The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
International Journal of Computational Engineering Research(IJCER)ijceronline
The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
Melting Heat Transfer in MHD Boundary Layer Stagnation-Point Flow towards a S...iosrjce
An analysis is carried out to study the MHD steady two-dimensional stagnation-point flow and heat transfer from
a warm, laminar liquid flow to a melting stretching sheet. The governing partial differential equations are transformed into
ordinary differential equations by similarity transformation, before being solved numerically using Runge-Kutta-Fehlberg
method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are
presented for different values of the governing parameters. Effects of the Magnetic parameter, melting parameter, stretching
parameter and prandtl number on the flow and heat transfer characteristics are thoroughly examined.
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
International Journal of Computational Engineering Research(IJCER)ijceronline
The document summarizes a study on the effect of thermal radiation on boundary layer flow of a second-grade fluid over a stretching sheet through a porous medium, where the fluid's viscosity and thermal conductivity are temperature dependent. The governing equations are non-dimensionalized using similarity transformations and then solved numerically. Results show the effects of various parameters like radiation, viscosity, thermal conductivity, and porosity on the fluid's velocity and temperature profiles, as well as the skin friction coefficient and Nusselt number.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document summarizes a study that examines heat and mass transfer over a vertical plate in a porous medium with Soret and Dufour effects, a convective surface boundary condition, chemical reaction, and magnetic field. The governing equations for the fluid flow, heat transfer, and mass transfer are presented. Similarity solutions are used to transform the governing partial differential equations into ordinary differential equations, which are then solved numerically. The results are presented graphically to show the influence of various parameters on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number.
Melting Heat Transfer in MHD Boundary Layer Stagnation-Point Flow towards a S...iosrjce
An analysis is carried out to study the MHD steady two-dimensional stagnation-point flow and heat transfer from
a warm, laminar liquid flow to a melting stretching sheet. The governing partial differential equations are transformed into
ordinary differential equations by similarity transformation, before being solved numerically using Runge-Kutta-Fehlberg
method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are
presented for different values of the governing parameters. Effects of the Magnetic parameter, melting parameter, stretching
parameter and prandtl number on the flow and heat transfer characteristics are thoroughly examined.
This document summarizes a study on the effects of radiation on magnetohydrodynamic (MHD) free convection flow of a viscous fluid past an exponentially accelerated vertical plate. The governing equations are solved numerically using an implicit finite difference Crank-Nicolson method. It is found that the fluid velocity decreases with increasing magnetic field or radiation parameter. Fluid temperature also decreases with stronger radiation. Shear stress and heat transfer at the plate increase and decrease, respectively, with higher radiation or magnetic parameters.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
This document presents a mathematical analysis of unsteady free convection flow along a porous vertical plate with constant heat and mass flux in a rotating system. The analysis considers the effects of heat source and thermal diffusion. Perturbation technique is used to obtain expressions for velocity, temperature, concentration profiles, skin friction, and Nusselt number. Key findings include that increasing Schmidt number decreases skin friction, increasing Grashoff number increases skin friction, and increasing Prandtl number decreases Nusselt number. Graphs and tables are used to discuss the effects of various parameters on flow variables.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a study on mixed convective heat and mass transfer flow of a visco-elastic fluid over a stretching sheet. The study considers the effects of chemical reaction, temperature gradient dependent heat sink, and magnetic field. The governing equations for momentum, energy and diffusion are presented and non-linear similarity transformations are applied to reduce the equations to an ordinary differential equation system. The system is solved numerically using a Runge-Kutta method with shooting techniques to determine skin friction coefficient, Nusselt number, and Sherwood number.
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
OSCILLATORY FLOW OF MHD POLAR FLUID WITH HEAT AND MASS TRANSFER PAST A VERTIC...IAEME Publication
The study of unsteady two-dimensional laminar boundary layer flow of a viscous incompressible fluid (polar fluid) through porous medium past a semi-infinite vertical porous stretching plate in the presence of transverse magnetic field is investigated.
