Vertical Porous Plate Research Articles

Casson nanofluid performance on MHD convective flow past a semi‐infinite inclined permeable moving plate in presence of heat and mass transfer

AbstractThis article investigates the radiation and chemical reaction effects on the free convection heat and mass transfer flow of Casson nanofluids (Cu and TiO2) over an inclined porous vertical plate embedded in a porous medium in the presence of radiation absorption and constant heat source under fluctuating boundary conditions. The plate is moved with a constant velocity of U0, and temperature and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The perturbation technique is applied to solve the governing equations of the flow and pointed out the variations in velocity, temperature, and concentration with the use of graphical presentations. The impact of several parameters on local skin friction, Nusselt number, and Sherwood number is also noticed and discussed. It is concluded that the resultant velocity reduces with increasing Casson parameter and suction parameter, velocity, and temperature enhanced with increasing radiation absorption and diffusion thermo parameters. Also, it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameters. It is because chemical molecular diffusivity reduces for higher values of Kr.

Transverse Magnetic Field Effect on Extracellular Fluid Flow along with a Semi-Infinite Vertical Rotating Porous Plate

The primary intention of this practice is to numerically investigate the extracellular fluid (ECF) flow for unsteady 2-dimenstional case along with a porous vertical plate with the appearance of a transverse magnetic field in a rotating system. The dimensional basic equations have been non-dimensionalized by necessary dimensionless variables. The EFDM has been practiced to solve the dimensionless equations. The numerical data have been evaluated by FORTRAN software version 6.6a. For a perfect conductivity, Magnetic Diffusivity Number values have been taken between 5 to 15 in the induction formula. For proper exactness, stability and convergence tests have been performed. For initial time , the outputs have been illustrated for the primary, secondary and angular velocity, primary and secondary induced magnetic field, temperature field with shear stresses for and -direction, couple stress for -direction, and -direction current densities and Nusselt number. Finally, the outcomes of different parameters are discussed separately and pictorial graphically by MATLAB R2018a.The findings of this research may be used to control cell temperature, measurement of extracellular fluid motion, and so on.

Free Convective MHD Radiative Flow Past a Porous Vertical Plate in a Porous Medium with Chemical Reaction

An analytical solution for two-dimensional steady, viscous, incompressible hydromagnetic free convective flow past a uniformly moving vertical porous plate embedded in a porous medium in the presence of the Soret effect and chemical reaction is investigated in this paper. A uniform magnetic field is applied perpendicular to the plate and directed into the fluid region. The asymptotic series expansion method is used to solve the non-dimensional governing equations. The effects of thermal diffusion, magnetic field, thermal radiation, Grashof number, and chemical reaction are mainly focused on discussing the present problem. One of the significant findings of this study includes that an upsurge in the chemical reaction causes a downfall in the fluid temperature. It is seen that the Soret number enhances the velocity and temperature. Further, the fluid's velocity, concentration, and temperature decrease with an increase in the magnetic field parameter. In most works dealing with convective MHD flow, ohmic dissipation and viscous dissipation are neglected. In this work, these two effects are considered. Further, the Soret effect and the effect of first-order chemical reactions are also considered.

Hall effects on the unsteady MHD flow of the Rivlin–Ericksen fluid past an infinite vertical porous plate

The unsteady magnetohydrodynamic (MHD) convective flow of the Rivlin–Ericksen fluid past an infinite vertical plate with Hall effects has many engineering applications such as heat exchangers, cooling of electronic types of equipment, nuclear reactors, solar devices, polymer processing industries, food industries, and petroleum reservoirs. Therefore, the unsteady MHD convective flow of an incompressible viscous electrically conducting Rivlin–Ericksen fluid over a semi-infinite vertical permeable moving plate taking heat absorption and Hall effects into account, has been discussed. The plate travels with the constant velocity in the direction of fluid flow, whereas the free stream velocity follows the exponentially enhancing small perturbed flow. The time-dependent wall suction transpires near the porous surface. The non-dimensional leading equations for the exploration are resolved systematically utilizing two-term harmonic and non-harmonic functions. The present results reduced to earlier published results on the particular cases of the investigation. The numerical evaluations of the analytical solutions are performed, and graphical results for velocity, temperature, and concentration profiles contained by the boundary layers are presented. The skin-friction coefficient, Nusselt number, and Sherwood numbers are also examined through the graphical profiles.

