Current Flow Problem Research Articles

Magnetohydrodynamic peristaltic flow of unsteady tangent‐hyperbolic fluid in an asymmetric channel

AbstractThe aim of the present numerical investigation is to explore the impact of magnetic field on peristaltic flow of an incompressible tangent‐hyperbolic fluid in an asymmetric channel. The present physical model is developed based on the considered flow configuration and with the help of small Reynolds number approximations. The current flow problem is revealed under the influence of applied magnetic field. The asymmetric channel has been considered to narrate the present physical problem. Considered physical situation in the current investigation gives the unsteady coupled highly nonlinear system of partial differential equations. Also, the simplified equations for pressure, pressure gradient, and streamlines have been obtained with the help of suitable transformations. A regular perturbation scheme is employed to produce the semi‐analytical results of the present problem. The influence of various physical parameters on pressure, pressure gradient, and streamlines are illustrated with the help of graphs. From the present analysis, it is observed that the increasing magnetic number decreases the pressure and pressure gradient in the channel. Also, the size of trapping bolus increases with increasing values of Weissenberg number.

Dynamics of bioconvection flow of micropolar nanoparticles with Cattaneo-Christov expressions

A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks. The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects. The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes. The flow equations are converted into an ordinary differential model by employing the appropriate variables. The numerical solution is reported by using the MATLAB builtin bvp4c method. The consequences of engineering parameters on the flow velocity, the concentration, the microorganisms, and the temperature profiles are evaluated graphically. The numerical data for fascinating physical quantities, namely, the motile density number, the local Sherwood number, and the local Nusselt number, are calculated and executed against various parametric values. The microrotation magnitude reduces for increasing magnetic parameters. The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes, especially in the suspension of flows. On the account of industrial applications, the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.

Significance of Activation Energy and Effective Prandtl Number in Accelerated Flow of Jeffrey Nanoparticles With Gyrotactic Microorganisms

Abstract This research addresses the interesting rheological features of Jeffrey nanofluid containing gyrotactic microorganism over an accelerated configuration. The additional consequences of activation energy and thermal radiation are also encountered in the current flow problem. The characteristics of nanofluid is utilized by using Buongiorno’s nanofluid model, while the phenomenon of bioconvection is evaluated by Kuznestov and Nield model. Unlike traditional attempts, the analysis for thermal radiation is performed by using “one parametric approach” by expressing the Prandtl number and thermal radiation parameter in combined form, namely, effective Prandtl number. The governing equations reflecting the flow problem are analytically treated with the help of homotopic algorithm. The impact of flow parameters is graphically elaborated with relevant physical significance. Further, the numerical expressions for effective local Nusselt number, local Sherwood number, and motile density number with variation of flow parameters in articulated tabular form. It is observed that magnitude of skin friction coefficient oscillates periodically with time and magnitude of oscillation increases with increment of Deborah number and mixed convection constant. It is further emphasized that the temperature distribution is enhanced with buoyancy ratio constant and bioconvection Rayleigh number. The microorganism distribution increases with buoyancy ratio constant but reverse trend has been examined for Peclet number. The observations from the reported problem can be more effective for the development of bifurcation processes, biofuels, enzymes, etc.

Interaction of Wu’s Slip Features in Bioconvection of Eyring Powell Nanoparticles with Activation Energy

The current continuation aim is to explore the rheological consequences of Eyring Powell nanofluid over a moving surface in the presence of activation energy and thermal radiation. The bioconvection of magnetized nanoparticles is executed with the evaluation of motile microorganism. The most interesting Wu’s slip effects are also assumed near the surface. The evaluation of nanoparticles for current flow problems has been examined by using Buongiorno’s model. The governing equations for the assumed flow problem are constituted under the boundary layer assumptions. After converting these equations in dimensionless form, the famous shooting technique is executed. A detailed physical significance is searched out in the presence of slip features. The variation of physical quantities, namely velocity, nanoparticles temperature, nano particles concentration, motile microorganism density, skin friction coefficient, local Nusselt number and motile organism density number are observed with detailed physical aspects for various flow controlling parameters.