The sheet makes with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. A uniform magnetic field acts perpendicularly to the porous sheet which absorbs the polar fluid with a suction velocity varying with time component. The effects of all parameters encountering in the problem are investigated for velocity and temperature fields across the boundary layer.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
Unsteady Free Convection MHD Flow of an Incompressible Electrically Conductin...IJERA Editor
In this paper we investigate unsteady free convection MHD flow of an incompressible viscous electrically
conducting fluid through porous medium under the influence of uniform transverse magnetic field between two
heated vertical plate with one plate is adiabatic. The governing equations of velocity and temperature fields with
appropriate boundary conditions are solved by the Integral Transform Technique. The obtained results of
velocity and temperature distributions are shown graphically and are discussed on the basis of it. The effects of
Hartmann number, Darcy parameter, Prandtl number and the decay factor, and effects of adiabatic plate on the
velocity and temperature fields are discussed.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
This document summarizes numerical analysis of unsteady magnetohydrodynamic (MHD) free convective flow in a rotating system with Dufour and Soret effects. The analysis considers flow through a porous medium along an infinite vertical porous plate. Similarity transformations are used to reduce the governing equations to ordinary differential equations, which are then solved numerically. The effects of varying parameters like the Prandtl number and Dufour number on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are discussed based on graphs of the numerical solutions. Increasing the Prandtl number decreases velocity and temperature but increases concentration, while increasing the Dufour number decreases velocity, temperature,
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
Effects of Variable Viscosity and Thermal Conductivity on MHD Free Convection...IRJET Journal
This document summarizes a numerical study that examines the effects of temperature dependent viscosity and thermal conductivity on the steady, laminar boundary layer flow of a dusty fluid near a vertically stretching sheet. The study considers magnetohydrodynamic (MHD) free convection flow with heat generation. The governing nonlinear partial differential equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. Results for velocity, temperature, species concentration, and skin friction, Nusselt, and Sherwood numbers are obtained and analyzed for various physical parameters, providing insights into heat and mass transfer with practical applications in industries like material processing and manufacturing.
Radiation Effects on MHD Free Convective Rotating Flow with Hall EffectsIJERA Editor
In this paper, we have studied the unsteady an incompressible MHD rotating free convection flow of Viscoelastic fluid through a porous medium with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field. The governing equations of the flow field are solved by a regular perturbation method for small elastic parameter. The expressions for the velocity, temperature, concentration have been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction, the Nusselt number and the Sherwood number are also obtained and their behaviour discussed.
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter . the effects of governing parameters on the flow variables are discussed graphically.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter . the effects of governing parameters on the flow variables are discussed graphically.
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
This document summarizes a study on thermal radiation effects on magnetohydrodynamic (MHD) free convection flow of a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The governing equations for momentum, angular momentum, and energy are solved numerically. Key findings include:
1) The micropolar fluid model helps reduce drag forces and acts as a cooling agent compared to classical fluids.
2) Parameters like the Darcy number, radiation, magnetic field, and porous medium properties influence the velocity, microrotation, temperature, skin friction, and heat transfer.
3) Increased microrotation constant and coupling constant reduce skin friction but increase heat transfer.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document summarizes a study on mixed convective heat and mass transfer flow of a visco-elastic fluid over a stretching sheet. The study considers the effects of chemical reaction, temperature gradient dependent heat sink, and magnetic field. The governing equations for momentum, energy and diffusion are presented and non-linear similarity transformations are applied to reduce the equations to an ordinary differential equation system. The system is solved numerically using a Runge-Kutta method with shooting techniques to determine skin friction coefficient, Nusselt number, and Sherwood number.
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
This document summarizes a research paper that examines the steady magnetohydrodynamic mass transfer flow of a polar fluid through a porous medium bounded by an infinite vertical porous plate. The paper presents the governing equations for the fluid flow, angular momentum, energy, and concentration considering effects such as magnetic field, thermal diffusion, and radiation. Exact solutions for the velocity, angular velocity, temperature, and concentration fields are obtained. The skin friction and heat transfer rate are also derived. Graphs illustrate the effects of various parameters on the flow behavior and transport properties.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
OSCILLATORY FLOW OF MHD POLAR FLUID WITH HEAT AND MASS TRANSFER PAST A VERTIC...IAEME Publication
The study of unsteady two-dimensional laminar boundary layer flow of a viscous incompressible fluid (polar fluid) through porous medium past a semi-infinite vertical porous stretching plate in the presence of transverse magnetic field is investigated.