Diffusion‐thermo effect on MHD dissipative flow past a porous vertical plate through porous media

AbstractIn this study, we investigate the heat and mass transfer in MHD convective flow past an infinite plate, through a porous media in presence of radiation, diffusion‐thermo effect, and heat sink. A uniform magnetic field is applied transversely in the fluid region. The novelty of the present work is to analyze the diffusion‐thermo effect on the flow phenomena in the presence of heat sink and thermal radiation. The governing equations are solved by perturbation technique to get expressions for velocity, temperature, and concentration fields. The influence of various physical quantities on the flow domain is studied graphically and in tabular form. It has been found that when heat flux is generated due to temperature gradient, the fluid velocity increases whereas the fluid temperature falls due to the diffusion‐thermo effect. The current results have been compared with the existing results in some cases and it has been found that the findings of the present study are consistent with earlier findings.

Experimental Study on Wave Attenuation Performance of A New Type of Floating Breakwater with Twin Pontoons and Multi Porous Vertical Plates

Experimental Study on Wave Attenuation Performance of A New Type of Floating Breakwater with Twin Pontoons and Multi Porous Vertical Plates

Effect of induced magnetic field, chemical reaction and thermal radiation on nonlinear mixed convective flow of Casson fluid over a vertical inclined porous plate embedded in porous medium

The aim of this paper is to study the combined effects of induced magnetic field and chemical reaction on MHD nonlinear mixed convective flow of Casson fluid over an inclined vertical porous plate embedded in a porous medium. The influence of viscous dissipation, heat source/ sink, and slip phenomena is taken into consideration. The effect of thermal radiation is also considered in the energy equation. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The main objective here is to analyze the induced magnetic field in a nonlinear mixed convective flow. At first, the appropriate similarity transformation is used to transform the governing nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations. The nonlinear ordinary differential equations are solved by a shooting technique with the help of bvp4c Matlab package. For the validation of the obtained results through the bvp4c Matlab solver, we have also solved this problem via R-K fourth-order method in Matlab and a good agreement is noted in both the results. The results of different physical parameters involved in the problem on the velocity, temperature, induced magnetic field and concentration are discussed by using graphs. It is noticed that the increasing values of the inclination angle cause rising of the induced magnetic field while induced magnetic field has opposite nature with magnetic parameter and magnetic Prandtl number. With increasing values of the thermal radiation parameter, the temperature profile diminishes. Apart from this, the numerical values of skin friction coefficient, Nusselt number and Sherwood number for the various values of parameters are displayed in tabular form.

Similarity solution for boundary layer flow near a moving vertical porous plate with combined effects of nonlinear thermal radiation and suction/injection having convective surface boundary condition

This piece of work explored the impact of nonlinear thermal radiation on natural convection flow in the vicinity of a constant moving vertical porous plate with suction/injection. The moving vertical porous plate is considered to be either move in the same direction with fluid in the free stream or move in the negative x-direction while the fluid move in the positive x-direction. The partial differential equations (PDEs) associated with the flow properties are simplified to ordinary differential equations (ODEs) using similarity variables. Then, the resulting ODEs and the boundary condition are translated into the IVP through the shooting method. Furthermore, the final IVP and the reduced boundary conditions are solved numerically through the Runge–Kutta method. The influence of the emerging dimensionless quantities is analyzed through tables and line graphs. The numerical results obtained revealed that with suction/injection, the shear stress could be enhanced by propagating the local convective heat transfer parameter Bix, nonlinear thermal radiation R and the local Grashof number Grx for the two cases of plate motion considered. The result also revealed that in the presence of suction/injection, the heat transfer rate decreases with Bix and Grx, whereas enhanced with R augment for the two plate motions considered. Furthermore, for a constant moving vertical porous plate and constant moving freestream velocity, the convective heat transfer parameter at any point x is proportional to the corresponding heat transfer coefficient related to hot fluid. The nonlinear thermal radiation enhances the velocity and temperature profiles.

Analytical study of chemical reaction, Soret, Hall and ion slip effects on MHD flow past an infinite rotating vertical porous plate

Heat and mass transport happen in absorption, distillation, extraction, drying, melt and crystallization, moreover evaporation, and the condensation. Mass transfer flows due to it are the temperature gradients are recognized as Soret effect. The Soret effects on the unsteady hydro magnetic free convective flow of an incompressible electrically conducting viscous fluid past a rotating vertical permeable surface by incidence of heat absorption, Hall and ion slip impacts has been investigated. The impacts of first order chemical reaction and thermal radiation are considered into description. The scheme of PDE is rendered into ODE and therefore solved analytically with the Laplace transform methodology. The significant impacts of prominent parameters on velocity, temperature and concentration distribution and the shear stress are investigated by the graphical illustrations and tables accordingly. The results are shown that, the velocity of the fluid is enhanced once the ion slip and Hall parameter significance are enhanced. It is also established that, the resultant velocity field is ascending with a growing in the Soret parameter and chemical reaction parameter. The temperature distribution is increased by an increasing in heat absorption parameter. In addition, the concentration is developed as the Soret parameter is improved throughout the fluid region.

