Vertical Permeable Plate Research Articles

Unsteady MHD mixed convection flow of a hybrid nanofluid with thermal radiation and convective boundary condition

Heat transfer enhancement is a current concern in a variety of areas. Nanofluid, a novel kind of heat transfer fluid, may be used as an efficient medium for improving heat transmission. A numerical investigation is necessary to approximate the flow properties. In this study, the flow and heat transfer of the unsteady magnetohydrodynamic mixed convective hybrid nanofluid along a permeable vertical plate is numerically elucidated. The imposition of thermal radiation and convective boundary condition is considered towards the model. A sophisticated similarity transformation is adapted to simplify the governing formulations of the model into similarity equations which then are being solved via numerical solver in Matlab. The numerical findings of this study in the absence of nanoparticles and unsteadiness effect are consistent with those analytical solutions available in the literature. Dual solutions are perceived to appear because of the opposing flow contributed by the combination of mixed convection, injection, and unsteadiness parameters. Hence, to confirm the practicality of the solutions, stability analysis is conducted, and the first solution is stable. Greater skin friction and heat transfer rate are established by only a small and reduced copper volume fraction and magnetohydrodynamic effect when the negative values of mixed convection and unsteadiness parameter are considered. Therefore, this present study suggests minimizing the hybrid nanofluid concentration and maximizing the thermal radiation to achieve a better heat transfer capability within the other considered flow effects.

Numerical simulation of bioconvective Darcy Forchhemier nanofluid flow with energy transition over a permeable vertical plate

In biological systems, the MHD boundary layer bioconvection flow through permeable surface has several applications, including electronic gadgets, heating systems, building thermal insulation, geological systems, renewable energy, electromagnetism and nuclear waste. The bioconvection caused by the hydromagnetic flow of a special form of water-based nanoliquid including motile microorganisms and nanoparticles across a porous upright moving surface is investigated in this report. The combination of motile microbes and nanoparticles causes nanofluid bioconvection is studied under the cumulative impact of magnetic fields and buoyancy forces. The Brownian motion, thermophoresis effects, heat absorption/generation, chemical reaction and Darcy Forchhemier impact are also unified into the nonlinear model of differential equations. The modeled boundary value problem is numerically computed by employing a suitable similarity operation and the parametric continuation procedure. The parametric study of the flow physical parameters is evaluated versus the velocity, energy, volume fraction of nanoparticles, motile microorganisms’ density, skin friction, Sherwood number and Nusselt number. It has been observed that the velocity profile reduces with the effect of porosity parameter k1, inertial parameter k2, Hartmann number and buoyancy ratio. While the energy transition profile significantly enhances with the flourishing values of Eckert number Ec, heat absorption/generation Q and Hartmann number respectively.

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

Unsteady Double Diffusive Mixed Convective Flow Over a Vertical Permeable Plate in a Porous Medium

In this article, we analytically investigated the effects of fluctuating free stream and suction velocities on unsteady mixed convective flow over a vertical permeable plate in the occurrence of an unvarying porous medium with a thin environment, time-dependent suction, and viscous dissipation. The governing equations of the physical phenomena give rise to a bunch of extremely non-linear coupled PDE's involving various non-dimensional parameters. An analytical solution has been obtained through the plots for distinct chief physical parameters like Grashof number, the amplitude of the fluctuating suction velocity parameter, amplitude of fluctuating free stream velocity parameter, Prandtl number, permeability parameter, solutal Grashof number, and Eckert number, which are involved in the solution. Also, a comparison has been made with published results in the absence of some non-dimensional parameters for a particular case and found in good agreement. The study results that the fluctuating free stream velocity increases the velocity, temperature increases, and a reverse tendency is observed in the Eckert number.

