Vertical Porous Plate Research Articles

Different approaches in scattering of water waves by two submerged porous plates over an elastic sea-floor

A hydroelastic model is presented here to look into the scattering of oblique water waves by two totally submerged vertical porous plates, placed at some distance from each other, in a homogeneous fluid flowing over an elastic sea-floor. Consideration of Euler–Bernoulli beam equation allows the elastic sea-floor to be approximated as a thin elastic plate whereas the porous plates follow the porous wave-maker theory. The complete analytical solution, under the assumption of small-amplitude theory and structural response, is obtained by employing eigenfunction expansion and least square method. Subsequently, numerical computation for the reflection and transmission coefficients and energy loss are carried out and discussed for different values of the elasticity of the sea-floor, porosity of the porous plates and other structural parameters. The present study establishes that reflection of the waves exhibits an oscillatory behaviour. It further shows that, due to an increase in the inertial effect of the porous plate, the minima in wave reflection occurs. The vertical porous plates are found to dissipate a significant portion of the wave energy when an increase in the inertial effect of the porous plates takes place. Furthermore, wave transmission decreases significantly due to the energy dissipation by the elastic sea-floor. Significant variation in the elastic specification of the sea-floor commands considerable influence when the propagating wave impinges upon the submerged vertical porous plates. In order to validate the present model, the obtained results are compared with available results which points towards a good agreement.

Hall effects on MHD chemically reacting flow of second grade fluid past a vertical porous plate

AbstractThe scrutiny of the consequences of radiation‐absorption, chemical reaction impacts on unsteady magnetohydrodynamics heat and mass transportation laminar flow of a gelatinous, electrical conducting by the heat generation or absorption second grade fluid embedded past a half‐unlimited porous surface within a gyratory structure taking Hall effects into account have been discussed. The plate is assumed to as in the motion by the invariable velocity contained by the direction of fluid movement. A uniform magnetic field performed at perpendicular to the porous plate; this is engrossing the fluid with the suction velocity changing with definite instants of time. The corresponding dimensionless governing equations of current configuration are solved by making use of perturbation technique with reference to harmonic and nonharmonic idioms. The velocity, temperature, and concentration profiles are discussed and examined with references to various governing parameters in detail. The results are verified with the published work. The velocity components are increased with increasing permeability and Hall parameters. It is noticed that practical application of Hall effects is as, washing machine dial to select the type of washing moves very smoothly. This problem has also applications in biomedical and aerospace engineering.

Numerical Investigation of Radiation Effects on MHD Convective Heat and Mass Transfer Flow Past a Semi-Infinite Vertical Moving Porous Plate in the Presence of Chemical Reaction

Abstract: The numerical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously vertical permeable surface in the presence of a radiation, a first-order homogeneous chemical reaction and the mass flux are considered. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The Equations of continuity, linear momentum, energy and diffusion, which govern the flow field, are solved by using a Finite Element Method. The results of the velocity, temperature, concentration, skin- friction, Nusselt number and Sherwood number has been discussed for variations in the governing parameters. Keywords: MHD, Radiation, Heat and Mass Transfer, Porous Medium, Unsteady flow, Finite Element Method.

Mitigation of Hydroelastic Responses in a Very Large Floating Structure by a Connected Vertical Porous Flexible Barrier

The hydroelastic response of an elastic thin plate combined with a vertical porous flexible plate floating on a single- or a two-layer fluid is analyzed in the two-dimensional Cartesian coordinate system. The vertical and the horizontal plates are placed in an inverted-L shape and rigidly connected together. The problem is studied with the aid of the method of matched eigenfunction expansions within the framework of linear potential flow theory. The fluid is assumed to be inviscid and incompressible, and the motion is assumed to be irrotational. Time–harmonic incident waves of the traveling mode with a given angular frequency are considered. Then, the least-squares approximation method and the inner product are used to obtain the expansion coefficients of the velocity potentials. Graphical results show the interaction between the water waves and the structure. The effects of several physical parameters, including the length and the complex porous-effect parameter of the vertical plate, on the wave reflection and transmission are discussed. The results show that a vertical plate can effectively eliminate the hydroelastic response of the very large floating structure. The longer a vertical plate is, the more waves are reflected by the vertical plate. With the increase in the porous-effect parameter, the deflection of vertical plate decreases. Besides the effects of the flexural rigidity, the lateral stress, the mooring line angle, the fluid density ratio, and the position of interface on the wave reflection and transmission are discussed. Numerical results show the significant mitigation effect due to the presence of the additional vertical plate.