Radiation effect on MHD flow past a porous vertical plate in the presence of heat sink

AbstractThis study investigates heat and mass transfer in MHD convective flow through a vertical plate via porous media in the presence of radiation and a heat source/sink. It is assumed that a uniform magnetic field of strength is imposed perpendicular to the plate and directed into the fluid area. The governing nondimensional equations are solved using the perturbation technique. We further derived the skin friction, Nusselt number, and Sherwood number. The computation of results is performed with the aid of mathematical software and results are presented in graphical and tabular forms for distinct flow impacting parameters. It is observed that fluid motion is retarded due to the application of the magnetic field. Furthermore, the fluid temperature comprehensively falls under the Prandtl number as well as the thermal radiation effect. It is important to note that the heat sink causes fluid velocity and fluid temperature to fall drastically.

An impact on non-Newtonian free convective MHD Casson fluid flow past a vertical porous plate in the existence of Soret, Dufour, and chemical reaction

The objective of this research is to explore the heat and mass transfer properties of an unsteady MHD natural convective Non-Newtonian, Casson fluid flow through a permeable vertical plate in the existence of Soret, Dufour, and chemical reaction. The aspects of heat and radiation absorptions are also factored in. Applications of the present study would be useful in magnetic material processing and chemical engineering systems. Mathematically, the flow field situation is expressed in terms of partial differential equations. The transformed flow-narrating partial differential equations of momentum as well as energy and species concentration were numerically solved using the finite element technique. Non-dimensional flow parameters were used to extract the numerical outcomes of velocity, temperature, and concentration, and the outcomes are envisioned graphically. The significance of the factors determining, Nusselt number, Sherwood number, and skin friction is also considered. The outcomes reveal that raising the permeability parameter causes the velocity to improve while enhancing the Casson parameter causes the velocity distribution to reduce.

Thermal outcomes for blood-based carbon nanotubes (SWCNT and MWCNTs) with Newtonian heating by using new Prabhakar fractional derivative simulations

The mixed convection flow of carbon nanotubes due to porous vertical plate has been presented via fractional simulations. The single and multi-wall carbon nanotubes are used to observe the thermal aspect of hybrid nanofluid model. The blood is treated as base material. The shear thinning and thickening aspect of blood are predicted by using the Casson fluid model. The comparative thermal observations of blood base fluid with multi-wall carbon nanotubes (MWCNTs) and single-wall carbon nanotubes (SWCNTs) are reported. The Prabhakar fractional derivative simulations are performed to analyze the physical pattern of problem. The Laplace transformations are implemented to the integrating task. It is noticed that fractional parameter reduces the velocity profile for both MWCNTs and SWCNTs suspension. With increment in volume fraction and fractional parameters reduces the thermal profile effectively.

Cattaneo\u2013Christov heat flow model for copper\u2013water nanofluid heat transfer under Marangoni convection and slip conditions

This report is devoted to the study of the flow of MHD nanofluids through a vertical porous plate with a temperature-dependent surface tension using the Cattaneo–Christov heat flow model. The energy equation was formulated using the Cattaneo–Christov heat flux model instead of Fourier’s law of heat conduction. The Tiwari–Das model was used to take into account the concentration of nanoparticles when constructing the momentum equation. The problem is described mathematically using the boundary layer approach as a PDE, which is then converted into an ODE with the help of the transformation process. The solution finding process was completed by running the bvp4c code in MATLAB. A quantitative analysis of the influence of some newly occurring parameters on physical quantities was carried out using graphics. The addition of nanoparticles to the base fluid leads to an increase in both skin friction and thermal conductivity. The increase in thermal conductivity is the advantage, while the increase in skin friction is the disadvantage of the nanoparticle concentration. Marangoni convection has proven to be one of the most cost-effective tools available that can reduce skin friction. Marangoni convection improves the heat transfer coefficient during suction but decreases the heat transfer coefficient during the injection.

