Infinite Plate Research Articles

Slip Condition Effects on Unsteady MHD Fluid Flow with Radiative Heatflux over a Porous Medium

The objective of this paper is to study unsteady magneto hydrodynamic (MHD) free flow of viscoelastic fluid (Walter’s B) past an infinite vertical plate through porous medium. The temperature is assumed to be oscillating with time. The solution obtained shows different profiles of effects of slip conditions on primary and secondary velocity. Also, the effects of various parameters on temperature, concentration, primary and secondary velocity profiles were presented graphically. The result indicated the secondary velocity is enhanced with increase in slip parameter. Primary velocity demonstrated opposite trend.

Investigation of MHD natural convective flow of optically thick medium-radiating CNT Casson nanofluid over an infinite flat plate with reference to Caputo fractional derivative: As an application to water purification

In this article, the application of Caputo fractional operators of order α, α∈ (0,1) has been studied. Heat transmission near the surface of a vertical plate in the flow of optically thick radiating Casson nanofluid along with mass diffusion in the presence of heat source/sink and constant magnetic flux is investigated. In the fluid problem, an H2O-based Casson nanofluid with carbon nanotube (CNTs) suspensions is investigated. The non-dimensionalized governing PDEs have been solved analytically via the combination of Fourier-sine and Laplace transform techniques and closed form of solutions are attained for the velocity, temperature, and concentration fields in terms of the Mittag-Leffler function. The physical behavior of the significant parameters has been scrutinized graphically. As a result, it is identified that the concentration, temperature, and velocity curves escalate drastically with the raising values of the fractional quantity α due to the alteration in mass, thermal, and momentum boundary layers with higher values of time t. When t>1, the species level in the fluid along with the fluid temperature and velocity rises with the fractional quantity α and decelerates when 0<t<1. Further analysis reveals that as the magnetic field is strengthened, the flow curves decelerate rapidly. Also, tables have been presented to show the influence of the controlling physical quantities on the friction drag and heat transmission rate.

Caputo–Fabrizio fractional model of MHD second grade fluid with Newtonian heating and heat generation

In this research article the heat transfer of generalized second grade fluid is investigated with heat generation. The fluid flow is analyzed under the effects of Magneto hydrodynamics over an infinite vertical flat plate. The Newtonian heating phenomenon has been adopted at the boundary. For this purpose the problem is divided into two compartments i.e. momentum equation and energy equations. Some specific dimensionless parameters are defined to convert the model equations into dimensionless system of equations. The solutions for dimensionless energy and momentum equations are obtained by using the Laplace transform technique. From obtained results by neglecting magneto hydrodynamic effects and heat source some special case are achieved which are already published in literature. The case for which the fractional parameter approaches to the classical order is also discussed and it has been observed that it is convergent. Finally, the influences of different physical parameters are sketched graphically. It has been observed that for increasing values of Prandtl number the velocity and temperature decreases, for increasing values of Grashof number the velocity of the fluid increases. Also it has been investigated that for increasing values of fractional parameter the velocity and temperature of the fluid increases.

Diffusion‐thermo effect on convective MHD flow of Cu‐water nanofluid including ramped wall temperature, velocity and concentration

An unsteady convective MHD flow of water based Cu-nanofluid past an impulsively started infinite vertical plate embedded in porous medium including ramped velocity, temperature and concentration in the existence of diffusion-thermo effect, radiation and chemical reaction has been investigated. The non-dimensional domain equations are computed by adopting Laplace transform technique. The impact of various pertinent parameters that are associated with the fluid velocity, temperature, concentration and moreover on skin friction coefficient, Nusselt number and Sherwood number has been represented graphically. It is figured out that, increase of Dufour effect causes to rise in both the momentum and temperature boundary layer. Further, it is ascertained that increase in the volume fraction of nanoparticles causes fall of velocity whereas it increases temperature together with the rate of heat transfer at the walls.

