Permeable Plate Research Articles

Three-Dimensional Radiative Flow of Hybrid Nanofluid Past a Shrinking Plate with Suction

Hybrid nanofluid has been widely used in various heat transfer applications especially as the heat exchanger due to the great thermal conductivity compared to the conventional fluid. However, numerous investigations should still be carried out to properly understand its properties. Hence, in this study, a three-dimensional radiative flow of hybrid Cu-Al2O3/water nanofluid past a permeable shrinking plate is numerically analyzed. The boundary layer including the energy equations are reduced to a system of ordinary differential equations using the similarity transformations and are then solved numerically by using the bvp4c solver in MATLAB. The application of suction through the permeable plate is necessary in aiding the fluid motion past the shrinking surface. Dual solutions are also observable, hence the stability analysis is conducted to mathematically validate the real solution. The enhancement of copper volumetric concentration in the hybrid nanofluid is capable in decelerating the boundary layer separation.

The Magneto-Natural Convection Flow of a Micropolar Hybrid Nanofluid over a Vertical Plate Saturated in a Porous Medium

In this study, we investigate the convective flow of a micropolar hybrid nanofluid through a vertical radiating permeable plate in a saturated porous medium. The impact of the presence or absence of the internal heat generation (IHG) in the medium is examined as well as the impacts of the magnetic field and thermal radiation. We apply similarity transformations to the non-dimensionalized equations and render them as a system of non-linear ODEs (Ordinary Differential Equations) subject to appropriate boundary conditions. This system of non-linear ODEs is solved by an adaptive mesh transformation Chebyshev differential quadrature method. The influence of the governing parameters on the temperature, microrotation and velocity is examined. The skin friction coefficient and the Nusselt number are tabulated. We determine that the skin friction coefficient and heat transport rate increase with the increment in the magnetic field. Moreover, the increment in the micropolarity and nanoparticle volume fraction enhances the skin friction coefficient and the Nusselt number. We also conclude that the IHG term improved the flow of the hybrid nanofluid. Finally, our results indicate that employing a hybrid nanofluid increases the heat transfer compared with that in pure water and a nanofluid.

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.

Investigation of Effects of Thermal Radiation, Magnetic Field, Eckert Number, and Thermal Slip on MHD Hiemenz Flow by Optimal Homotopy Asymptotic Method

Analytical investigation of thermal radiation, Prandtl number, Eckert number, permeability parameter, magnetic field, velocity, and thermal slip effects on magnetohydrodynamic Hiemenz flow over a permeable plate with forced convection has been presented. Similarity variable conversion method has been applied to transmute the fundamental governing equations of the fluid dynamics in flow into a pair of nonlinear third-order ordinary differential equations and is analytically solved by the optimal homotopy asymptotic method (OHAM). The influences of several relevant physical parameters in the model on velocity and temperature of the fluid have been studied and analysed profoundly by use of graphs and tables. It is detected that, with mounting value of suction/blowing parameter and magnetic field parameter, the skin friction coefficient enhances. Likewise, it is seen that the Nusselt number increases with enhancing value of magnetic parameter. It is also witnessed that the velocity increases as the Eckert number, blowing/suction parameter, and permeability parameter increase, but it decays against magnetic field and velocity slip parameter. Moreover, the result reveals that the fluid temperature upsurges along with snowballing the radiant heat, magnetic field parameter, and the Eckert number. However, it descends against thermal slip parameter, Prandtl number, wall temperature exponent, and velocity slip parameter. A comparison with previous studies has been made, and the result shows an excellent agreement.

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.

Pressure and temperature driven fully-developed rarefied gas flow in a channel with uniform injection/suction through its permeable walls

The pressure and temperature driven fully-developed rarefied gas flow between two parallel permeable plates, with uniform gas injection and suction from the bottom and top plates respectively, is investigated, based on the linearized Shakhov (S) model and the linearized Boltzmann equation (BE). Both flow configurations are characterized by the gas rarefaction parameter and the injection/suction velocity magnitude. Computational results for the so-called kinetic coefficients, as well as for the macroscopic quantities are provided in a wide range of the two parameters. The Onsager-Casimir reciprocity relation between the mechanocaloric and thermal creep coefficients has been proven to hold for arbitrary values of the injection velocity and has been used to validate the accuracy of the obtained results. It is shown that, the kinetic coefficients and macroscopic quantities are significantly affected as the injection velocity is increased. In addition, the kinetic results properly recover the corresponding analytical solutions in the free molecular and slip regimes. The examined prototype rarefied injection/suction flows may be useful to the investigation of more complex and realistic flow configurations in channels of various cross-sections with permeable walls where the injection velocity is not constant in the whole flow domain.