A Numerical Study on Newtonian Heating Effect on Heat Absorbing MHD Casson Flow of Dissipative Fluid past an Oscillating Vertical Porous Plate

The numerical study of Newtonian heating effect on unsteady free convection MHD Casson flow of radiating and chemically reacting fluid past an oscillating vertical porous plate embedded in a porous medium was conducted by considering the effects of heat sink and viscous dissipation. The fluid motion is persuaded due to the periodic oscillations of the plate along its length. This phenomenon is represented as nonlinear PDEs with initial and boundary conditions. By introducing suitable nondimensional variable and parameters, the leading equation with initial and boundary conditions is converted into dimensionless form, which are then solved numerically using a finite difference method. The effects of several relevant parameters on the velocity, temperature, and concentration are displayed graphically, whilst the effects of these parameters on the skin friction and Nusselt and Sherwood numbers are exhibited in tabular format and then discussed in detail. The final outcomes divulge that the radiation parameter and Eckert number have an increasing effect on the velocity and temperature, whilst reverse tendency is detected with increasing Prandtl number and heat absorption parameter. Newtonian heating parameter and thermal and mass buoyancy forces boost fluid velocity, whilst Schmidt number and chemical reaction have the opposite impact. It is noteworthy to point out in this study that the velocity boundary layer thickness for the Newtonian fluid is larger than the Casson fluid.

Influence of viscous dissipation and spanwise cosinusoidally fluctuating temperature on MHD free convective boundary layer flow with radiation absorption and chemical reaction

AbstractThe current reconnaissance emphasis on spanwise cosinusoidally fluctuating temperature along with time deepened as well as radiation absorption on unsteady magneto‐hydrodynamics free convective heat and mass transfer boundary layer flow with viscous dissipation, constant suction normal to an infinite hot vertical porous plate in the existence of chemical reaction by means of heat generation. The analytical solution of nonlinear PDE's governing the flow has been accomplished by employing a second‐order multiple regular perturbation method within the stipulated boundary conditions. Velocity, temperature, concentration as well as Sherwood have been exemplified graphically; along with Skin friction, and Nusselt numbers are ascertained in tabular form. Eventually, it was found that velocity, temperature, and Skin friction accelerated with the accumulative values of Eckert number and radiation absorption, but conflicting results emerged in the case of Prandtl number. Contemporaneously Sherwood's number depreciated with the magnification of the chemical reaction parameter as well as the Schmidt number.

MHD, thermal radiation, thermophoresis and Soret–Dufour mechanism contributions on unsteady motion of Casson fluid over a semi‐infinite porous vertical plate

AbstractThis paper examined the contribution of MHD, thermal radiation, thermophoresis and Soret–Dufour mechanism on unsteady motion of Casson non‐Newtonian fluid. The flow model which resulted in partial differential equations (PDES) was transformed into a dimensionless form of PDES using suitable quantities. The contributions of controlling flow parameters were graphically presented for velocity, temperature, and concentration. The quantities of engineering interest were calculated for flow parameters and presented using table. A considerable value of Soret parameter was noticed to elevate the skin friction and Sherwood number. Impact of the magnetic parameter has great impact on the motion of Casson fluid by lowering its motion. This is because as the value of magnetic parameter increases the Lorentz force added more strength and hereby slow down the motion of an electrically conducting fluids. The present outcomes were examined with previously published work and was in conformity with each other.

Aspects of parabolic motion of MHD fluid flow past a vertical porous plate with cross‐diffusion effects

AbstractIn the presence of Soret and Dufour effects, a numerical analysis is performed for an unstable magnetohydrodynamics convective flow of parabolic motion with variable temperature and concentration. The finite‐difference method is used to solve the set of nondimensional governing equations with boundary conditions numerically. Graphs are used to investigate the effect of various physical characteristics on flow quantities. Variations in skin friction, Nusselt number, and Sherwood number are also examined using tables for physical curiosity. This study is unique in that it takes into account changeable temperature as well as concentration with Soret and Dufour effects. The magnetic parameter, Prandtl number, heat source, radiation parameter, Schmidt number, and chemical reaction parameter show a significant increase in skin friction, whereas the Grashof number, modified Grashof number, permeability parameter, radiation absorption parameter, Dufour number, and Soret number show the opposite trend. As the Soret number rises, the concentration rises as well, whereas the opposite is true for the Schmidt number and the chemical reaction parameter. The current study is highly supported by previously published data that have been verified.

