Mhd Flow

The magneto hydrodynamic flow with Hall effect plays important role in engineering and astrophysics. Some applications are in the field of MHD generators, MHD bearings, ion propulsion, stellar and solar structure, inter planetary and inter stellar matter, solar storms and the three-dimensional channel flow MHD pumps etc. Some articles are worth mentioning. Deka [5] has discussed Hall effects on MHD flow over an accelerated plate. Watanabe et al. [7] have studied Hall effects on MHD boundary layer flow on a continuous moving plate. Katagiri [9] has discussed the effect of Hall current on the MHD boundary layer flow past a semi-infinite plate. Unsteady Hartmann flow with heat transfer has been studied by Attia [6]. Further, mass diffusion effects on infinite vertical plate with heat flux have been studied by Deka et al [8]. Raptis et al. [4] have analysed viscous flow on stretching sheet with chemical reaction. Ibrahim et al. [3] have studied MHD boundary layer flow on moving vertical plate. Rajput and Sahu [2] have studied effects of chemical reaction on MHD flow between two vertical parallel plates. H. Kumar [1] has studied MHD free convection flow on a stretching porous sheet with heat source. We are considering Chemical reaction effect on unsteady MHD flow on a plate with Hall current. The results are shown with tables and some graphs.

The magnetohydrodynamics (MHD) flow problems find also applications in a large variety of physical, geophysical and industrial fields [5]. It is also interesting to study the flow of non- Newtonian fluids with externally imposed magnetic fields. To the author knowledge MHD flow of non-Newtonian fluids was first studied by Sarpkaya [ 6 ] . In [ 7 ] Sapunkov derived the equations describing the similarity solutions for the non-Newtonian flow when the external

In all the above cases, the fluid models have been considered as Newtonian. But the mechanisms of non- Newtonian fluid flows are used in various manufacturing processes and hence play an important role in modern technology and industrial applications. Authors like Kelly et al.[16], Shbhash et al. [17], Sonth et al. [18], Abel et al. [19], Choudhury and Mahanta [20], Choudhury and Dey [21], Choudhury and Das [22] etc. have analyzed some problems of physical interest in this field. Bachok et al. [23] have studied MHD flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a micropolar fluid.

The present work concentrates on the similarity solutions for MHD flow of a non-Newtonian fluid to study the flow of an electrically conducting Sisko fluid. The similarity analysis of governing equation is discussed using the deductive group theoretic method which is already been successfully applied to several non-linear problems [Abd-el-Malek et al (2002); Parmar and Timol (2011)].

There are many problems in science and engineering where the solution shows a boundary layer character. Near the boundary the gradient is large in contrast with the smooth behaviour in the central core. A uniform grid is, therefore, not suitable for a numerical solution. MHD flow problems belong to this category where a velocity and induced magnetic field profiles get flattened in a transverse flow. In the present paper an optimized grid has been generated using interpo- lating wavelets. The results are compared with those obtained using uniform grid, the finite element method and also from the analytical solution.

Study of MHD flow with heat and mass transfer plays an important role in biological Sciences. Effects of various parameters on human body can be studied and appropriate suggestions can be given to the persons working in hazardous areas having noticeable effects of magnetism and heat variation. Study of MHD flows also has many other important technological and geothermal applications. Some important applications are cooling of nuclear reactors, liquid metals fluid, power generation system and aero dynamics. The effects of radiation on free convection on the accelerated flow of a viscous incompressible fluid past an infinite vertical porous plate with suction has many important technological applications in the astrophysical, geophysical and engineering problem. The flow of an incompressible viscous fluid past an impulsively started infinite plate, in its

. Form this computation it can be observe that as the parameter values increases the effect of R also increases. The effect of Sc over the velocity which shown in figure 10. In the interval [0, 2] as the numerical value of Sc increased the velocity of flow increased and after a particular value of y in that interval velocity flow starts decreasing. From Figure 1 to 10 the velocity flow profile decreases or increases as the corresponding parameters increases. Effects of prandtl number, thermal radiation parameter, buoyancy ratio, radiation limit, Schmidt number with numerical computation over temperature are presented from Figure.11-14. From all these diagrams we observed that as the parameters increased the temperature profile decreases except absorption of radiation parameter R. The influence of Prandtl quantity Pr on the profile of temperature distribution shown in Figure 11. It is because, the smaller numerical values of Pr increases the thermal conductivity. So the heated surface differ away rapidly than for higher values of Pr. Therefore, rate of heat transfer reduced due to thick layer of boundary. This figure shows that the temperature declines with the growth of Prandtl numeral Pr. Figure.14 is diagram for distinct numerical values of the absorption of radiation parameter R. It can be notice, in the interval [0, 2.8] temperature profile increased and after that interval flow decreased with an increase of the numerical values for R. Figures.17 and Figure.18 are the effects of Sc and Kr over the concentration respectively. As the corresponding numerical values increased the flow profile decreased in the situation of Sc parameter and increased in the case of Kr respectively. The computational tables are also presented for Sherwood number, Nusslet

