Action Of Transverse Magnetic Field Research Articles

Heat transfer analysis of Walters’-B fluid with Newtonian heating through an oscillating vertical plate by using fractional Caputo–Fabrizio derivatives

This paper presents a study of Walters’-B fluid with Caputo–Fabrizio fractional derivatives through an infinitely long oscillating vertical plate by Newtonian heating under the action of transverse magnetic field. The fractional calculus approach is employed to obtain a system of fractional partial differential equations. The governing equations of momentum and energy are converted first into dimensionless form and then solved by employing Laplace transformation. The Laplace inverse transform has been evaluated both analytically and numerically. The graphical illustrations represent the behavior of material parameters on the solutions. A comparison between exact and numerical solutions is presented in tabular and graphical form. The variation in Nusselt number with the change in fractional and physical parameters is also presented. The velocity and temperature of the fluid decreases with the enhancement in the fractional parameter for small values of time, and it has the opposite behavior for greater values of time.

Porosity effect on unsteady MHD free convection flow of Jeffrey fluid past an oscillating vertical plate with ramped wall temperature

The unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid embedded in porous medium past an oscillating vertical plate generated by thermal radiation with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under the action of transverse magnetic field towards the flow. Constitutive relation of Jeffrey fluid is employed to model the governing equations in terms of partial differential equations with some physical conditions. The transformed dimensionless governing equations are solved analytically using Laplace transform technique. The impact of various pertinent parameters namely material parameter of Jeffrey fluid , dimensionless parameter of Jeffrey fluid , phase angle , Hartmann number , permeability parameter , Grashof number , Prandtl number , radiation parameter and dimensionless time on velocity and temperature distributions are presented graphically and discussed in details. It is observed that, the permeability parameter tend to retard the fluid velocity for ramped wall temperature but enhance the velocity for an isothermal plate. Besides that, this study shows, the amplitude of velocity and temperature fields for ramped wall temperature are always lower than isothermal plate. A comparison with the existing published work is also provided to confirm the validity of the present results and an excellent agreement are found.

Numerical Simulation of Vacuum Arc Behavior Considering Action of Adjacent Phases in Vacuum Circuit Breakers

In the interrupting process of a three-phase vacuum interrupter, there exists a transverse magnetic field (TMF) in the interelectrode region, which is produced by adjacent phases. The deflection of the vacuum arc caused by TMF will affect the interrupting process of vacuum circuit breakers. In this paper, the vacuum arc characteristics considering the action of TMF produced by adjacent phases is simulated based on a steady 2-D asymmetrical magnetohydrodynamic model. The simulation results show that the vacuum arc will swing around and is especially obvious at the smaller current moments near current-zero during one ac half-cycle, because of the changed direction of TMF produced by adjacent phases. This kind of swing phenomena can also be observed in the electrode erosion of unsuccessful interruption. At the moments near current-zero, axial magnetic field is relatively weaker, while TMF generated by adjacent phases is relatively stronger, therefore, the offset phenomenon of plasma parameters is more significant. Compared with smaller diameter electrode arc, larger diameter electrode has larger arc deflection distance, while its value of plasma parameters is much smaller.

Numerical Study on MHD Mixed Convection Flow in a Vertical Insulated Square Duct with Strong Transverse Magnetic Field

A numerical study on steady laminar magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid in a vertical square duct under the action of transverse magnetic field has been investigated. The walls of the duct are electrically non-conducting. In this study both forced and free convection flows are considered. The viscous dissipation and Joule heat are also considered in the energy equation and moreover the walls of the duct are kept at constant temperature. The governing equations of momentum, induction and energy are first transformed into dimensionless equations by using dimensionless quantities, then these are solved employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature distribution are presented graphically for different dimensionless parameters Hartmann number , Prandtl number , Grashof number and magnetic Reynolds number .

Diffusion-Thermo and Thermal-diffusion Effects on MHD Visco-Elastic Fluid Flow over a Vertical Plate

Unsteady MHD visco-elastic fluid flow has been studied numerically under the action of transverse magnetic field with diffusion-thermo and thermal diffusion for small magnetic Reynolds number. The governing equations are non-dimensionalized by usual non-dimensional variables. The obtained equations are solved by explicit finite difference technique. The solutions of the dimensionless velocity, temperature and concentration equations are shown graphically. The effects of parameters on the shear stress, Nusselt number and Sherwood number are discussed in graphical form. Finally, a qualitative comparison with previous work is tabulated.