Newtonian Heating Effect on Heat Absorbing Unsteady MHD Radiating and Chemically Reacting Free Convection Flow Past an Oscillating Vertical Porous Plate

In this article, we have discussed in detail the effect of Newtonian heating on MHD unsteady free convection boundary layer flow past an oscillating vertical porous plate embedded in a porous medium with thermal radiation, chemical reaction and heat absorption. The governing PDEs of the model together with related initial and boundary conditions have been solved numerically by the finite element method. The dimensionless velocity, temperature and concentration profiles are analyzed graphically due to the effects of key parameters in the concerned model problem. Computed results for the skin friction coefficient, Nusselt number and Sherwood number are put in tabular form. It is observed that the thermal and mass buoyancy effects support the velocity whilst a reverse effect is noticed when the strength of the magnetic field is increased. The velocity and temperature enhances with an increase in the Newtonian heating and thermal radiation whilst a reverse effect is observed with an increase in the Prandtl number and heat absorption parameter. Increasing Schmidt number and chemical reaction parameter tends to depreciate both velocity and concentration. The Newtonian heating, thermal radiation and magnetic field tends to decrease in the skin friction. The Nusselt number increases with increasing Newtonian heating and heat absorption parameters. An increase in the Schmidt number and chemical reaction rate tends to improve the Sherwood number.

Hall current effects on MHD flow of chemically reacting fluid through a porous medium with heat source

AbstractWe considered the magnetohydrodynamic (MHD) free convective flow of an incompressible electrically conducting viscous fluid past an infinite vertical permeable porous plate with a uniform transverse magnetic field, heat source and chemical reaction in a rotating frame taking Hall current effects into account. The momentum equations for the fluid flow during absorbent medium are controlled by the Brinkman model. Through the undisturbed state, both the plate and fluid are in a rigid body rotation by the uniform angular velocity perpendicular to an infinite vertical plate. The perpendicular surface is subject to the homogeneous invariable suction at a right angle to it and the heat on the surface varies about a non‐zero unvarying average whereas the warmth of complimentary flow is invariable. The systematic solutions of the velocity, temperature, and concentration distributions are acquired systematically by utilizing the perturbation method. The velocity expressions consist of steady‐state and fluctuating situations. It is revealed that the steady part of the velocity field has a three‐layer characteristic while the oscillatory part of the fluid field exhibits a multi‐layer characteristic. The influence of various governing flow parameters on the velocity, temperature, and concentration are analyzed graphically. We also discuss computational results for the skin friction, Nusselt number, and Sherwood number in the tabular forms.

Hall and Rotation Effects on Radiating and Reacting MHD Flow past an Accelerated Permeable Plate with Soret and Dufour Effects

This article investigates numerically the effects of Hall current and rotation effects on radiating and chemically reacting unsteady MHD natural convection flow past an accelerated infinite vertical permeable plate in the presence of Soret and Dufour effects. The dimensionless coupled non-linear governing partial differential equations of the problem are solved numerically by employing finite element method. The influence of various physical parameters influencing the flow on the primary velocity, secondary velocity, temperature and the species concentration are displayed graphically whilst the numerical results of the primary skin friction, secondary skin-friction, Nusselt number and the Sherwood number are presented in tabular form. Results reveals that magnetic parameter, radiation parameter and chemical reaction rate tends to depreciate both primary and secondary velocity components whilst Hall, Soret and Dufour effects have reverse trend. Rotation parameter tends to retard fluid flow in the primary flow direction and accelerate fluid flow in the secondary flow direction. Thermal boundary layer thickness decreases with increasing radiation parameter whilst the reverse trend is noticed with increasing Dufour effect. Thermal diffusion effect causes to improve concentration boundary layer thickness whilst chemical reaction rate has reverse impact. These parameters have similar effect on the primary and secondary skin-frictions whilst opposite effect was noticed on the Nusselt and Sherwood numbers. This model problem finds an important in engineering and industrial application such as MHD generators, food processing, heat exchangers devices and internal rotation rate of the sun.
 HIGHLIGHTS
 
 The problem investigate the effects of Hall current and rotation effects on radiating and reacting on unsteady magnetohydrodynamics (MHD) natural convection heat and mass transfer flow over an infinite vertical porous plate embedded in a uniform porous medium taking Soret and Dufour effects into account
 The resulting partial differential equations governing the fluid flow are solved numerically using the finite element method. In order to determine the effects of various pertinent parameters and to investigate the important flow features, the numerical calculations for fluid velocity, temperature and species concentration are computed and shown graphically whereas skin friction, Nusselt number and Sherwood number at the plate are evaluated and depicted in tabular form
 The model problem finds an important in engineering and industrial application
 
 GRAPHICAL ABSTRACT