Non-linear radiative heat transfer analysis during the flow of Carreau nanofluid due to wedge-geometry: A revised model

In this article, an innovative revised Buongiorno's model is employed to investigate the flow of Carreau nanofluids generated by a wedge-shaped geometry. Moreover, heat and mass transfer characteristics are explored under the influence of non-linear thermal radiation. At first, the developed flow equations are made dimensionless via suitable transformations and then resulting set of nonlinear ordinary differential equations are solved numerically using built-in MATLAB solver bvp4c. It is observed that the solution of current flow problem is highly dependent on the contribution of several physical parameters like Weissenberg number, power-law index, wedge angle parameter, velocity ratio parameter, non-linear radiation parameter, suction parameter, Brownian motion and thermophoresis parameters, Lewis and Prandtl numbers. Detailed analysis for the novel results of dimensionless velocity, temperature and nanoparticles concentration with in the boundary layer region is exhibited graphically. The core physical implication of the computed results is that the thermal boundary layer is thinned by higher radiation parameter. This study reveals that an enhancement in the local Nusselt number is noted with higher temperature ratio parameter. On the other hand, an incremental skin friction ate the wall can be achieved by growing values of power-law index. The obtained data is distinguished with earlier studies and admirable agreement has been noted.

Modeling the electromagnetic processes in a technological device for producing ultradispersed particles in pulsed arc discharges

The article contains a brief description of the operation principles of the device for creating ultrafine metal powders under the action of electrically charged flows with a high power density. The results of creating a mathematical model of electromagnetic processes in the installation are presented. The results of solving the problem of current flow in the installation during its operation are presented. The dependence of the magnetic field strength in the section of the plasma bunch during the operation of the apparatus is illustrated.

Integrating Electrical Analogy and Computer Modeling of Groundwater Flow for Teaching Flownet Concepts

Laplace equation is the basic differential equation that governs the steady flow of a fluid through an isotropic and homogeneous porous medium and also the steady flow of current in a conducting medium. Therefore, a steady-state groundwater flow problem can be formulated as an analogous electrical current flow problem. A flow net, set of grids formed by orthogonally intersecting equipotential lines and flow lines, is a graphical solution to the equations of steady groundwater flow. By definition, flownet for the original groundwater problem and the corresponding analogous electrical problem should be similar. This feature allows the possibility of introducing the concepts of flownets to students using the easily demonstrable electrical counterpart of the problem in a laboratory setting. This paper discusses the efforts of the authors to widen the scope of an experiment already included in the Fluid Mechanics laboratory course of a Civil Engineering curriculum and to better teach flownet principles using the electrical analogy of groundwater flow problems. Students used a simple experimental setup to obtain flownets for selected groundwater flow situations with different boundary conditions using the electrical analogy concept. Students also used a groundwater flow computer model to obtain flownets for the same flow situations and compared the results. The laboratory lesson plan consisted of five steps: (i) study and understand the selected physical groundwater problems, (ii) conceptualize the corresponding analogous electrical problems (iii) use the electrical analogy experimental setup to obtain flownets, (iv) study and understand the mathematical formulation of the problems, and (v) compare the analogous results with those obtained from a groundwater flow computer model. Sample results obtained by students are presented. The student feedback indicated that this approach resulted in an effective learning of the concepts involved.

A $p$-Adaptive Scheme for Scalar Fields, Using High-Order, Singular Finite Elements

For problems with sharp edges, where the electric or magnetic field is singular, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaptive finite-element analysis loses some of its effectiveness. This can be remedied by including singular elements which are better able to model the potentials near such edges. The singular elements are hierarchal and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> -adaption takes place over the combined set of singular and regular elements. An energy-based error indicator guides the adaption. Three test cases are considered: an electrostatic problem for finding the capacitance of a stripline gap; a steady current flow problem for finding busbar resistance; and a magnetostatic problem for finding the torque on a prism of permeable material. Results show that, although the use of singular elements does not increase the dimension of the global matrix, more conjugate gradient iterations are needed to solve the matrix equation. Nevertheless, the use of singular elements leads to a greatly improved adaptive convergence, with final accuracies about one order of magnitude higher, for a similar computational cost.