Thermal radiation and chemically reactive aspects of mixed convection flow using water base nanofluids: Tiwari and Das model

The current investigation focuses on the magneto-nanofluid mixed convective boundary-layer flow of nanofluid caused by a vertical permeable plate with nonlinear thermal radiation. Furthermore, heat and mass transfer for water-base fluids influenced by heat generation/absorption and viscous dissipation have been analyzed. The convective boundary condition is also imposed on the vertical sheet. The main aim of the study is to investigate the five different types of nanoparticles, namely, silver , copper , alumina copper oxide , and titanium dioxide in the base fluid water. Moreover, the governing partial differential equations are converted into a set of ordinary differential equations via Sparrow–Quack–Boerner local nonsimilarity method. Additionally, nonlinear ODEs are successfully tackled by the Runge–Kutta–Fehlberg method. Physical parameters are examined graphically along with the velocity, temperature, and concentration distribution. Further, the skin friction coefficient, local Nusselt number, and Sherwood numbers are also studied in detail using graphs. The results show that increasing the value of buoyancy parameter and magnetic parameter fluid exhibits more resistance in the fluid, thereby fluid velocity and momentum boundary layer reduce. Moreover, the radiation parameter transmitted more heat from the surface to the fluid; as a result, the fluid temperature is boosted.

Numerical study on MHD radiating and reacting unsteady slip flow past a vertical permeable plate in a porous medium

This paper examines the unsteady hydro-magnetic boundary layer flow of a reacting and radiating electrically conducting fluid past a slippery permeable vertical plate embedded in a porous medium. The governing partial differential equations are obtained and tackled numerically via Galerkin finite element method. Pertinent results with respect to the effects of emerging thermo physical parameters on the velocity, temperature and concentration fields together with skin-friction, Nusselt number and Sherwood number are elucidated graphically and in tabular form. Numerical validation of the present work special case results with the one already in the literature shows an excellent agreement. It is found that buoyancy forces enhanced the momentum boundary layer while magnetic field and radiative heat absorption lessen it. Both heat and mass transfer rates diminished with a rise in the rate of chemical reaction.

Hybrid Carbon Nanotube Flow near the Stagnation Region over a Permeable Vertical Plate with Heat Generation/Absorption

This research explored the mixed convection flow past a vertical plate immersed in a hybrid carbon nanotube near the stagnation point. The hybrid carbon nanotube was synthesized by the mixture of two nanoparticles, namely multi-wall (MWCNT) and single-wall (SWCNT) carbon nanotubes immersed in water (base fluid). In addition, attractive aspects of suction/injection and heat generation/absorption effects were incorporated. Similarity variables were used to convert the partial differential equations describing the fluid into ordinary (similarity) differential equations before being solved numerically using Matlab software. The simultaneous impact of several parameters on velocity and temperature profiles, skin friction coefficient, and local Nusselt number were represented with graphs. Dual solutions were observed for some pertinent parameters, which led to stability analysis. This analysis interpreted that merely the first numerical solution is stable. In addition, hybrid nanoparticle, injection effect, and heat-generation parameters led to a decreased range of solutions, whilst the suction effect and heat-absorption parameters acted in the opposite manner. Besides, it is noted that the rate of heat transfer for hybrid carbon nanotube was higher when compared with carbon nanotube and ordinary fluid. Additionally, the heat absorption and buoyancy-assisting flow parameters magnified the heat transfer rate.

AN UNSTEADY MHD FLOW OF CASSON FLUID PAST AN EXPONENTIALLY ACCELERATED VERTICAL PLATE

An unsteady, magnetohydrodynamic, incompressible, radiative Casson fluid flow past an infinite vertical permeable plate, which is accelerated exponentially, in presence of heat sink parameter and first-order chemical reaction taking account of Soret effect, is considered. Governing equations are solved for the profiles of velocity, temperature and concentration with the help of Laplace transform. The effects of various physical parameters on velocity, temperature and concentration profiles are discussed with the help of graphs.

Dual similarity solutions because of mixed convective flow of a double-nanoparticles hybrid nanofluid: critical points and stability analysis

Purpose The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions. Design/methodology/approach The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable. Findings It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime. Originality/value A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

MHD mixed convection flow of a hybrid nanofluid past a permeable vertical flat plate with thermal radiation effect

The magnetohydrodynamic (MHD) radiative flow of a hybrid alumina-copper/water nanofluid past a permeable vertical plate with mixed convection is the focal interest in this present work. Dissimilar to the traditional nanofluid model that considers only one type of nanoparticles, we consider the hybridization of two types of nanoparticles in this work which are alumina and copper. The governing flow and heat transfer equations are simplified to the ordinary differential equations (ODEs) with the adaptation of conventional similarity transformations which are then evaluated by the bvp4c solver (MATLAB) to generate the numerical solutions. The solutions are generated and illustrated in the form of graph to be easily observed. Although dual solutions are obtained in this study, only one solution is determined to be stable. By reducing the concentration volume of copper and increasing the magnetic and radiation parameters, the boundary layer separation can be hindered. With the occurrence of opposing flow due to the mixed convection parameter, the heat transfer can be enhanced when the concentration volume of copper is being reduced and when the magnetic and radiation parameters are being proliferated.

