the non-linear deformation affects the critical magnetic induction considerably.     

TiO<Subscript>2</Subscript>-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.     

TiO_2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO_2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically solved with the homotopy analysis method(HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO_2 nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO_2 nanoparticles increases. This confirms the fact that the occurrence of the TiO_2 nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased.An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water,while the Nusselt number of the nanofluid is larger than that of pure water. However,both the parameters increase if the magnetic field intensity increases.     

Effects of radiation in an optically thin gray gas flowing past a vertical infinite plate in the presence of a magnetic field

This paper studies the two dimensional flow of an electrically conducting fluid which is an optically thin gray gas past a stationary vertical infinite plate in the presence of radiation. It is assumed that the temperature of the plate and the suction at the plate are constant. The presence of the induced magnetic field is also taken into account. Numerical solutions for the velocity and the induced magnetic field are derived and the effects of the radiation parameter are discussed.     

Magnetohydrodynamic unsteady free convection past a hot vertical plate

The free convection flow of an electrically conducting liquid from an infinite plate has been studied in the presence of a uniform magnetic field. General expressions for the velocity field, induced magnetic field, skin-friction and temperature distribution have been obtained when the plate is a perfect conductor and its temperature varies with the law t ⁿ e ^at . The results have been presented through some graphs and tables with the magnetic Prandtl number unity as its value.     

The skin friction on accelerated plates in magnetohydrodynamics

A uniform transverse magnetic field acts across an infinite flat plate immersed in a conducting fluid of arbitrary magnetic Prandtl number. The skin friction on the plate for the class of accelerated motions Ut ^k is discussed for a), a perfect conductor and b), an insulator. Residual stresses are demonstrated in both instances.     

MHD forced convection boundary layer flow with a flat plate and porous substrate

The flow and heat transfer for an electrically conducting fluid with a porous substrate and a flat plate under the influence of magnetic field is considered. The magnetic field is assumed to be uniform and also along normal to the surface. The momentum and energy equations are transformed to ordinary differential equations by using suitable similarity transformation and are solved by standard techniques. But the energy equation is solved by considering two boundary layers, one in the porous substrate and the other above the porous substrate. Numerical results are presented through graphs with various values of magnetic parameter for both velocity and thermal boundary layers along with Nusselt number and for various values of Prandtl number and Eckert number in thermal boundary layer.     

铁磁矩形简支板的磁弹塑性弯曲行为分析

基于广义变分原理得到的磁力计算公式,采用塑性增量理论,Mises屈服准则和有效的增量有限元计算方法,研究了线性强化材料铁磁矩形板的磁弹塑性弯曲行为。在文中定量模拟了铁磁简支矩形板在外加磁场作用下的挠度特征曲线,铁磁板发生塑性变形时的构型图和不同外加磁场下的中截面构型,以及铁磁板在卸载后的残余挠度特征曲线等力学特征,分析了塑性区域随磁场增加而扩展的情况。数值结果表明:当铁磁矩形板上的部分区域发生塑性屈服后,其变形明显大于相同磁场条件下铁磁板发生的弹性变形值;且随着外加磁场倾角的增大(0°<α≤45°),铁磁板进入塑性屈服状态的临界屈服磁场值减小;铁磁板的中截面构形为双半波型,其塑性区域由铁磁板两侧挠度最大的区域向板的中心区域扩展,板的中心最后进入塑性区域等。     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

The unsteady hydromagnetic thermal boundary layer with suction

The unsteady two-dimensional laminar flow of a viscous incompressible and electrically conducting fluid near an oscillating porous plate in the presence of uniform suction, is investigated. The solutions for the velocity, magnetic field, electric current density, temperature and Nusselt number are given in a closed form for the case of the magnetic Prandtl number being equal to unity. The other significant constants are the Eckert number, the fluid Prandtl number and the frequency of oscillation. The influence of these parametres on the solutions is given in both tabulated and graphical forms.     

Boundary layer on a flat plate with strong longitudinal magnetic field

The influence of a magnetic field on the boundary layer on a flat plate in a sufficiently strongly ionized gas stream is studied. The magnetic field is parallel to the plate and to the velocity of the free stream, and it is so strong that the transport coefficients become anisotropic (the cyclotron rotation frequency of the charged particles is greater than or equal to the order of the frequency of the particle collisions). Using the results of [1–3] it is shown that the effect of the strong longitudinal magnetic field with a sufficiently high degree of gas ionization leads to a reduction in the thermal flux to the plate. For low degrees of ionization this effect is very small, since the viscosity and heat conduction in this case are determined by the neutral component of the gas.Results are presented of numerical calculations of the considered problem with account for the dependence of the transport coefficients on the thermodynamic parameters. It is assumed throughout that the magnetic Reynolds number is small (R_m1).     

Combined forced and free convection MHD row past a semi-infinite vertical plate

Effects of a transversely applied magnetic field on the forced and free convective flow of an electrically conducting fluid past a vertical semi-infinite plate, on taking into account dissipative heat and stress work, have been presented. Without magnetic field, it has been discussed by the authors [1] in an earlier paper. The effects of Gr (Grashof number, Gr>0 cooling of the plate by free convection currents, Gr<0 heating of the plate by free convection currents), Pr (Prandtl number), F (Froude number) and M² (the magnetic field parameter) are discussed. It is observed that reverse type of flow of air exists near the plate when Gr<0.

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Gemischte erzwungene und freie Konvektions-MHD-Strömung an einer halbunendlichen senkrechten Platte

Zusammenfassung Die Wirkung eines transversalen Magnetfeldes auf die erzwungene und freie Konvektion einer elektrisch leitenden Flüssigkeit an einer halbunendlichen senkrechten Platte wurde unter Berücksichtigung der Dissipationswärme und der Kompressionsarbeit mitgeteilt. Das Problem wurde ohne Magnetfeld schon früher [1] behandelt. Diskutiert wurde die Wirkung der Grashof-Zahl Gr (Gr>0 Kühlung der Platte durch freie Konvektion), der Prandtl-Zahl Pr, der Froude-Zahl F und des magnetischen Feldparameters M₂. Bei Gr<0 wird Umkehr strömung in Plattennähe betrachtet.

     

A new approach on MHD natural convection boundary layer flow past a flat plate of finite dimensions

A new approach on MHD natural convection boundary layer flow from a finite flat plate of arbitrary inclination in a rotating environment, is presented. This problem plays a significant role on boundary layer flow control. It is shown that taking into account the pressure rise region at the leading edge of the plate leads to avoid separation and the back flow is reduced by the strong magnetic field. It is also shown that the frictional drag at the leading edge of the plate is reduced when the inclination angle α=π/4. In the case of isothermal flat plate, the bulk temperature becomes identical for any value of Gr (Grashof number) when the value of M ² (Hartmann number) and K ² (rotation parameter) are kept fixed.