The sheet makes with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially increasing or decreasing small perturbation law. A uniform magnetic field acts perpendicularly to the porous sheet which absorbs the polar fluid with a suction velocity varying with time component. The effects of all parameters encountering in the problem are investigated for velocity and temperature fields across the boundary layer.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Chemical reaction and radiation effect on mhd flow past an exponentially acce...Alexander Decker
This document describes a mathematical analysis of MHD fluid flow past an exponentially accelerated vertical plate embedded in a porous medium. The analysis considers the effects of variable temperature, mass diffusion, radiation, and a heat source on the flow characteristics. The governing equations for this problem are derived and non-dimensionalized. The non-dimensional equations are then solved using the Laplace transform technique. The effects of various physical parameters like the magnetic field, radiation, heat generation, and chemical reaction on the velocity, temperature, and concentration profiles are determined.
Unsteady Free Convection MHD Flow of an Incompressible Electrically Conductin...IJERA Editor
In this paper we investigate unsteady free convection MHD flow of an incompressible viscous electrically
conducting fluid through porous medium under the influence of uniform transverse magnetic field between two
heated vertical plate with one plate is adiabatic. The governing equations of velocity and temperature fields with
appropriate boundary conditions are solved by the Integral Transform Technique. The obtained results of
velocity and temperature distributions are shown graphically and are discussed on the basis of it. The effects of
Hartmann number, Darcy parameter, Prandtl number and the decay factor, and effects of adiabatic plate on the
velocity and temperature fields are discussed.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
This document summarizes numerical analysis of unsteady magnetohydrodynamic (MHD) free convective flow in a rotating system with Dufour and Soret effects. The analysis considers flow through a porous medium along an infinite vertical porous plate. Similarity transformations are used to reduce the governing equations to ordinary differential equations, which are then solved numerically. The effects of varying parameters like the Prandtl number and Dufour number on velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number are discussed based on graphs of the numerical solutions. Increasing the Prandtl number decreases velocity and temperature but increases concentration, while increasing the Dufour number decreases velocity, temperature,
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
Effects of Variable Viscosity and Thermal Conductivity on MHD Free Convection...IRJET Journal
This document summarizes a numerical study that examines the effects of temperature dependent viscosity and thermal conductivity on the steady, laminar boundary layer flow of a dusty fluid near a vertically stretching sheet. The study considers magnetohydrodynamic (MHD) free convection flow with heat generation. The governing nonlinear partial differential equations are reduced to ordinary differential equations using similarity transformations and then solved numerically using a shooting method. Results for velocity, temperature, species concentration, and skin friction, Nusselt, and Sherwood numbers are obtained and analyzed for various physical parameters, providing insights into heat and mass transfer with practical applications in industries like material processing and manufacturing.
Radiation Effects on MHD Free Convective Rotating Flow with Hall EffectsIJERA Editor
In this paper, we have studied the unsteady an incompressible MHD rotating free convection flow of Viscoelastic fluid through a porous medium with simultaneous heat and mass transfer near an infinite vertical oscillating porous plate under the influence of uniform transverse magnetic field. The governing equations of the flow field are solved by a regular perturbation method for small elastic parameter. The expressions for the velocity, temperature, concentration have been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters with the help of graphs. The skin friction, the Nusselt number and the Sherwood number are also obtained and their behaviour discussed.
Effects of conduction on magneto hydrodynamics mixed convection flow in trian...Alexander Decker
This document summarizes research on magnetohydrodynamic (MHD) mixed convection flow in triangular enclosures. Key points:
1) The study investigates the effects of conduction on MHD mixed convection flow in triangular enclosures using a finite element method.
