Permeable Stretching Sheet Research Articles

Unsteady Inclined MHD Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet with Zero Mass Flux and Slip Condition

Unsteady Inclined MHD Powell-Eyring Fluid with Microorganisms Over an Inclined Permeable Stretching Sheet with Zero Mass Flux and Slip Condition

Two-Dimensional Viscous, Steady, 2-D Nanofluid Flow Past a Permeable Stretching Sheet in Presence of Magnetic Field, Soret and Dufour Effects

Two-Dimensional Viscous, Steady, 2-D Nanofluid Flow Past a Permeable Stretching Sheet in Presence of Magnetic Field, Soret and Dufour Effects

Radiative Mixed Convection Flow of Casson Nanofluid through Exponentially Permeable Stretching Sheet with Internal Heat Generation

This paper investigates the mixed convection boundary-layer flow of Casson nanofluid with an internal heat source on an exponentially stretched sheet. The Buongiorno model, incorporating thermophoresis and Brownian motion, describes fluid temperature. The modeled system is solved numerically using bvp4c routine to analyze the impact of different fluid parameters on velocity, temperature, and concentration profiles. The analysis reveals that the suction effect, magnetic field, and Casson parameter reduce momentum boundary layer thickness and hence slow fluid motion. Conversely, buoyancy forces increase mass boundary layer thickness which results in accelerating fluid motion. Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.

Inclined Magnetic Field on Mixed Convection Darcy–Forchheimer Maxwell Nanofluid Flow Over a Permeable Stretching Sheet With Variable Thermal Conductivity: The Numerical Approach

The behavior of a Maxwell nanofluid in mixed convection Darcy–Forchheimer inclined MHD flow across a stretched sheet is investigated in this research study. In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. These ODEs are then solved using the shooting method and a fourth‐order Runge‐Kutta methodology. The study explores how fluid flow velocity is affected by magnetic field inclination and suction/injection effects. This is attributed to the strengthening of the magnetic field with an increase in the inclination angle α. Additionally, the imposed magnetic field generates an opposing force, known as the Lorentz force, which contributes to a reduction in the velocity curve. Furthermore, various parameters affect the profiles of concentration, temperature, velocity, and Nusselt number. A number of parameters are looked at, such as the response rate constant, mixed convection, buoyancy ratio, suction/injection, Brownian motion, Lewis number, and thermophoresis. Interestingly, the results show that activation energy and mixed convection parameters, respectively, have an increasing effect on concentration and velocity curves.

Flow And Heat Transfer of Unsteady Two-Phase Boundary Layer Flow Past an Inclined Permeable Stretching Sheet with Electrification of Particles

In the present study, an analysis has been carried out for a particle laden boundary layer flow with existence of electrification of particles has been studied over an inclined permeable stretching sheet. In most of the MHD fluid flow problems, either the plate is externally supplied by the magnetic/electric field or the fluid is electrically conducting. In the present problem, neither the plate is electrified nor the fluid is electrically conducted, but due to the random motion of the particles, collision of particle-particle and particle–wall, the particles are electrified. This electric field affects the fluid flow and heat transfer of the flow problem. Again, in the previous literatures, Buoyancy force is considered in momentum equations of fluid phase only. But in reality, both the phases are affected by the buoyancy force. For this reason, a reasonable mathematical model for two-phase buoyancy driven flow has been formulated with the consideration of electrification of particles in both fluid and particle phase. The governing system of PDEs are transferred to system of ODEs by applying similarity transformations and then computed by implementing Runga-Kutta method. The impact of electrification and other fluid parameters on flow and heat transfer has been studied. The results are represented through graphs and tables

Outlining the Slip Effects on MHD Casson Nanofluid Flow over a Permeable Stretching Sheet in the Existence of Variable Wall Thickness

Outlining the Slip Effects on MHD Casson Nanofluid Flow over a Permeable Stretching Sheet in the Existence of Variable Wall Thickness

Boundary Layer Flow of Williamson Hybrid Ferrofluid over A Permeable Stretching Sheet with Thermal Radiation Effects