A transverse magnetic field is applied perpendicular to the flow of the fluid. The induced magnetic effect is negligible in comparison with the transverse magnetic field due to low magnetic Reynolds’s number, as a result of slightly conducting fluid [15]. Further the electric force E given by ohm’s law J  ( E  V  B ) when B  ( H 0 , 0 , 0 ) and the electrical conductivity is assumed to be a null vector for the simplicity of the problem.

Hartmann flow is a classical problem that has many important applications in magnetohrdrodynamics (MHD) generators and first studied an incompressible viscous electrically conducting fluid flow between two infinite conducting stationary disks under the action of a transverse magnetic field. Under different physical conditions it 1966), Cowling (1957) . The solutions for the velocity fields in closed Sutton and Sherman, 1965; Alpher, 1961; under different physical effects. Due to Newtonian fluids material in many manufacturing and processing industries, considerable efforts have been directed towards understanding their flows. Many Rajagopal and Gupta, 1981; Ersoy, Newtonian fluid in different dimensional rate type viscoelastic has been used to characterize diverse viscoelastic materials; food products such as cheese, , Siddiqui et al. (?) and has studied the Burgers’ fluid. Burgers dimensional rate type visco-elastic model to describe the response of materials such as asphalt. Murali et a fully three dimensional

Mittal [25] also studied some features of two dimensional magnetohydrodynamic flows, in steady state and under force free magnetic fields, by using the phenomenon of superposability and self-superposability. Shruti Rastogi, B. N. Kaul and Sanjeev Rajan [31] have taken the work of Mittal et al. further. In their work they dis- cussed about some magnetic fields with conservative Lorentz force in confocal paraboloidal coordinates. They showed that under some conditions magnetohydrostatic configuration may be formed by self-superpoable flow of an electrically conducting incompressible fluid permeated by a magnetic field with conservative Lorentz force. V. Singh and S. Rajan [32] have extended Mittal’s work further in Ellipsoidal ducts.

In this paper, the influence of heat generation and absorption on the electrically conducting flow of Casson fluid with characteristics of heat transfer over stretching wedge is studied. The similarity solutions are obtained by Keller-box method. The accuracy of method is checked through comparison with the results of available literature and revealed in close agreement. Effects of Casson parameter 𝛽, magnetic parameter 𝑀, stretching wedge parameter 𝛾, Prandtl number 𝑃𝑟, radiation parameter 𝑁, Eckert number 𝐸𝑐, heat generation and absorption parameter 𝜀 suction/injection parameter 𝑆 and Newtonian heating parameter 𝛿 are presented graphically with the following key points: (a) Fluid velocity decreases as 𝛽 and 𝑆 increase

It has been established that the biological systems, in general, are greatly addicted by the application of the external magnetic field. Moreover, the MHD flow of a fluid in a channel with elastic rhythmically contracting walls (peri- staltic flow) is of interest in connection with certain problems of the move- ment of conductive physiological fluids, and with the need for theoretical re- search on the operation of a peristaltic MHD compressor, also the principle of magnetic field may be used in clinical application (magnetic resonance imag- ing MRI). The effect of moving magnetic field on blood flow was studied by Agrawal and Anwaruddin [1], they observed, for the flow of blood in arteries with arterial disease like arterial stenosis or arteriosclerosis, that the influ- ence of magnetic field may be utilized as a blood pump in carrying out cardiac operations. Also, the magnetohydrodynamic flow with suspension has been studied by Parsad and Ramacharyulu [6], and Srivastava and Agrawal [17] con- sidered the blood as an electrically conducting fluid and that it constitutes a suspension of red cells in plasma.