2) Parameters like the Hartmann number, Prandtl number, Reynolds number, and Rayleigh number are found to strongly influence the flow and thermal fields.
3) Validation of the numerical code is done by comparing average Nusselt numbers to previous research on natural convection in triangular enclosures.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter . the effects of governing parameters on the flow variables are discussed graphically.
Soret Effect And Effect Of Radiation On Transient Mhd Free Convective Flow Ov...inventionjournals
The present paper is concerned to analyze the radiation, Magneto hydrodynamic and soret effects on unsteady flow heat and mass transfer characteristics in a viscous, incompressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media the porous plate is subjected to a transverse variable suction velocity. The transient, non linear and coupled dimensionless governing equations for this investigation are solved analytically using perturbation technique about a small parameter . the effects of governing parameters on the flow variables are discussed graphically.
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
This document summarizes a study on thermal radiation effects on magnetohydrodynamic (MHD) free convection flow of a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The governing equations for momentum, angular momentum, and energy are solved numerically. Key findings include:
1) The micropolar fluid model helps reduce drag forces and acts as a cooling agent compared to classical fluids.
2) Parameters like the Darcy number, radiation, magnetic field, and porous medium properties influence the velocity, microrotation, temperature, skin friction, and heat transfer.
3) Increased microrotation constant and coupling constant reduce skin friction but increase heat transfer.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
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nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
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International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
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Slip Flow and Magneto-NANOFLUID over an Exponentially Stretching Permeable Sheet with Heat Generation/Absorption
1. International Journal of Engineering Inventions
e-ISSN: 2278-7461, p-ISSN: 2319-6491
Volume 3, Issue 9 (April 2014) PP: 47-60
www.ijeijournal.com Page | 47
Slip Flow and Magneto-NANOFLUID over an Exponentially
Stretching Permeable Sheet with Heat Generation/Absorption
Thommaandru RangaRao1
, Kotha Gangadhar2
, B.Hema Sundar Raju3
,
M. Venkata Subba Rao4
1
Department of Mathematics, SVKP College, Markapur, Prakasam DT-523316, India
2
Department of Mathematics, Acharya Nagarjuna University, Ongole, Andhra Pradesh -523001, India
3, 4
Department of Mathematics, Vignan University, Guntur, Andhra Pradesh-522213, India
Abstract: The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an
exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian
motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting
technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals
that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number,
the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and
thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume
fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
Keywords: MHD, nanoparticle, slip flow, heat transfer, heat generation/absorption.
I. Introduction
Among the tasks facing by the engineer is the development of ultrahigh-performance cooling in many
industrial technologies. This is where nanotechnology takes important part for further development of high
performance, compact, cost-effective liquid cooling systems. Other than that, nanofluids have effective
applications in many industries such as electronics, transportation, biomedical and many more [1].
Nanotechnology has been an ongoing topic of discussion in public health as some of the researchers claimed
that nanoparticles could present possible dangers in health and environment [2]. Hamid et al.[3] studied the
problem of two-dimensional laminar Marangoni-driven boundary layer flow in nanofluids with the effects of
radiation. Three different types of nanoparticles, namely Cu, Al2O3, and TiO2 are considered.
During the last many years, the study of boundary layer flow and heat transfer over a stretching surface
has achieved a lot of success because of its large number of applications in industry and technology. Few of
these applications are materials manufactured by polymer extrusion, drawing of copper wires, continuous
stretching of plastic films, artificial fibers, hot rolling, wire drawing, glass fiber, metal extrusion and metal
spinning etc. After the pioneering work by Sakiadis [4], a large amount of literature is available on boundary
layer flow of Newtonian and non-Newtonian fluids over linear and nonlinear stretching surfaces [5-10]. Nadeem
and Lee [11] investigated the steady boundary layer flow of nanofluid over an exponential stretching surface is
investigated analytically.