This research investigated the convective boundary layer flow and heat transfer of Williamson hybrid ferrofluid over a permeable stretching sheet with thermal radiation effects. Human blood is employed as a based fluid while magnetite (Fe3O4) and copper (Cu) are taken as the hybrid ferroparticle. The study started with transforming the non-linear partial differential equation system that governed the model to a more convenience non-linear dimensionless ordinary differential equations using the similarity transformation. The transformed equations obtained then are solved numerically using the Runge-Kutta-Fehlberg (RKF45) method in Maple software. The characteristics and effects of stretching parameter, permeability parameter, thermal radiation parameter as well as the ferroparticle volume fraction in the Williamson hybrid ferrofluid towards the temperature profiles, velocity profiles as well as the Nusselt number and the skin friction coefficient are analysed and discussed. The result of this research for various pertinent parameter varies differently. It can be concluded that the increase in magnetic parameter, the Williamson parameter, the stretching parameter, and the permeability rate parameter increase the skin friction and reduced the velocity profile. Furthermore, the increase in stretching parameter, thermal radiation parameter and the permeability rate results to the increase in the Nusselt number.

The Effects of Thermal Radiation and Viscous Dissipation on the Stagnation Point Flow of a Micropolar Fluid over a Permeable Stretching Sheet in the Presence of Porous Dissipation

In this paper, the effects of thermal radiation and viscous dissipation on the stagnation–point flow of a micropolar fluid over a permeable stretching sheet with suction and injection are analyzed and discussed. A suitable similarity transformation is used to convert the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations, which are then solved numerically by a fourth–order Runge–Kutta method. It is found that the linear fluid velocity decreases with the enhancement of the porosity, boundary, and suction parameters. Conversely, it increases with the micropolar and injection parameters. The angular velocity grows with the boundary, porosity, and suction parameters, whereas it is reduced if the micropolar and injection parameters become larger. It is concluded that the thermal boundary layer extension increases with the injection parameter and decreases with the suction parameter.

Mathematical Study of MHD Micropolar Fluid Flow with Radiation and Dissipative Impacts over a Permeable Stretching Sheet: Slip Effects Phenomena

Mathematical Study of MHD Micropolar Fluid Flow with Radiation and Dissipative Impacts over a Permeable Stretching Sheet: Slip Effects Phenomena

Chemical Reaction Effects on of Nanofluid Past a Permeable Stretching Sheet with Slip Boundary Conditions and MHD Boundary Layer Flow

The overall exploration is excited to investigate the MHD limit layer float of a nanofluid with the results of attractive field, slip limit situation, warm radiation and synthetic reaction has been researched. Closeness change is utilized to change over the administering non-straight limit layer conditions into coupled better request non-direct normal differential conditions. those conditions are mathematically addressed utilizing fourth request R-k technique alongside shooting strategy. An assessment has been accomplished to explain the outcomes of overseeing boundaries like assorted materially conditions. Mathematical results are gotten for the speed, temperature and mindfulness, as well as, for the pores and skin rubbing, close by Nusselt reach and neighborhood Sherwood range for a few benefits of overseeing boundaries. The mathematical results are talked about through graphically and referenced subjectively.

Unsteady MHD Williamson Fluid Flow with the Effect of Bioconvection over Permeable Stretching Sheet

The unsteady flow of Williamson fluid with the effect of bioconvection in the heat and mass transfer occurring over a stretching sheet is investigated. A uniform magnetic field, thermal radiation, thermal dissipation, and chemical reactions are taken into account as additional effects. The physical problem is formulated in the form of a system of partial differential equations and solved numerically. For this purpose, similarity functions are involved to transmute these equations into corresponding ordinary differential equations. After that, the Runge-Kutta method with shooting technique is employed to evaluate the desired findings with the utilization of a MATLAB script. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. The parameters of Brownian motion and thermophoresis are responsible for the rise in temperature and bioconvection Rayleigh number diminishes the velocity field. This study on nanofluid bioconvection has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.