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.

On the process of filtration of fractional viscoelastic liquid food

In the process of filtration, fluid impurities precipitate/accumulate; this results in an uneven inner wall of the filter, consequently leading to non-uniform suction/injection. The Riemannian–Liouville fractional derivative model is used to investigate viscoelastic incompressible liquid food flowing through a permeable plate and to generalize Fick’s law. Moreover, we consider steady-state mass balance during ultrafiltration on a plate surface, and a fractional-order concentration boundary condition is established, thereby rendering the problem real and complex. The governing equation is numerically solved using the finite difference algorithm. The effects of the fractional constitutive models, generalized Reynolds number, generalized Schmidt number, and permeability parameter on the velocity and concentration fields are compared. The results show that an increase in fractional-order α in the momentum equation leads to a decrease in the horizontal velocity. Anomalous diffusion described by the fractional derivative model weakens the mass transfer; therefore, the concentration decreases with increasing fractional derivative γ in the concentration equation.

Non-dermal applications of microneedle drug delivery systems.

Microneedles (MNs) are micron-scaled needles measuring 100 to 1000μm that were initially explored for delivery of therapeutic agents across the skin. Considering the success in transcutaneous drug delivery, the application of microneedles has been extended to different tissues and organs. The review captures the application of microneedles to the oral mucosa, the eye, vagina, gastric mucosa, nail, scalp, and vascular tissues for delivery of vaccines, biologics, drugs, and diagnostic agents. The technology has created easy access to the poorly accessible segments of eye to facilitate delivery of monoclonal antibodies and therapeutic agents in management of neovascular disease. Microporation has been reported to drastically improve the drug delivery through the poorly permeable nail plate. Curved microneedles and spatially designed microneedle cuffs have been found to be capable of delivering stem cells and therapeutic macromolecules directly to the cardiac tissue and the vascular smooth muscle cells, respectively. Besides being minimally invasive and patient compliant, the technology has the potential to offer viable solutions to deliver drugs through impermeable barriers owing to the ability to penetrate several biological barriers. The technology has been successful to overcome the delivery hurdles and enable direct delivery of drug to the target sites, thus maximizing the efficacy thereby reducing the required dose. This review is an attempt to capture the non-dermatological applications of microneedles being explored and provides an insight on the future trends in the field of microneedle technology. Pictorial representation of different microneedle application.

Dual Solutions of MHD Stagnation Slip Flow Past a Permeable Plate

In this paper, dual solution to the problem of steady laminar magnetohydrodynamics boundary layer stagnation slip flow of the electrically conducting fluid over a permeable plate with suction effect is performed. The governing partial differential equations of the boundary layer are transformed into nonlinear ordinary differential equations via similarity transformations, and then numerically solved using the bvp4c method, which is the integrated algorithm of MATLAB. The effect of magnetic, slip and suction parameters on the skin friction coefficients and the velocity profiles and are presented in graphical form and discussed in detail. Dual solutions have been identified when suction is implied.

Micropolar couple stress thermofluidics and entropy in Forchheimer channel

AbstractThis paper presents an analysis of the entropy generated in thermofluidic configuration involving micropolar couple stress fluid flow inside a Forchheimer channel. The channel is composed of a porous medium trapped between two parallel permeable plates separated by distance H through which the fluid can be sucked out/injected in. One of the plate bears a constant temperature and other is subjected to a uniform heat flux. A Cartesian coordinate system is chosen to model the flow configuration. The nondimensional nonlinear governing equations are solved by the differential transform method and Runge–Kutta–Fehlberg method to ascertain the accuracy of the results. Both the methods do match to the order of 10−6 for the quantities velocity, microrotation, and temperature. These quantities and their gradients are required to the compute entropy generation number. The effects of the parameters on entropy generation and Bejan number are discussed through various plots.

Solving the boundary layer problems with buoyancy effect over a moving and permeable plate by a boundary shape function method

The steady boundary layer problems with buoyancy effect over a moving and permeable plate are studied in the present paper. By using the boundary layer approximations with similarity variables, we obtain coupled nonlinear velocity and temperature equations. Then, we derive boundary shape functions for velocity and temperature, which automatically satisfy the specified boundary conditions, including a convective boundary condition. Generally, numerical method is difficult to keep all the specific boundary conditions exactly and accurately. Because this will lead to the decline of the accuracy of numerical solution, we are motivated to develop a novel iterative algorithm which is based on the boundary shape functions. It transforms the nonlinear boundary layer problems into the initial value problems for new variables. The unknown terminal values of these variables can be determined by iteration, while the initial values of them can be arbitrarily given. The high-performance of the iterative boundary shape functions method (BSFM), which is convergent very fast, can be confirmed by numerical examples. The parametric studies in terms of the Grashof number, Prandtl number and Biot number with different suction/injection and velocity ratio values, as well as the flow instability area in terms of the Biot number and velocity ratio are carried out by the BSFM.