We consider a FEM-BEM coupling approach for the approximate solution of the MHD flow through a circular pipe under the influence of a transverse magnetic field when the outside medium is also electrically conducting. Coupled equations with coupled boundary conditions are solved first on the boundary of the pipe by transforming the modified Helmholtz equations and Laplace equation. Then, velocity and induced magnetic field inside the pipe are calculated by considering SUPG typed stabilized finite element method, and induced magnetic on the external region is calculated with constant boundary ele- le 1 values of the velocity and induced current.

T he case of variation of flow rate with respect to various flow entities in situation of MHD flow over a moving infinite vertical porous plate in the presence of thermal radiation has been examined in detail in this paper. It is observed that, as the pore size decreases the flow rate is found to be decreasing. In each of these illustrations, it is seen that the applied transverse magnetic field influences the flow rate significantly. Further, as the magnetic intensity increases the flow rate is found to be inversely proportional. Also, increase in the intensity of the magnetic field contributes to the decrease in flow rate. For a constant pore size of the bounding surface and the frequency of excitation, increase in the magnetic intensity amounts to the decrease in the flow rate. Also, a back flow is observed in certain cases and is illustrated graphically. Further, decrease in Grashoff number (Gr) contributes to the increase in the flow rate.

decrease with increase in the magnetic parameter. Jana et al. [7] and Seth and Maiti [8] have presented detailed analysis of the flow of a viscous incompressible fluid through the rotating channel. Mohan [9] has studied the free convection effects for a similar configuration. It is found that when the Grashoff number is large, the fluid in the vicinity of the two plates move in the opposite directions and the flow separation take place only at the lower plate. Hall effects on unsteady MHD free and forced convection flow in a porous rotating channel have been investigated by Sivaprasad et al. [10]. The forced convective heat transfer in a MHD channel with Hall and Ion-slip currents has been presented by Mittal and Bhat [11]. Rao et al. [12] have studied the combined effects of free and forced convection on MHD flow in a rotating porous channel. The magnetohydrodynamic combined convective flow through a horizontal channel is studied by Mori [13], Yu [14], Datta and Jana [15], Ghosh and Bhattacharyya [16] and Pop et al. [17]. Guria et al. [18] have studied the Hall effects on the hydromagnetic convective flow through a rotating channel under general wall conditions. The effects of wall conductance on MHD fully developed flow with asymmetric heating of the wall have been investigated by Guria et al [19]. Seth et al. [20] have studied the combined free and forced convection MHD flow in a rotating channel with perfectly conducting walls. Analytical solution to the problem of MHD free convective flow of an electrically conducting fluid between two heated parallel plates in the presence of an induced magnetic field has been presented by Singha[21]. The combined free and forced convection flow of a viscous incompressible electrically conducting fluid in a rotating channel have been investigated by Seth et al [22]. Ahmed [23] has analyzed the mixed convection hydromagnetic oscillatory flow and periodic heat transfer of a viscous incompressible and electrically conducting fluid past an infinite vertical porous plate. The exact solution of MHD mixed convection periodic flow in a rotating vertical channel with heat radiation has been presented by Singh [24]. Seth et al. [25] have studied the combined free and forced convection Couette- Hartmann flow in a rotating system with Hall effects.

Agarwal et al. [2] studied the effects of Hall Current on the hydro-magnetic free convection with mass transfer in a rotating fluid. Takhar and Ram [3] studied the effects of Hall current on hydro-magnetic free convective flow through a porous medium. Chaudhary and Sharma [4] have analytically analyzed the steady combined heat and mass transfer flow with induced magnetic field. Bhaskar Kalita [5] investigate the magnetic field effect on unsteady free convection MHD flow between two heated vertical plate. Dileep and Priyanka [6] studied the effects on heat transfer of rotating cautte flow in a channel partially filled by a porous medium with hall current. B. P. Garg [7] studied combined effects of thermal radiations and hall current on moving vertical porous plate in a rotating system with variable temperature. Sahin et al. [8] established a mathematical model on magneto- hydro-dynamic transient free and forced convective flow with induced magnetic field effects. Magneto-hydrodynamic flow and heat transfer of two immiscible fluids with induced magnetic field effects is investigated by Zivonin et al. [9] Dufour and Soret Effects On Steady MHD Free Convection And Mass Transfer Fluid Flow Through A Porous Medium in A Rotating System have been investigated by Nazmul and Alam [10]. Sandeep et al [11] investigated the effect of inclined magnetic field on unsteady free convection flow of dissipative fluid past a vertical plate. Seth et al. [12] studied Effect of Rotation on Unsteady Hydromagnetic Natural Convection Flow Past an Impulsively Moving Vertical Plate with Ramped Temperature in a Porous Medium with Thermal Diffusion and Heat Absorption. Rajput and Kumar [13] investigated the Rotation and Radiation Eects on MHD Flow Past an Impulsively Started Vertical Plate with Variable Temperature. The main objective of the present study is to investigate numerically MHD Free Convection fluid flow over a Vertical Porous Plate in a Rotating System in the presence of Soret effect, hall effect, Mass and Heat transfer effect with Induced Magnetic Field.