Numerical solution of MHD, Soret, Dufour, and thermal radiation contributions on unsteady free convection motion of Casson liquid past a semi‐infinite vertical porous plate

AbstractIn this paper, the unsteady motion of Casson liquid over a half‐infinite penetrable vertical plate with MHD, thermal radiation, Soret, and Dufour contributions have been explored numerically. In the physical geometry, the Casson liquid flows to the layer from the penetrable vertical plate. At the layer, Casson liquid is set into motion and the flow equations are illustrated using coupled partial differential equations (PDEs). This set of PDEs is simplified to form dimensionless PDEs with the use of normal nondimensional transformation. The controlling parameters' effects on the working fluid are extensively discussed on velocity, concentration, and temperature and presented graphically. Computational values of Nusselt plus Sherwood number and skin friction for controlling parameters are depicted in a tabular form. Our outcomes show that a raise in the Casson term depreciates the velocity because of the magnetic parameter influence on the fluid flow. The Soret parameter was found to accelerate the skin friction along with the Sherwood number coefficients. An incremental value of the Dufour parameter was detected to hike the skin friction alongside the Nusselt number. Results of this study were found to be in conformity with previously published work.

Scattering of water waves by dual asymmetric vertical flexible porous plates

In this article, we focus on investigating the problem of water wave scattering by dual asymmetric vertical flexible porous plates submerged at different depths within the framework of two-dimensional linear potential theory. Employing Havelock's theorems for water wave potential and using the plate boundary conditions the problem is reduced to a pair of coupled hypersingular integral equations. Numerical solutions to the integral equations are determined by using polynomial approximations to the unknown functions together with a technique to tackle the hypersingular integral part and finally by collocating at finite number of points. The energy balance relation for the present scattering problem involving two flexible porous plates is obtained using Havelock's theorem. The present method is verified by comparing the numerical results for limiting cases with the known results available in the literature and through the energy balance relation. Also, a number of selective results for the reflection coefficient, the energy loss coefficient and the hydrodynamic forces on the plates are presented graphically. It is observed that a proper arrangement of the dual plates may dissipate sufficient amount of wave energy thereby providing an efficient model of breakwater.

Thermodiffusion and chemical reaction on MHD free convective flow past a rotating vertical porous plate with constant heat and mass discharge

Simultaneous heat and mass transport have played significant roles in different substantial chemical, and biomedical processes. Heat and mass transports happen in absorptions, distillations, extractions, drying, melt along with crystallizations, moreover, evaporations, and condensations. Mass flows due to the temperature gradients are recognized as the Soret effect. The Soret effects on the unsteady hydromagnetic liberated convective flow of a non-incompressible electrically performing gelatinous liquid over the rotating perpendicular absorbent plate in the incidence of temperature amalgamation have been investigated. The effects of the first order chemical reaction along with heat radiation are considered. The scheme of partially differential equalities is rendered into ordinarily differential equalities and therefore solved systematically with the Laplace transforms methodology. The impacts of different pertinent flow parametrics on velocities, temperature as well as concentration distributions, in addition, the shear stress is examined through the graphical profiles along with tables accordingly. This is established that resultant velocity field is ascending through an increase in the Soret parameter and chemically reacting parameter. The temperature distribution is increased by an increasing heat absorption parameter. Also, when the Soret parameter increases, then concentration increases throughout the fluid region.