Plate capacitor problem as a benchmark case for verifying the finite element implementation

In this work, parallel plate capacitors are numerically simulated by solving weak forms within the framework of the finite element method. Two different domains are studied. We study the infinite parallel plate capacitor problem and verify the implementation by deriving analytical solutions with a single layer and multiple layers between two plates. Furthermore, we study the finite parallel plate capacitor problem and verify it by Love’s potential equation and Xiang’s capacitance equation. Moreover, the fringing effect is considered and extended to problems with multiple dielectric layers, such a solution is not possible by means of the existing analytical solutions. Besides, we realize the possibility of choosing different boundary conditions (electric potential boundary conditions and charge density boundary conditions) by changing the weak form. Finally, a transient solution that includes dielectric loss and calculates the quality factor of a capacitor is presented, which may be used in capacitor design. Convergence and consistency of results are demonstrated by comparing the results between analytical and numerical solutions and also the results from different boundary conditions.

Characterization of adsorption properties inherent to zirconia dioxide for different positions of yttrium in the ZrO2–Y2O3 lattice

Presented in this paper is theoretical studying redistribution of electric charges in the layer of a tetragonal plate of yttrium-stabilized zirconia based on the position of yttrium atom in the crystal lattice for both dry and humid ambient atmosphere. The density functional theory with local density approximation (DFT-LDA) has been employed for this modelling. Calculations have been performed for layer-by-layer electron density distribution over the thickness of an infinite plate 001 of yttrium-stabilized tetragonal zirconium dioxide, which show that a change in the position of stabilizing yttrium atom and its symmetry in the layer leads to changing the total energy of zirconium dioxide both for the dry 001 surface and for the hydrated one. It has been ascertained that the surface charge density for the 001-surface of an infinite tetragonal zirconia plate increases in proportion to the degree of hydration.

Semi-Analytical Finite Element Method for the Analysis of Guided Wave Dispersion in the Pre-stressed Composite Plates

Ultrasonic guided wave techniques offer an accurate and efficient procedure for damage monitoring in the structures. To develop reliable damage monitoring systems, it is essential to have a thorough understanding of the quantitative nature of ultrasonic guided waves that can be transmitted in composite laminates. In the present paper, the Semi-Analytical Finite Element (SAFE) method is employed due to its efficiency in the treatment of wave propagation problems involving complex materials and geometry. SAFE method is considered for the analysis of dispersion behaviour of guided waves in composite laminates by accounting the effect of in-plane load. The present study considers an infinite width plate such that the cross-section of the waveguide is modelled using 3 noded isoparametric 1-D elements representing the thickness of the plate. Equation of motion is formulated by using Hamilton’s equation. Finally, various parametric studies are carried out. The study includes analysing the effect of wave velocity in the plate subjected to applied in-plane load, and understanding the effect of dispersion characteristics on the direction of propagation (slowness curve). The study shows that at the lower frequency thickness product, the group velocity of the wave increases with the increase in the applied tensile load and vice-versa.

Fracture analysis of functionally graded materials by the method of fundamental solutions

In this paper the Method of Fundamental Solutions (MFS) incorporating Erdogan’s solutions for Functionally Graded Materials (FGM) is presented for analysis of 2D fracture problems subjected to static and dynamics loads. Erdogan derived analytical solutions for a pair of static concentrated force in an infinite isotropic plate with a straight cut. Based on homogenous isotropic analysis, the contribution from non-homogeneity in equilibrium equations is treated as body forces and domain integrals based on the Erdogan’s fundamental solutions are required. In the domain integrals, all singularities are cancelled by introduction of a polar coordinate system at collocation points and crack tips. In the dynamic cases, the Laplace transformation with the Durbin inversion technique is adopted to determine the time-dependent variables such as the stress intensity factors at crack tips. The domain integrals are obtained numerically with the sub-region technique. The accuracy of the MFS is demonstrated with four numerical examples and comparisons are implemented with different numerical approaches.