NUMERICAL MODELING OF MHD CONVECTIVE HEAT AND MASS TRANSFER IN PRESENCE OF FIRST-ORDER CHEMICAL REACTION AND THERMAL RADIATION

An analysis was carried out numerically to study unsteady heat and mass transfer by free convection flow of a viscous, incompressible, electrically conducting Newtonian fluid along a vertical permeable plate under the action of transverse magnetic field taking into account thermal radiation as well as homogeneous chemical reaction of first order. The fluid considered here is an optically thin gray gas, absorbing-emitting radiation, but a non-scattering medium. The porous plate was subjected to a constant suction velocity with variable surface temperature and concentration. The dimensionless governing coupled, nonlinear boundary layer partial differential equations were solved by an efficient, accurate, extensively validated, and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields were studied for the effects of Hartmann number (M), radiation parameter (R), chemical reaction (K), and Schmidt number (Sc). The local skin friction, Nusselt number, and Sherwood number are also presented and analyzed graphically. It is found that velocity is reduced considerably with a rise in the magnetic body parameter (M), whereas the temperature and concentration are found to be markedly boosted with an increase in the magnetic body parameter (M). An increase in the conduction-radiation parameter (R) is found to escalate the local skin friction (τ), Nusselt number, and concentration, whereas an increase in the conduction-radiation parameter (R) is shown to exert the opposite effect on either velocity or temperature field. Similarly, the local skin friction and the Sherwood number are both considerably increased with an increase in the chemical reaction parameter. Possible applications of the present study include laminar magneto-aerodynamics, materials processing, and MHD propulsion thermo-fluid dynamics.

Effect of thermal diffusion and chemical reaction on heat and mass transfer in an MHD micropolar fluid with heat generation

Unsteady heat and mass transfer by free convective MHD micropolar fluid flow bounded by a semi- infinite porous plate in a rotating frame under the action of transverse magnetic field with chemical reaction in the presence of heat generation is considered. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The governing system of partial differential equations are transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. Also the effects of the pertinent parameters on the local skin friction coefficient and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are presented numerically in tabular form. The results show that the observed parameters have significance influence on the flow, heat and mass transfer.

Magnetohydrodynamic free convection flow above an isothermal horizontal plate

In the present study a new similarity theory is developed to study the fluid flow and heat transfer characteristics for the steady laminar natural convection boundary layer flow of an incompressible and electrically conducting fluid past a semi-infinite horizontal plate subjected to a constant wall temperature under the action of transverse magnetic field. The governing parabolic boundary layer PDEs are transformed to ordinary differential equations using similarity transformation. This results in a set of three coupled, non-linear ordinary differential equations with variable coefficients (representing the interaction of the temperature and velocity fields) which are then solved by the shooting method. Asymptotic analyses and series solutions are also constructed to explore the mathematical behaviour of the solutions. The numerical results are obtained for various values of Prandtl number and magnetic field parameter ζ. The effects of various values of Prandtl number and magnetic field parameter ζ on the velocity profiles, temperature profiles, wall shear stress and heat transfer coefficients are presented. The results indicate that the wall shear stress τw decreases whereas the local Nusselt number Nux increases with increase in Prandtl number if the magnetic field parameter ζ is held constant at a particular value. On the other hand, both the wall shear stress and Nusselt number decrease with increase in the magnetic field parameter ζ for a fluid with constant Prandtl number. Generic correlations for Nux and τw have been developed in terms of the fluid Prandtl number Pr and magnetic field parameter ζ. A generic relation for free convection flow with magnetohydrodynamic effects, that is equivalent to the well-known Reynolds analogy for forced convection flow, has also been formulated in the present work.

UNSTEADY FREE CONVECTION HEAT AND MASS TRANSFER IN AN MHD MICROPOLAR FLUID IN THE PRESENCE OF THERMO DIFFUSION AND THERMAL RADIATION

This present study investigates the effects of thermo-diffusion and thermal radiation on unsteady heat and mass transfer of free convective MHD micropolar fluid flow bounded by a semi- infinite porous plate in a rotating frame under the action of transverse magnetic field with suction. The plate is assumed to oscillate in time with constant frequency so that the solutions of the boundary layer are the same oscillatory type. The governing system of partial differential equations is transformed to dimensionless equations using di- mensionless variables. The dimensionless equations are then solved analytically using perturbation technique. With the help of graphs, the effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. Also the effects of the pertinent parameters on the local skin friction coefficient and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are presented numerically in tabular form. The results shows that

Effect of magnetic field on the blood flow in artery having multiple stenosis: a numerical study

In the present study a mathematical model for the blood flow in stenosed artery in the presence of magnetic field is proposed. The laminar, incompressible, fully developed, non-Newtonian flow of blood in an artery having multiple stenosis is numerically studied under the action of transverse magnetic field. The governing equations are transformed by using a radial transformation and the numerical results are obtained using a finite difference technique. Effect of overlapping stenosis and externally applied magnetic field in the blood flow is discussed with the help of graph. All the flow characteristics are found to be affected by the presence of multiple stenosis and exposure of magnetic field of different intensities. Keywords: Blood flow, Magnetic Field, Overlapping Stenosis, generalized Power Law, Finite Difference Method