Unsteady MHD fluid flow past an inclined vertical porous plate in the presence of chemical reaction with aligned magnetic field, radiation, and Soret effects

AbstractThe aim of the present paper is to investigate the Soret effect due to mixed convection on unsteady magnetohydrodynamics flow past a semi‐infinite vertical permeable moving plate in the presence of thermal radiation, heat absorption, and homogenous chemical reaction subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using the perturbation technique. Graphical results for the velocity distribution, temperature distribution, and concentration distribution based on the numerical solutions are presented and discussed. Also, the effects of various parameters on the skin‐friction coefficient and the rate of heat transfer in the form of Nusselt number, and rate of mass transfer in the form of Sherwood number at the surface are discussed. Velocity distribution is observed to increase with an increase in Soret number and in the presence of permeability, whereas it shows reverse effects in the case of the aligned magnetic field, inclined parameter, heat absorption coefficient, magnetic parameter, radiation parameter, and chemical reaction parameter.

Impact of nonlinear thermal radiation on nonlinear mixed convection flow near a vertical porous plate with convective boundary condition

This study presents similarity solution for boundary layer flow near a vertical porous plate with combined effects of nonlinear density variation with temperature and nonlinear thermal radiation. To accurately predict the flow phenomenon near the porous plate, the convective boundary condition is considered at the plate surface. The two-dimensional partial differential equations are transformed to ordinary differential equations through the similarity transformation. The resulting ordinary differential equations are solved numerically in Maple software using the Runge–Kutta–Ferhlberg fourth-fifth order (RKF45) algorithm. The influence of the inherit parameters like the nonlinear thermal radiation parameter, suction/injection parameter, nonlinear Boussinesq approximation parameters, local convective heat transfer parameter, local Grashof number, and Prandtl number governing the fluid behaviour is discussed. We found that the rate of heat transfer improves with the injection and nonlinear thermal radiation parameter whereas decreases with suction, local convective heat transfer parameter and local Grashof number when air and mercury are used as the working fluids. Furthermore, with the growth in the values of local Grashof number, convective heat transfer parameter and nonlinear thermal radiation parameter and in the presence of suction/injection, the porous plate surface friction witnessed an observable growth. Suction growth plays a supportive role on the velocity curve near the porous plate but a contrary trend is seen in the free stream. The temperature distribution also decays with suction augment. Injection growth is inversely proportional to the velocity profile near the porous plate but we recorded the opposite phenomenon in the free stream.

Soret and Dufour Effects of Unsteady MHD Flow Through Infinite Vertical Porous Plates with Thermal Radiation

Soret and Dufour Effects of Unsteady MHD Flow Through Infinite Vertical Porous Plates with Thermal Radiation

MHD Free Convection from a Semi-infinite Vertical Porous Plate with Diffusion-Thermo Effect

An analytical solution for two-dimensional unsteady MHD free convective mass transfer flows of viscous incompressible optically thin fluid past a semi-infinite vertical porous plate in the presence of thermal radiation and chemical reaction is presented in this paper. A uniform magnetic field is applied normally to the plate with a first-order chemical reaction. The non-dimensional governing equations are solved analytically by using the regular perturbation technique. The effects of various physical parameters like radiation parameter Q, Dufour effect Du, chemical reaction parameter K, thermal Grashof number Gr, Hartmann number M, porosity parameter k, etc., are studied and demonstrated graphically. One of the significant findings of this analysis includes that an intensification of the chemical reaction effect causes a downfall in the fluid concentration. In contrast, another important outcome of the present study is that the rate of heat transfer and shear stress at the wall increases under the diffusion thermo effect or Dufour effect. Still, it tends to fall for high radiation. Further, the rate of mass transfer rises under the chemical reaction effect.