Study of Unsteady Two Phase Flow over An Inclined Permeable Stretching Sheet with Effects of Electrification and Radiation

An analysis on flow and heat transfer with in a two-dimensional unsteady radiative boundary layer with fluid-particle interaction has been studied. The flow is occurred due to the suddenly linear movement of an inclined permeable stretching sheet. The flow is considered in a neutral medium where no external electric or magnetic field is supplied. But due to the random motion of particles leads to interaction between fluid-particle, particle-particle and particle-wall, a tribo-electric effect occurs. As a result, both the fluid as well as particles are electrified which creates a major impact on flow field. Hence, a balanced mathematical model has been formulated considering both electrification and radiation parameter on both the phases. Using similarity transformation, the governing equations are transferred to ODEs and solved by built in solver Bvp4c of MATLAB. The impacts of various parameters on the flow field have been discussed and determined the heat transfer characteristics. The stronger electric filed significantly enhances the temperature of both fluid and particle phase, which occurs more heat transfer on the surface.

Thermally Radiant Williamson Nanofluid Flow Over a Permeable Stretching Sheet with Viscous Dissipation and Joule Heating Effects

The present paper focuses on the study of an incompressible flow of a steady two-dimensional electrically conducting thermally radiant Williamson nanofluid over a permeable stretching sheet with viscous dissipation and joule heating effects. The governing partial differential equations are reduced to a couple of nonlinear ordinary differential equations by using suitable transformation equations; these equations are then solved numerically with the use of the conventional fourth-order Runge Kutta method accompanied by the shooting technique. Graphical results of the flow, temperature, and nanoparticles volume fraction profiles are displayed. Effects of the physical parameters on velocity, temperature, nanoparticles volume fraction, skin friction coefficient, and the rates of heat and mass transfer are investigated. The results indicate that the velocity ratio parameter enhances the skin friction coefficient, the velocity profile, and the rate of heat transfer whereas it minimizes the rate of mass transfer. On the other hand, increasing the values of the mass suction parameter results in both the velocity and the temperature boundary layer thickness decrease whereas increasing the mass injection enhances both the velocity and the temperature profiles; but it vigorously enhances the rate of heat transfer. The non-Newtonian parameter fosters the rate of heat transfer whereas it lessens both the velocity and rate of mass transfer of the nanofluid.

Unsteady Heat and Mass Transfer Slip Flow over an Exponentially Permeable Stretching Sheet

In this paper, the problem of unsteady two-dimensional boundary layer heat and mass transfer flow over an exponentially stretching sheet embedded in a porous medium in the presence of a uniform magnetic field with thermal radiation, heat generation/absorption, and suction/blowing is analyzed numerically. Instead of no-slip boundary conditions, velocity slip, thermal slip, and mass slips at the boundary are considered. Using a suitable similarity transformation, the governing partial differential equations are transformed to a system coupled with nonlinear ordinary differential equations. The reduced equations are solved numerically by using bvp4c with the MATLAB package. A detailed parametric study is performed to illustrate the physical parameters on the velocity, temperature, and concentration profile and the local skin-friction coefficient and Nusselt and Sherwood number. Then the results are exhibited in both graphical and tabular forms. It is observed that the present results have been in close agreement with the previously published studies under some special cases.

Effect of Non-Linear Thermal Radiation and Partial slip on Unsteady MHD Flow of a Nanofluid Past a Permeable Stretching Sheet through a Porous Medium with Suction/Injection, convective Heat Transfer

We discuss the effect of non-linear thermal radiation on the boundary layer flow of a thermophoretic magnetohydrodynamics dissipative nanofluid over an unsteady stretching sheet in a porous medium with space and temperature dependent internal heat source/sink. The governing equations are transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using the Shooting Technique. The effects of non-dimensional governing parameters on the velocity, temperature, concentration profiles, friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. We observed that the Radiation parameter (Rd) to enhance the velocity, temperature profiles, heat and mass transfer rates of the fluid and reduce the concentration profiles. An increase in slip parameter (A11), reduces the velocity, enhances the temperature and nano-concentration., Nu and Sh reduce with increasing Rd & A11 on =0. Accuracy of the results compared with the existing ones. Excellent agreement is found with earlier studies.