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.

Hydromagnetic Heat and Mass Transfer on a Permeable Flat Surface Embedded in a Porous Medium

The steady boundary layer viscous incompressible fluid flow on a permeable flat plate embedded in a porous medium has been considered in the present study. The momentum transport phenomena are subjected to external magnetic field, permeability of the porous medium and cross flow due to presence of suction and injection. Moreover, the heat transfer phenomena consider the loss of thermal energy due to radiation and mass transfer phenomena accounts for the generative/destructive chemical reaction of the reactive species as well. Most importantly, the temperature dependent viscosity and thermal conductivity of the fluid makes the present study more realistic. The numerical solution presented through graphs brings out the interesting outcomes: The higher rate of suction enhances the fluid temperature. This observation is akin to the fact that the higher suction brings the molecules closure hence the heat transfer increases. The porous medium, embedding the plate, acts as a coolant by reducing the fluid temperature.

Radiative Boundary Layer Flow of Casson Fluid Over an Exponentially Permeable Slippery Riga Plate with Viscous Dissipation

This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

Finite Difference Solution for MHD Flow Between Two Parallel Permeable Plates with Velocity Slip

The problem of Hydromagnetic steady laminar flow of an electrically conducting viscous incompressible fluid between parallel pates has been studied. The nonzero tangential slip velocity at the permeable boundary is considered. A numerical solution is derived for the governing nonlinear boundary value problem using a novel Keller box scheme. The effect of suction Reynold number , Hartman number and slip coefficient on derived quantities such as velocity filed and skin friction at the boundaries are analyzed. The physical significance of the flow parameters is also discussed.

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.

Cattaneo-Christov double diffusions (CCDD) in entropy optimized magnetized second grade nanofluid with variable thermal conductivity and mass diffusivity

In this research communication, mathematical model is developed to scrutinize the two-dimensional magnetohydrodynamic boundary layer flow of non-Newtonian nanofluid (second grade) toward a permeable and stretchable Riga plate surface. To examined the thermal and solutal relaxation characteristics the proposed model of Cattaneo-Christov double diffusions (CCDD) model is supposed. Furthermore, variable thermal conductivity and variable mass diffusivity are accounted. In addition, the convective condition of heat transfer is involved. The concept of entropy generation is also highlighted. Formulation also consists of thermal radiation, mixed convection and thermophoresis. The resulting problems are computed by modern approach known as optimal homotopy analysis method (OHAM). OHAM is a powerful method to used for the series solution of highly non-linear equations in comparison to other analytical and numerical methods. Total square residual error is computed. Velocity distribution enhances for second grade fluid parameter but reverse trend is seen for larger estimation of inverse Darcy number. Temperature profile increases for larger estimation of thermal relaxation parameter and characterize temperature (ɛ1). Nanoparticles concentration decays for boost values of solutal relaxation parameter and characterize concentration (ɛ2). Physical arguments for important parameters of interest are organized.

Effect of suction on the stagnation point flow of hybrid nanofluid toward a permeable and vertical Riga plate

AbstractThe application of appropriate wall mass suction (transpiration) has been reported as the key factor to generate steady solutions in the opposing flow (shrinking or opposing buoyancy). This study features the impact of the suction and mixed convection parameters in the stagnation point flow toward a permeable Riga plate. Due to the capability of hybrid nanofluids in enhancing the heat transfer performance, the combination of copper (Cu) and alumina (Al2O3) nanoparticles are used, including water as the base fluid. It appears that the dual solutions are potential in this problem with the negligence of the suction parameter. However, this transpiration effect is efficient in delaying the separation process of the hybrid nanofluid flow and enhancing the heat transfer rate. The heat transfer rate augments with the addition of and . The increment of heat transfer rate is reported between 34% and 39% when 30% of the suction parameter is applied. Besides, the addition of the mixed convection parameter from the opposing to assisting flow enlarges the velocity profile while reduces the temperature profile. The reduction of temperature distribution with an upsurge of suction, mixed convection, and EMHD parameters implies the operating heat transfer process.

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 , , , .