flow of an electrically conducting fluid up a hot vertical wall in the presence of strong magnetic field has been studied by several authors such as Crammer [4], Hossain[5] and Kuiken[3]. In our daily life, the combined heat and mass transfer phenomenon is observed in the formation of fog. The convective flow associated with the combined heat and mass transfer has many applications in various branches of science and engineering. Singh and Singh[6] discussed the MHD free convection flow and mass transfer past a flat plate. Al-Qadat and Al-Azab[7] studied the influence of chemical reaction on transient MHD freeconvective flow over a moving vertical plate. The study of combined heat and mass transfer in mixed convective MHD flow along a vertical plate in presence of heat source has been shown by Zueco and Ahmed[19]. Palani and Srikanth[8] explained the mass transfer effects on MHD flow past a semi infinite vertical plate. Chaudhary and Jain[9] analyses the combined heat and mass diffusion in a MHD free convective flow past a surface embedded in a porous medium. Effects of chemical reaction on transient MHD free convective flow over a vertical plate in slip-flow regime are explained by Sahin[10]. It is proposed to study the effect of Heat and Mass Transfer For Visco-Elastic MHD Boundary Layer Flow Past a Vertical Porous Plate Of Slip Flow Region In The Presence Chemical Reactive Spices

In fluid dynamics, the stagnation point flow and flow over a stretching surface are important in theoretical and applications point of view. In fluid dynamics, stagnation is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object. Stagnation flow towards a stretching sheet is investigated by Wang [7]. Mixed convection MHD stagnation point flow on vertical, linearly stretching sheet is explained by Ishak [8]-[10]. The steady two-dimen- sional stagnation point flow on a stretching sheet was first discussed by Chaim [11]. Stagnation point flow over a stretching surface is explained by T. R. Mahapatra and A. S. Gupta [12]. Recently Bhattacharya [13] investigated heat transfer in boundary layer stagnation point flow over a stretching sheet. In many electronic applications, temperature becomes an important role when designing a system. We have practical applications for various heat source/sink arrangements. An effect of heat source/sink on MHD flow over a shrinking sheet is explained by Krishnendu Bhattacharyya [14]. F. M. Hady [15] described the effects of heat source/sink on MHD viscoelastic fluid over a non linear stretching sheet. Mahapatra, T. R. and A. S. Gupta [16] discussed heat transfer in stagnation point flow over a stretching sheet. The effects of viscous dissipation and internal heat generation of a viscous fluid on a stretching sheet are investigated by Vajravelu K. and Hadjinicolaou A. [17]. Sharma P. R. and Singh G. [18] described the effects of viscous dissipation and heat source/sink on MHD stagnation point flow over a linearly stretching sheet.

The present work is compared it with the works of Wubshet and Bandari, Anderson and Hayat et al [18-20]. (MHD flow and heat transfer over permeable stretching sheet with slip conditions). The results from this work with regards to good was found to be in agreement with theirs comparison of Results for the skin friction `′′(0) and reduced Nusselt number - u b (0) are presented in tables 1 and 2. Numerical values of skin friction coefficient, local Nusselt number, and local Sherwood number and motile microorganism local density are presented in Table 3 against all the pertinent parameters.

Magneto hydrodynamics (MHD) is a subject that studies the behavior of an electrically conducting fluid in the presence of an electromagnetic field. MHD boundary layers with heat and mass transfer over flat surfaces are found in many engineering and geophysical applications such as geothermal reservoirs, thermal insulation, enhanced oil recovery, packed-bed catalytic reactors, cooling of nuclear reactors. Because of its wide range applications, many researchers tend to apply MHD flow into their problems [12–16].