Effect of Partial Ground and Partial Ceiling on Propeller Performance

Finite extent flat obstacles behind a propeller (“partial ground”) and ahead of the propeller (“partial ceiling”) were examined experimentally for a small-scale fixed-pitch propeller in hover. Cases included circular and annular plates, which can be summed up or superimposed. Near-surface smoke and flow visualization show a projected time-averaged streamline on the ground plate, dividing a swirling flow inboard and a radial flow outboard. The flow pattern was juxtaposed with pressure data on the ground plate. Changes in propeller thrust and power due to ground/ceiling effect were measured by a force balance and correlated with flow visualization. For a plate of diameter equal to that of the propeller, ground effect on thrust and power was comparable to that of an “infinite” plate, while the flowfield also resembles that of the infinite plate. For a plate of less than half of the propeller diameter, ground or ceiling effect was found to be negligible. Thrust and power effects for circular and respective annular plates were superimposed to determine whether the increase in thrust or decrease in power required is itself additive to the respective effects seen with the constituent obstacles. For ceiling effect, this holds but less so for ground effect. A curve fit to thrust and power data resulted in a predictive model accurate to within 6%.

Comprehensive analysis of thermal radiation impact on an unsteady MHD nanofluid flow across an infinite vertical flat plate with ramped temperature with heat consumption

The present article deals with the influence of a magnetic field on unsteady MHD water-based nanofluid flow across an infinite flat plate with a ramped temperature gradient and radiative heat transfer in a porous material is investigated. Two forms of water-based nanofluids comprising silver, and titanium dioxide are considered. The finite element technique is used to solve the governing partial differential equations, and the approximate results are provided. The temperature, velocities, rate of heat transfer, and shear stresses of nano-fluids at the plate are depicted graphically for a range of relevant parameter values. It has been observed that the velocity and temperature profiles upsurge with rising values of the radiation factor, whilst the velocity diminishes for larger values of the Magnetic parameter. The comparison research that was performed reveals a remarkable degree of concordance with the earlier investigation.

Complex Potentials and Integral Equations for Thermoelasticity Problem of Orthotropic Cracked Plate

In the present article, the plane thermoelasticity problem of an infinite orthotropic cracked plate, is studied. The interaction between thermal and mechanical field, in a plate containing a crack and a heat source is investigated. The plate is submitted to normal stresses at infinity, where a heat flow is also activated. Applying the complex potentials method and the technique of Cauchy integrals, a system of singular integral equations is obtained. These equations, allow the determination of the temperature’s distribution, but also of the stress state at any point of the medium.

Unsteady Radiative Flow of Particular Nanoliquids Along an Infinite Vertical Flat Plate in the Proximity of Convective Boundary Condition

In this article, the heat transfer and flow pattern characteristics are restudied in the proximity of convective boundary condition for three kinds of nanoliquids, namely copper oxide-water nanoliquid (CuO–H2O), silverwater nanoliquid (Ag–H2O), and titanium dioxide-water nanoliquid (TiO2–H2O). The thermal radiation impact is assumed into account. The partial differential equations are shifted into ordinary differential equations by applying an acceptable transformation and then exact solutions are acquired by promoting the Laplace transform technique. Solid volume fraction is fluctuated as 5%, 10%, 15%, and 20%. The variations of nanoliquid motion and energy transmit are displayed graphically as well as the numerical values of friction factor and rate of heat transfer at the plate are displayed in tabular pattern. In particular, the least shear stress occurs for silverwater nanoliquid and the greatest shear stress occurs for titanium dioxide-water nanoliquid as well as the least heat transfer coefficient occurs for titanium dioxide-water nanoliquid and the greatest heat transfer coefficient occurs for copper oxide-water nanoliquid. This report can be further utilized to authenticate the effectiveness of acquired mathematical results for another sophisticated nanoliquid stream problems.