Simulation of Electrical Conduction in Geomaterials by SPICE

Electrical responses of the subsurface can be used to identify geologic strata, locate anomalies, detect and delineate contamination, among many other applications. All these applications depend on the spatial variations of electrical properties in the subsurface and the resulting flow pattern of electric current. Due to the heterogeneity of the subsurface and complex boundary conditions, three-dimensional electric current flow problems are not easy to analyze, in particular when the response is frequency- and/or time-dependent. In this paper, a method of electric circuit analogy is proposed to simulate the electrical responses of geomaterials using the circuit simulator SPICE. The technique will allow simulation of more complex electrical conduction behavior of geomaterials without much extra effort. The excellent agreement between simulated results and analytical solutions developed for surface geophysical techniques establishes the viability of the method. Limitations of the approach and potential solutions to relax these limitations, and other potential applications of the technique in geosciences are also discussed.

The effective conductivity of two-phase two-dimensional media as a function of the geometric parameters of the medium

The paper deals with the problem of current flow in doubly periodic two-dimensional media whose unit cell is a parallelogram. Local distributions of currents (fields) are found, and the effective conductivity of such media is calculated for equal phase concentrations. The dependence of conductivity on the angle of parallelogram is determined. This dependence is shown to be threshold in media of the metal-insulator type.

Quantum hall effect in inhomogeneous media: Effective characteristics and local current distribution

An analysis is made of the problem of current flow in heterophase inhomogeneous media in the quantum Hall effect regime. Duality relations are derived and expressions are obtained for the effective conductivity of inhomogeneous media over the entire range of concentrations. Local current distributions (fields) are determined in the quantum Hall effect regime.

Nondestructive Evaluation of a Bifurcated Crack by Means of D.C. Potential Drop Technique Using Adjacent Probes.

The d.c. potential drop technique based on the use of adjacent probes is applied to the nondestructive evaluation of a crack bifurcated from a nonplanar crack in a rail. The method of evaluation is based on the measurement of the potential drop on the top surface of the rail. The problem of current flow in a material which contains nonplanar and bifurcated cracks is analyzed numerically using a 3-D finite element method. The relationship between the potential drop on the measured surface and the depth of a bifurcated crack is obtained and it is verified in experiments using rail specimens that the cracks can be characterized quantitatively using the 3-D numerical analysis. It is also shown that the sensitivity of the present method using adjacent probes is higher than that of the conventional method in which the uniform current flow in a region far from the crack is used.

FEM computation of the forces on the arc of a DC-furnace

A finite element model of a DC arc furnace is investigated in order to predict the forces acting on the arc due to the magnetic field. The currents have an a priori unknown distribution in the steel tank wall, in the anode, in the melt and in the cathode, so a current flow problem is analysed in the first step. The current density is solved for in terms of a current vector potential whose edge element representation is used in the subsequent nonlinear magnetic field calculation to act as impressed magnetic field. The current dependence of the shielding provided by the steel tank is investigated. It is shown that by providing an asymmetrical feed of the current, the force on the arc can be reduced substantially.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

POTENTIAL DROP TECHNIQUE FOR NONDESTRUCTIVE EVALUATION OF BIFURCATED CRACK IN RAIL

Abstract The potential drop technique was applied to nondestructive evaluation of a crack bifurcated downwards from a non-planar crack in a rail, since the case of non-planar cracks is more often observed than that of horizontal cracks. The method of evaluation was based on the measurement of the distribution of d.c. electrical potential on the top surface of the rail. A problem of current flow in a plate, which contained non-planar and bifurcated cracks modelled in practical shape and was subjected to a uniform current, was analyzed numerically by using a 2-D finite clement method. The potential distribution on the measuring surface of the plate was obtained for various combinations of the cracks. The potential distribution showed a remarkable change in its slope just above the tips of the non-planar crack. Also the relation between the vertical depth of penetration of the whole crack and the total potential difference above the non-planar crack was revealed to be independent of the combinations of the c...