Analysis of Entropy Generation in Hydromagnetic Micropolar Fluid Flow over an Inclined Nonlinear Permeable Stretching Sheet with Variable Viscosity

A numerical analysis is performed on entropy generation in a radiative and dissipative hydromagnetic micropolar fluid prompted by a nonlinearly stretching sheet with the impact of non-uniform heat source/sink, variable magnetic field, electrical conductivity, and dynamic viscosity. The main equations are computationally solved via shooting techniques in the company with Runge-Kutta algorithms. The impact of the prominent controlling parameters is graphically checked on the velocity, temperature, microrotation, entropy generation, and Bejan number. An excellent relationship exists between the results obtained with related studies previously reported in the literature in the limiting conditions. More so, it is revealed by the findings that the irreversibility due to heat transfer is dominant over viscous dissipation irreversibility as the radiation parameter advances while the trend changes with the Brikman number parameter.

A Study of MHD Casson Fluid Flow over a Permeable Stretching Sheet with Heat and Mass Transfer

In this paper, we study the numerical approach of MHD Casson fluid flow over a permeable stretching sheet with heat and mass transfer taking into cognizance the various parameters present. A set of suitable local similarity transformations are used to non-dimensionalize the governing equations of the present problem. The system of ordinary differential equations are solved numerically by MATLAB bvp4c solver. The effect of the involved parameters on Velocity, Temperature, and Concentration, Skin friction coefficient, Nusselt number and Sherwood number has been studied and numerical results are presented graphically and in tabular form. The numerical results are in good agreement with those of the results previously published in the literature.

Analytical and Numerical Investigation of Second Grade Magnetohydrodynamics Flow over a Permeable Stretching Sheet

In this paper, the steady laminar boundary layer flow of non-Newtonian second grade conducting fluid past a permeable stretching sheet, under the influence of a uniform magnetic field is studied. Three different methods are applied for solving the problem; numerical Finite Element Method (FEM), analytical Collocation Method (CM) and 4th order Runge-Kutta numerical method. The FlexPDE software package is used for modeling and solving the problem by FEM. In most new analytical methods used for solving nonlinear equations, it is impossible to solve problems with infinity boundary conditions. In this article by using a special technique, the infinity boundary condition transformed to a finite one, then the governing equation solved analytically. In the physical aspect, the effects of the non-Newtonian, magnetic and permeability parameters on the velocity distribution have been investigated. As a result, the present suggested technique can be used for the analytical solution of many such problems with infinite boundary conditions. Moreover, the comparison between the results obtained from our modified analytical method and numerical solutions shows an excellent agreement.

Outcome of Nanofluid Flow Containing Arbitrary Shape Nanoparticles Induced by a Permeable Stretching Sheet

In this work we have discussed the impact of thermal radiation on heat transfer to nanofluid flow over an unsteady permeable stretching sheet using various types of arbitrary shape nanoparticles of Copper (Cu), Silver (Ag), Alumina (Al<sub>2</sub>O<sub>3</sub>), and Titania Oxide (TiO<sub>2</sub>) in the base fluid. Suitable transformations have been employed to build ODEs from the partial differential equations. Numerical results are therefore obtained particularly for cylindrical shape and spherical shape nanoparticles. Our analysis substantiates that the velocity and temperature profiles increases with enhanced thermal radiation parameter. Further, Nusselt number is more advanced for the nanofluid that contains cylindrical shape nanoparticles as compared to spherical shape nanoparticles.

Finite Element Simulation of Multiple Slip Effects on MHD Unsteady Maxwell Nanofluid Flow over a Permeable Stretching Sheet with Radiation and Thermo-Diffusion in the Presence of Chemical Reaction

The aim of the present study is to investigate the multiple slip effects on magnetohydrodynamic unsteady Maxwell nanofluid flow over a permeable stretching sheet with thermal radiation and thermo-diffusion in the presence of chemical reaction. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations with the aid of appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The effects of various physical parameters on the velocity, temperature, solutal concentration, and nanoparticle concentration profiles as well as on the skin friction coefficient, rate of heat transfer, and Sherwood number for solutal concentration are discussed by the aid of graphs and tables. An exact solution of flow velocity, skin friction coefficient, and Nusselt number is compared with the numerical solution obtained by FEM and also with numerical results available in the literature. A good agreement between the exact and numerical solution is observed. Also, to justify the convergence of the finite element numerical solution, the calculations are carried out by reducing the mesh size. The present investigation is relevant to high-temperature nanomaterial processing technology.