The Influence of Thermal Expansion on Flow Past an Inclined Accelerated Sectional Plate with Persistent Mass Diffusion

In this article, we examined the solution of a homogeneously intensified isothermal inclined infinite plate with constant temperature. The plate is elevated to &lt;i&gt;Tw&lt;/i&gt;, and the species accumulation is enhanced at a consistent speed. Under appropriate boundary conditions, the non-dimensional guiding formulae are remedied using the Laplace transform procedure. The effect of velocity, temperature, and concentration on various factors, including thermal and mass Grashof numbers, Schmidt numbers, and duration, is discussed. The velocity increases proportionally to the thermal and mass Grashof numbers, but decreases as the inclined angle, Schmidt numbers and time increase.

An implicit Keller box approach for solution of MHD three-dimensional flow through a porous medium

The present study investigates the Soret and Dufour effect on free-convection flow of a viscous incompressible fluid through a porous medium bounded by an infinite vertical porous plate with chemical reaction and viscous dissipation is investigated with aid of Implicit Keller box and regular perturbation methods. The flow is assumed in the presence of transverse magnetic field. Characteristics of Velocity, Temperature and Concentration are obtained and graphical interpretation is made. The observation of these results reflects that velocity and thermal boundary layer thickness decrease with the increase of radiation parameter. Graphical interpretations establish a good agreement in a realistic sense.

Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative

Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter β,γ→1, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.

Keller box analysis for thermal efficiency of magneto time-dependent nanofluid flowing in solar-powered tractor application applying nano-metal shaped factor

This research looks at the generating of entropy in the magnetohydrodynamic (MHD) flowing of a Williamson-nanofluid (W-NF) across an infinite horizontal plate which is located in the solar-powered tractor. The non-linear, homogeneous surface stretching then induces flow. Furthermore, as external sources, the current study includes penetrable material, thermal radiative flux, heat source/sink, viscous dissipative flow, and Ohmic heating characteristics. Using similarity variables, a solution is achieved by transforming controlling PDEs into ODEs. After that, the Keller-box finite-difference technique is used to approximate the solution of diminished ODEs. The findings of two nanofluid tests, copper-engine oil (Cu-EO) and silver-engine oil (Ag-EO), were addressed in this paper. According to the results, a considerable porous medium decreased the Nusselt number while increasing the skin friction coefficient. Furthermore, increasing the Reynolds and Brinkman numbers enhanced the system's total entropy. This study shows that W-NF can improve heat collector performance. The comparative heat transference rate of Cu/Ag-EO is the study's clincher. Cu-EO-based NF is shown to be a good quality thermal conductance than Ag-EO-based NF. Additionally, compared to a sphere, hexahedron, tetrahedron, column shape nanoparticles, lamina has more effect on the function of temperature and entropy.

Unsteady EMHD free convective second grade fluid flow past an exponentially accelerated vertical porous plate

This paper presents a detailed account of unsteady, incompressible, viscous, electrically conducting, unidirectional, free convective second grade fluid through an exponentially accelerated vertically infinite plate with both applied electric field and magnetic field being present. The equation of motion and energy manifested as nonlinear partial differential equation are represented as algebraic equations using implicit finite difference scheme and solved numerically by implementing the damped-Newton method. With the help of the momentum and energy equation, we defined the expressions for skin friction and Nusselt number. The cases n = 1(constant acceleration) and n = 0.5(variable acceleration) are also taken into consideration. The solution obtained is eventually simulated using MATLAB and the resulting graphs representing the influence of non-dimensional parameters on flow field and temperature field are discussed thoroughly. We have also validated the results obtained from the present methodology with the results obtained from already existing methodologies under some limited cases. It is interesting to note that when the plate is being cooled by free convection current, with increase in viscoelastic parameter the viscous forces are dominated by the elastic effects which results in accelerating the velocity flow profile. For comparatively smaller values of Ec the temperature distribution decreases with increasing Re as the suction propagation facilitates decrease in boundary layer thickness which consequently enhances heat transfer rate. The effect of Ec is to raise the temperature profile due to enhancement in viscous dissipation effects. Practically, the combined effects of the physical parameters are remarkably important in various engineering, medical and industrial applications.