Complementary solutions of direct current flow problems

An error-based approach is used for the systematic derivation of complementary variational principles for the problem of steady current flow in conductors. Using two-dimensional finite-element solution results, the significance of combined presentation of complementary computational results is discussed, and the distribution of the numerical error is displayed graphically. It is shown that the limits of the theory of complementary variational principles are decreed by boundary specifications, and that, under certain circumstances, a treatment is available for transcending them. Finally, the error-based approach is applied to the circuit version of the direct-current flow problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

NONDESTRUCTIVE CHARACTERIZATION OF BIFURCATED CRACK BY POTENTIAL DROP TECHNIQUE

Abstract A method was presented for the nondestructive evaluation of a crack bifurcated from a horizontal crack in a rail. The method was based on the measurement of the difference and distribution of d.c electrical potential on the top surface of thc rail.First, a problem of current flow in a plate, which contained horizontal and bifurcated cracks and was subjected to a uniform current, was analyzed numerically by using a 2-D finite clement method. The potential distribution on the measuring surface of the plate was obtained for various combinations of the cracks. The potential distribution showed a remarkable change in its slope just above both ends of thc horizontal crack. Also the relation between the vertical component of the bifurcated crack and the total potential difference above the horizontal crack was revealed to be independent of the combinations of the cracks. Next, in order to characterize the cracks in actual rail based on the 2-D numerical analysis, a method was introduced for obtaining a ...

Current and magnetic field penetration into a plasma: Application to high power-density flow in transmission lines

When a material is heated sufficiently to cause a conducting plasma to blow off, the resulting layer shields this material from magnetic fields and currents that may be present. Theoretical considerations relevant to the simulation of such situations are discussed. Results are presented for the problem of current flow in transmission lines undergoing surface blowoff due to high current densities. For a typical case of interest only 10% of the current is found to flow in the plasma blowoff. Moreover, the transmission-line properties are not substantially changed on time scales of interest.

Finite element solution of 3-D eddy current flow in magnetically linear conductors at power frequencies

For eddy current flow problems in which the conductors have a constant permeability it has been found convenient to use scalar potentials outside the eddy region and vectors inside The vectors E and H have each been tried and a manner of coupling the different field quantities together in a way which is compatible with the finite element solution technique is discussed. The method has been tested in 2-D, quasi 3-D and 3-D.

A Principle for Solving a Class of Anisotropic Current Flow Problems and Applications to Electrocardiography

In studies of electrocardiographic lead performance, theoretical analyses of the influence of the anisotropic heart and skeletal muscle are particularly difficult. In this paper, the basic differential equations of static fields and steady current flow are arranged to emphasize the field and conductivity dependent charge distributions which arise in anisotropic media. The equations are applied to two types of problems of immediate interest. Firstly, the equations are used to explain how anisotropic media may be included in current digital computer studies of the heart-lead relation and to conclude that the techniques which made the computer studies possible tend to lose their advantage when applied to arbitrary anisotropic configurations. Secondly, the equations are used to develop a principle which permits exact solutions for the fields of numerous simple anisotropic configurations. Three such configurations useful for heart-lead studies are analyzed with the following results: the anisotropic skeletal muscle can be treated in special cases such as a head-foot heart-vector lead approximately as isotropic with resistivity of 280 ohm cm; the closed dipolar layer in an anisotropic, inhomogeneous heart produces the same null electric field as it does in homogeneous isotropic media; bounds on the influence of the heart's anisotropy on a heart-vector lead field are estimated at plus or minus 12 percent of the average lead field intensity.

Space charge injection into impurity semiconductors—II

The problem of current flow in a large gap semiconductor sandwiched between metal electrodes is considered. Equations are derived which describe space charge conduction in a material containing both donor and acceptor impurities. Numerical solutions to these equations are obtained for several situations having particular physical interest. It is shown that reported discrepancies between trap densities in CdS derived from the Trap Filled Limit theory and from other data using specimens about 50 μ. thick cannot be attributed to the fact that earlier workers have ignored the diffusive contribution to the current. However, for specimens of the order 5 μ. thick, a serious error is introduced by ignoring the diffusive term. It is also shown that predictions based on the authors' earlier work, in which only donors are considered, are qualitatively confirmed for the case of materials having both kinds of impurity and a compensation ratio near one.