MHD free convective dissipative flow past a porous plate in a porous medium in the presence of radiation and thermal diffusion effects

AbstractThe problem of a hydromagnetic convective flow of an electrically incompressible viscous conducting fluid past a uniformly moving vertical porous plate is investigated analytically, taking into consideration radiation and thermal diffusion effects. A constant suction velocity is applied to the plate. A uniformly strong magnetic field is supposed to be applied normally to the plate and directed into the fluid region. To find a solution to the problem, an asymptotic series expansion method is used. The effects of thermal diffusion, magnetic field, porosity parameter, thermal radiation, and Grashof number are mainly focused on the discussion of the current problem. Increasing Soret number (Sr) hikes the velocity profile and skin friction but declines Sherwood number. Also, it has been found that, when the magnetic parameter (M) increased, the fluid velocity and the concentration profile decreased. The current results show a good deal of agreement with previously published work. The findings of this study could be relevant in a variety of applications, including diffusion processes involving molecular diffusion of species with molar concentration.

SORET AND VARIABLE THERMAL CONDUCTIVITY EFFECTS ON HYDRO-MAGNETIC RADIATING FLUID PAST A VERTICAL PLATE WITH POROUS MEDIUM

Thermal diffusion and variable thermal conductivity effects on unsteady magnetohydrodynamic (MHD), heat and mass transfer flow past an infinite vertical porous plate have been investigated and analyzed numerically. The resultant flow governing equations are resolved numerically by the finite-difference scheme of the Crank-Nicolson type implicit method. The non-dimensional velocity, fluid temperature, and species concentration distributions are conferred through graphs for different fluid parameters involved such as joule-heating parameter, suction parameter, chemical reaction parameter, radiation parameter, etc. The coefficient of skin friction, Nusselt number and Sherwood number were tabulated. The concentration of the fluid rises with an increase in Soret number, whereas the Sherwood number reduces due to its increase.

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

AbstractThis article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.

Surface wave propagation over small bottom undulations in the presence of a submerged flexible porous barrier

The problems of scattering of surface gravity waves over an undulated bottom in the presence of either a porous vertical elastic plate or a tensioned porous membrane are addressed. A simplified perturbation technique is employed to split the governing boundary value problem into a series of problems involving the zeroth and the first-order potential functions. The solution to the problem associated with zeroth-order potential is obtained by reducing it to a Fredholm integral equation with the help of Havelock’s theorems. An approximate solution of the integral equation is obtained by applying the multi-term Galerkin technique. Application of Green’s integral theorem leads to finding the first-order reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation and the solution of the zeroth-order problem. The accuracy of the present results is established by generating some previous results for the case of an elastic plate submerged in water with bottom deformation. From the graphical presentation of the results it is observed that at certain values of frequency related to the ripple wavenumber, the first-order reflection coefficient exhibits resonant nature, whereas the net reflection is affected by the flexibility characteristics as well as the porosity of the structure.

Heat and mass transfer on MHD convective unsteady flow of a Jeffrey fluid past an inclined vertical porous plate with thermal diffusion Soret and Aligned magnetic field

This article has the objective of examining to perform unstable magnetohydrodynamic flow over an inclined plate enclosed in a penetrable mechanism with Soret-aligned magnetic field and chemical reaction. Once momentum and energy and mass are equal, they can be combined using the diffusion equation to yield the dimensionless momentum/energy/mass model. Aligned Magnetic field, Jeffrey Parameter, Inclined angle, and Chemical Reaction Model outlines are used to study the effect of numerous physical parameters on boundary layer properties, including Soret temperature, chemical reaction velocity, Temperature and concentration on the resulting heat accumulation profile, are tested using parametric models. The findings derived from skin friction, Nusselt number, and Sherwood numbers are included in the tables provided for several parameters. It is observed from the results that the velocity profile increases with increase Thermal and Mass Grashof Numbers, Jeffery Parameter and Porous media but the opposite trends are seen with increase in the magnetic field parameter, inclined parameter and Aligned magnetic field parameter. One of the important findings of this analysis includes that intensification in the Newtonian heating effect causes a gradual downfall in the rate of heat transfer at the plate and the concentration of the fluid decreases under the impact of chemical reaction. Their physic- Chemical features have been dealt with in detail. This fluid flow model has several industrial applications in the field of chemical, polymer, medical sciences, etc.