Attenuation band splitting in a finite plate strip with two-dimensional acoustic black holes

Acoustic black holes (ABH) lattice is an effective way to realize the bandgaps (BGs) through lightweight design. The predicted BGs using infinitely large periodic structures are commonly believed to enable corresponding attenuation bands (ABs) even the structure only contains a limited number of unit cells. This paper reports an unusual splitting phenomenon in the ABs of a finite plate strip with two-dimensional (2D) ABHs. A wide AB predicted by BG is split into two ABs in the finite strip separated by a high resonance peak, which challenges the aforementioned common belief. Results show that the increasing number of periodic unit cells has a negligible effect on the frequency and amplitude of the resonance peak. Its underlying mechanism is clarified by investigating the relationship between the BGs and ABs, obtained from infinite and finite periodic plate strips with the same 2D ABHs respectively. Complex wavenumber analysis results show the existence of two flexural wave modes in the considered frequency range due to the finite width of the strip. Two types of BGs, in which one satisfies the Bragg condition, are found when both wave modes fail to propagate. Analysis of structural modes further uncover the physical reason for the emerging AB splitting: a certain natural frequency of the boundary portion of the 2D ABHs strip falling into the theoretical BG. Due to the boundary reflection and energy concentration, this structural portion can loosely be regarded as a clamped-free plate strip. It is demonstrated that the resonance peak splitting the AB becomes tunable via disrupting the structural details of finite ABH strips. In particular, extending the terminal end of a finite ABH strip allows the change in boundary portion, which is conducive to eliminating the splitting peak. The reported study is helpful for the design of finite periodic structures with broadband attenuation bandgap.

Steady-State Solutions for MHD Motions of Burgers’ Fluids through Porous Media with Differential Expressions of Shear on Boundary and Applications

Steady-state solutions for two mixed initial-boundary value problems are provided. They describe isothermal MHD steady-state motions of incompressible Burgers’ fluids over an infinite flat plate embedded in a porous medium when differential expressions of shear stress are given on a part of the boundary. The fluid is electrically conductive under the influence of a uniform transverse magnetic field. For the validation of the results, the expressions of the obtained solutions are presented in different forms and their equivalence is graphically proved. All of the obtained results could easily be particularized to give exact solutions for the incompressible Oldroyd-B, Maxwell, second-grade, and Newtonian fluids that were performing similar motions. For illustration, the solutions corresponding to Newtonian fluids are provided. In addition, as an application, the velocity fields were used to determine the time required to reach the steady or permanent state for distinct values of magnetic and porous parameters. We found that this time declined with increasing values of the magnetic or porous parameters. Consequently, the steady state for such motions of Burgers’ fluids was earlier reached in the presence of a magnetic field or porous medium.

Voltage-controlled topological interface states for bending waves in soft dielectric phononic crystal plates

The operating frequency range of passive topological phononic crystals is generally fixed and narrow, limiting their practical applications. To overcome this difficulty, here we design and investigate a one-dimensional soft dielectric phononic crystal (PC) plate system with actively tunable topological interface states via the mechanical and electric loads. We use nonlinear electroelasticity theory and linearized incremental theory to derive the governing equations. First we determine the nonlinear static response of the soft dielectric PC plate subjected to a combination of axial force and electric voltage. Then we study the motion of superimposed incremental bending waves. By adopting the Spectral Element Method, we obtain the dispersion relation for the infinite PC plate and the transmission coefficient for the finite PC plate waveguide. Numerical results show that the low-frequency topological interface state exists at the interface of the finite phononic plate waveguide with two topologically different elements. By simply adjusting the axial force or the electric voltage, an increase or decrease in the frequency of the topological interface state can be realized. Furthermore, applying the electric voltage separately on different elements of the PC plate waveguide is a flexible and smart method to tune the topological interface state in a wide range. These results provide guidance for designing soft smart wave devices with low-frequency tunable topological interface states.