Unsteady MHD free convection flow past a vertical permeable flat plate in a rotating frame of reference with constant heat source and variable thermal boundary condition in a nanofluid

Abstract The problem of unsteady magnetohydrodynamics (MHD) free convection flow of nano-fluid past an oscillation moving vertical semi-infinite permeable flat plate with constant heat source and vertical variable thermal boundary condition in a rotating frame of reference is studied theoretically. The boundary layer has the oscillatory type of solution because slip velocity is assumed to oscillate in time with constant frequency. The governing equations are solved using small perturbation approximation. For this investigation, we use two types of nano-particles in base fluid, namely Cu (copper) and Al2O3 (aluminium oxide). The effect of various types of suspended metallic nano-particles and non-dimensional physical parameters on the fluid flow and heat transfer rate are presented and discussed through the graphs.

Influence of radiative heat flux in nonlinear convection of quartic order in Casson fluid past a vertical permeable plate with variable suction and Hall current

The current study centralizes on unsteady free convection slip flow of Casson fluid past a vertical permeable plate with Hall current, radiative heat flux, and variable suction. The nonlinear convection is subjected to quartic order. Perturbation method is used to convert the non-linear coupled partial differential equation of the momentum and energy to a system of ordinary differential equations. The dimensionless governing equations are solved analytically for velocity and temperature profiles. The graphs are plotted for sundry parameters for variations in the distinct flow fields w.r.t distance from the plate. Variation in the skin friction for the axial and transverse cases are presented in the form of graphs for various parameters. It is observed that with the increase in the order of non-linear convection and value of radiation parameter, the velocity field increases in Casson fluid. The increase in heat absorption parameter and Prandtl number decreases the temperature profile and increase in radiative heat flux parameter increases the temperature profile.

WATER WAVE SCATTERING BY A THIN VERTICAL SUBMERGED PERMEABLE PLATE

An alternative approach is proposed here to investigate the problem of scattering of surface water waves by a vertical permeable plate submerged in deep water within the framework of linear water wave theory. Using Havelock’s expansion of water wave potential, the associated boundary value problem is reduced to a second kind hypersingular integral equation of order 2. The unknown function of the hypersingular integral equation is expressed as a product of a suitable weight function and an unknown polynomial. The associated hypersingular integral of order 2 is evaluated by representing it as the derivative of a singular integral of the Cauchy type which is computed by employing an idea explained in Gakhov’s book [7]. The values of the reflection coefficient computed with the help of present method match exactly with the previous results available in the literature. The energy identity is derived using the Havelock’s theorems.

MHD and Stability for Convective Flow of Micropolar Nanofluid over a Moving and Vertical Permeable Plate

This work mainly studies the effect of the magnetic field, the suction /injection, the Brownian and thermphorese diffusions and the stability on heat transfer in a laminar boundary layer flux of micropolar nanofluids flow adjacent to moving vertical permeable plate. The appropriate governing equations developed are reduced by the transformation of similarity which are solved using the finite difference method that implements the 3-stage Lobatto collocation formula. A parametric study of the physical parameters is carried out to show their influence on the different profiles. The results show that the microrotation of the suspended nanoparticles and the presence of the magnetic field become important on the heat transfer with good chemical stability of the micropolar nanofluids.

Analysis of MHD free convective stream past a vertical permeable plate and a warmth source through permeable material underneath oscillatory pull

The mass exchange with the warmth source on the free convective progression of a gooey incompressible electrically directing liquid past vertically permeable plate through a permeable medium in nearness of a cross over attractive field with time dependant penetrability and oscillatory pull is considered in this paper. The arrangement is acquired by the Perturbation strategy for speed field temperature and fixation dissemination. The impacts of different boundaries on the speed field, temperature, and fixation dissemination are examined through diagrams. Likewise, the skin contact and Sherwood number are determined.