The Effect of Heat Transfer on Unsteady Hydromagnetic Flow in a Parallel-Plate Channel of an Electrically Conducting, Viscous, Incompressible Fluid

An analytical study has been performed to examine the effect of heat transfer characteristics on the flow of a viscous, incompressible electrically conduction fluid in a parallel plate channel under the action of transverse magnetic field when (i) the two plates are kept at different but constant temperatures, (ii) the upper plate is given to move with constant velocity while the lower plate is adiabatic. The governing partial differential equations of this problem, subject to boundary conditions are solved analytically for fluid velocities, magnetic field and temperature distributions. The graphical representation for the velocity, the induced magnetic field, temperature distributions and the heat transfer are depicted graphically for different values of dimensionless parameters of the problem and the analysis of the results showed that the flow field is appreciably influenced by the applied magnetic field.

Transport through a double barrier in Large Radius Carbon Nanotubes with a transverse magnetic field

We discuss the Luttinger Liquid behaviour of Large Radius Carbon Nanotube e.g. the Multi Wall ones (MWNT), under the action of a transverse magnetic field B. Our results imply a reduction with B in the value of the bulk critical exponent, αbulk, for the tunneling density of states, which is in agreement with that observed in transport experiments. Then, the problem of transport through a Quantum Dot formed by two intramolecular tunneling barriers along the MWNT, weakly coupled to Tomonaga-Luttinger liquids is studied, including the action of a strong transverse magnetic field B. We predict the presence of some peaks in the conductance G versus B, related to the magnetic flux quantization in the ballistic regime, at a very low temperature T, and also at higher values of T, where the Luttinger behaviour dominates. The temperature dependence of the maximum Gmax of the conductance peak according to the Sequential Tunneling follows a power law, G ∝Tγe-1 with γe linearly dependent on the critical exponent, αend, strongly reduced by B.

Thermodynamic analysis of mixed convection in a channel with transverse hydromagnetic effect

An analysis has been performed to study the First and Second laws (of thermodynamics) characteristics of flow and heat transfer inside a vertical channel made of two parallel plates under the action of transverse magnetic field. Combined free and forced convection inside the channel is considered. Flow is assumed to be steady, laminar, fully developed of electrically conducting, and heat-generating/absorbing fluid. Both vertical walls are kept isothermal at the same or different temperatures. Governing equations in Cartesian coordinates are first simplified and solved analytically to develop the expressions for velocity and temperature, entropy generation number ( N S ), and irreversibility distribution ratio. Velocity, temperature, and entropy generation profiles are presented graphically. Full form of the governing equations are solved numerically using control-volume based finite volume method. Based on the numerical calculations, average entropy generation numbers are calculated for channels with different aspect ratios. Finally, a correlation is proposed which essentially expedite for calculating a geometric parameter ( α 0) that will be characterized by minimum irreversibility at a particular value of Gr/ Re (ratio of Grashof number and Reynolds number) and M (Hartmann number).

Entropy generation in a porous channel with hydromagnetic effect

An analytical work has been performed to study the First and Second Laws (of thermodynamics) characteristics of flow and heat transfer inside a vertical channel made of two parallel plates embedded in a porous medium and under the action of transverse magnetic field. Combined free and forced convection inside the channel is considered. Flow is assumed to be steady, laminar, fully developed of electrically conducting and heat-generating/absorbing fluid. Both vertical walls are kept isothermal at the same or different temperatures. Governing equations in Cartesian coordinate are simplified and solved analytically to develop expressions for velocity and temperature, entropy generation number and irreversibility distribution ratio. Velocity, temperature and entropy generation profiles are presented graphically.

Inhomogeneity and local negative magnetoresistance of aluminum

The peculiarities of potential distribution and current flow in aluminum plate conductors are investigated under an inhomogeneous action of transverse magnetic field. A magnetic field inhomogeneity is arranged along a transport direction with a method of curving of electric current lines. For relative magnetic field gradient of about 0.3 cm−1 a potential dependence on transport direction is complicated and an inversion of spatial dependence of potential takes place. That is an increase of potential along total current vector is observed on one of conductor side as a magnetic field decreases a local resistance.

Heat transfer in unsteady MHD couette flow of an electrically conducting, viscous, incompressible rarefied gas

An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (i) suction velocity normal to the plate is constant, (ii) the second plate oscillates in time about a constant non-zero mean, (iii) fluid is subjected to a constant heat source of absorption type. Apprximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated in Table I.

Marangoni convection in a liquid layer under the simultaneous action of a transverse magnetic field and rotation

Asymptotic stability characteristics with respect to the onset of Marangoni convection in a liquid layer under the simultaneous action of a large transverse magnetic field and a large rate of rotation are investigated. In certain parameter ranges there is a decrease in critical Marangoni number for increasing magnetic field and rotation depending on the coupling between interfacial perturbations and rotation.

Hypersonic viscous flow near the stagnation streamline of a blunt body. i - a test of local similarity

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