Three‐dimensional flow past a porous vertical plate in a porous medium with sinusoidal suction and permeability in the presence of thermal diffusion

AbstractAn analytical solution, based on the asymptotic series expansion method, for the problem of a fully developed chemically reactive laminar three‐dimensional flow through a porous vertical infinite plate in a porous medium with sinusoidal permeability as suction in the existence of appreciable radiation is presented. The effects of the physical parameters entering into the problem on the flow and transport characteristics are studied and demonstrated through graphs. The flow is three‐dimensional due to sinusoidal suction as well as porosity. It is found that concentration of the fluid rises due to thermal diffusion (Soret) effect. Furthermore, it is seen that fluid velocity is increased for increasing thermal diffusion effect. Also, viscous drag at the plate is increased under the Soret effect.

Characteristics of MHD Casson fluid past an inclined vertical porous plate

This paper addresses the effects of Soret on unsteady free convection flow of viscous incompressible fluid through a porous medium with high porosity bounded by a vertical infinite moving plate under the influence of thermal diffusion, chemical reaction, and heat source. The fluid is considered to be gray, absorbing, and emitting but non-scattering medium. Rosseland approximation is considered to describe the radiative heat flux in the energy equation. The dimensionless governing equations for this investigation are solved analytically using perturbation technique. The effects of various governing parameters on the velocity, temperature, concentration, skin-friction coefficient, Nusselt number and Sherwood number are shown in figures and tables and analyzed in detail. It was noticed that velocity distribution increased with increasing buoyancy parameters; temperature decreased with increasing Prandtl number, and concentration decreased with increasing the Schmidt number and chemical reaction parameter.

Unsteady MHD oscillatory Casson fluid flow past an inclined vertical porous plate in the presence of chemical reaction with heat absorption and Soret effects

AbstractThe purpose of this paper is to perform unsteady hydrodynamic flow over an inclined plate embedded in a porous medium with Soret‐aligned magnetic field and chemical reaction. Once momentum, energy, and mass are equal, they can be combined using the diffusion equation to yield the dimensionless momentum/energy/mass model. Computations were performed to analyze the behavior of fluid velocity, temperature and concentration on the inclined vertical plate with the variation of emerging physical parameters like aligned magnetic field, Casson parameter, inclined angle, chemical reaction including soret parameter. The findings derived from skin friction, Nusselt number, and Sherwood number are included in the tables provided for different parameters. The results match with a special case of previously published work. From the present analysis, it is reported that the presence of angle of inclination, aligned magnetic field, and Casson fluid parameters sustains a retarding effect on velocity. The velocity decreases with increasing angle of inclination, aligned magnetic field parameter, and Casson fluid parameter. Comparisons with previously published work performed and the results are found to be in excellent agreement.

Investigation of MHD Casson fluid flow past a vertical porous plate under the influence of thermal diffusion and chemical reaction

AbstractThe paper presented here discloses a detailed analytical study as to how the Casson fluid flows with characteristic properties of heat and mass transfer in an unsteady convective magnetohydrodynamic environment under the influence of thermal diffusion and chemical reaction. With the said characteristics, the fluid flows past over an oscillating vertical plate. The applicable partial differential equations are solved analytically using the perturbation technique and numerically using Matlab software. With the help of velocity, temperature and concentration, skin friction, Nusselt number, and Sherwood number are obtained and represented in tabular form. One of the important findings of this analysis includes that intensification in the Newtonian heating effect causes a gradual downfall in the rate of heat transfer at the plate and the concentration of the fluid decreases under the impact of a chemical reaction. Their physicochemical features have been dealt with in detail. This fluid flow model has several industrial applications in the fields of chemicals, polymers, medical sciences, and so forth.