Quadratic convective transport of Cu‐Al2O3hybrid nanoliquid with Hall current, variable suction, and exponential heat source

The time‐dependent slip flow and heat transport of the Cu‐Al2O3hybrid nanofluid through a vertical permeable plate with Hall current and variable suction is investigated. An exponential heat source and quadratic convection effects are considered. The dimensionless governing equations are solved analytically using the regular perturbation method. The graph of variation of the different flow fields with respect to the distance from the plate is drawn for the analysis. It is established that the exponential heat source aspect increased the temperature profile while the quadratic convection aspect decreased the temperature profile. The applied magnetic field and nonlinear convection aspects reduce the axial velocity field. The quadratic convection and exponential space‐dependent heat source phenomena are favorable to friction factors. Furthermore, the global heat transfer is increased in the presence of an exponential space dependent heat source and hybrid nanoparticles.

Numerical Investigation of Natural Convection Viscoelastic Jeffrey’s Nanofluid Flow from a Vertical Permeable Flat Plate with Heat Generation, Thermal Radiation, and Chemical Reaction

The boundary layer flow of an incompressible viscoelastic Jeffrey’s nanofluid from a vertical permeable flat plate is investigated. We consider the effects of heat generation, thermal radiation, and chemical reaction on the fluid flow. The nonlinear transformed coupled differential equations that describe the transport processes are solved numerically using a multidomain bivariate spectral quasilinearization method (MD-BSQLM). This innovative method involves blending the quasilinearization idea with the bivariate Lagrange interpolation. The solutions of the resulting system of equations are then obtained sequentially on multiple intervals using the Chebyshev spectral collocation method. The method is shown to give accurate solutions for boundary layer-type equations. The influence of various physical parameters on velocity, temperature, and nanoparticle concentration fields, as well as on the skin friction and heat and mass transfer coefficients, is shown and discussed in detail. The range of the values of the governing parameters considered in this study is between 0 , 4 . For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, temperature, and nanoparticle concentration fields for selected physical parameter values. The results obtained were found to correlate with the results from published literature. For quantitative verification of our findings, the MD-BSQLM numerical solutions were again confirmed against published results reported in the literature, and the results were observed to be in perfect agreement. This study’s findings indicate that the Deborah number and suction parameter have related effects on the velocity profile, which is to suppress both the flow velocity and the momentum boundary layer thickness. Increasing the heat generation and thermal radiation parameters enhances both the temperature and thermal boundary layer depths. In contrast, an increase in the chemical reaction parameter causes a decrease in the fluid concentration.

APPLICATION OF TAGUCHI EXPERIMENTAL METHOD IN NUMERICAL SIMULATION OF VARIABLE VISCOSITY AND INTERNAL HEAT GENERATION EFFECTS ON NATURAL CONVECTION IN POROUS MEDIA

This study uses an optimization approach representation of the numerical solution for the variable viscosity, the uniform blowing/suction and the internal heat source effects on the free convection flow over a vertical permeable plate in porous media with a non-linear Boussinesq approximation. The internal heat source is of an exponential decaying form. The partial differential equations are transformed into non-similar equations and solved by Keller box method (KBM). Compared with the previously published articles, the results are considered to be very consistent. Numerical results for the local Nusselt number with the four parameters: 1) the blowing/suction parameter , 2) the viscosity-variation parameter , 3) internal heat source coefficient , 4) the non-linear temperature parameter are expressed in tables. Through the Taguchi method to predict the best point of the maximum of local Nusselt number is , , , .

Multivariate Jeffrey Fluid Flow past a Vertical Plate through Porous Medium

An analysis is suggested to study the impact of Hall currents in Jeffrey fluid which is chemically reactive through a porous medium limited by a semi-infinite vertical permeable plate within the existence of heat generation. An evenly distributed magnetic field turns vertically on the porous surface which absorbs the Jeffrey fluid with a changed suction velocity with time. The analytical expressions are solved by means of three terms harmonic and non-harmonic functions. Statistical calculations are carried out for the point of resultant outcomes which are shown graphically and the impacts of the parameters velocity, temperature and concentration are listed. In addition, the results of skin-friction coefficient (τ), Nusselt number (Nu) and Sherwood number (Sh) are taken in to consideration. It is revealed that the impact of the Hall parameter on the channel velocities and skin friction coefficient is subjected to the estimation of the wall suction parameter.