Magnetohydrodynamics (MHD) boundary-layer flow of nanofluid and heat transfer over a linearly
stretched surface have received a lot of attention in the field of several industrial, scientific, and engineering
applications in recent years. Nanofluids have many applications in the industries since materials of nanometer
size have unique chemical and physical properties. With regard to the sundry applications of nanofluids, the
cooling applications of nanofluids include silicon mirror cooling, electronics cooling, vehicle cooling,
transformer cooling, etc. This study is more important in industries such as hot rolling, melt spinning, extrusion,
glass fiber production, wire drawing, and manufacture of plastic and rubber sheets, polymer sheet and filaments,
etc. Khan et al. [12] studied the Unsteady MHD free convection boundary-layer flow of a nanofluid along a
stretching sheet with thermal radiation and viscous dissipation effects using finite difference method. Liu [13]
investigated the flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet
subject to a transverse magnetic field. Khan et al. [14] studied the viscoelastic MHD flow, heat and mass
transfer over a porous stretching sheet with dissipation of energy and stress work.
An effect of viscous dissipation and work done by deformation on the MHD flow and heat transfer of a
viscoelastic fluid over a stretching sheet was investigated by Cortell [15].Bhattacharyya [16] analyzes the
boundary layer flow and heat transfer caused due to an exponentially shrinking sheet and Bhattacharyya and
Pop [17] show the effect of external magnetic field on the flow over an exponentially shrinking sheet. Recently,
Bhattacharyya and Layek [18] investigated the magnetohydrodynamic boundary layer flow of nanofluid over an
exponentially stretching permeable sheet.
2. Slip Flow And Magneto-Nanofluid Over An Exponentially Stretching Permeable Sheet With Heat
www.ijeijournal.com Page | 48
The transient oscillatory MHD convection past a flat plate adjacent to a porous medium with heat
generation effects was solved in [19] and transient MHD natural convection with viscous heating was
considered by Zueco [20]. Recently the effects of variable suction and thermophoresis on steady MHD flow
over a permeable inclined plate was analyzed by Alam et al. [21] while the heat and mass transfer of
thermophoretic hydromagnetic flow with lateral mass flux, heat source, Reddy et al.[22] investigated the thermo
diffusion and chemical reaction effects on unsteady free mhd convection flow past a vertical porous plate in
slip-flow regime using perturbation technique.
However, the interactions of magneto-nanofluid due to an exponentially permeable stretching sheet in
the presence of heat generation/absorption and slip effects. The governing boundary layer equations have been
transformed to a two-point boundary value problem in similarity variables and the resultant problem is solved
numerically using the fourth order Runge-Kutta method along with shooting technique. The effects of various
governing parameters on the fluid velocity, temperature, nanoparticle volume friction, local Nusselt number and
local Sherwood number are shown in figures and analyzed in detail.
II. Mathematical Formulation
Consider the steady boundary layer flow of nanofluid over an exponentially stretching sheet in
presence of a transverse magnetic field. The governing equations of motion and the energy equation may be
written in usual notation as [18, 23, 24]
Continuity equation
0
u v
x y
(2.1)
Momentum equation
2 2
2
f
u u u B
u v u
x y y
(2.2)
Energy equation
22
2
p T
B
f
cT T T N T D T
u v D q T T
x y y c y y T y
(2.3)
Volumetric species equation
2 2
2 2
T
B
N N N D T
u v D
x y y T y
(2.4)
The boundary conditions are
2 2
0 0, , ,
x x
L L
w w w w
u
u U L v v T T T T e N N N N e
y
at 0y
0, ,u T T N N as y (2.5)
Where u and v are the velocity components in x and y directions, respectively, is kinematic viscosity and
is thermal conductivity. f is density of the base fluid, f
c and p
c are heat capacities of base fluid
and nanoparticles, respectively, T is temperature, q is heat generation/absorption rate constant, DB is Brownian
diffusion coefficient, N is nanoparticle volumetric fraction, DT is thermophoretic diffusion coefficient and T is
the ambient fluid temperature. wT is the variable temperature at the sheet with 0T being a constant which
measures the rate of temperature increase along the sheet, wN is the variable wall nanoparticle volume fraction
with 0N being a constant, and N is constant nanoparticle volume fraction in free stream.
3. Slip Flow And Magneto-Nanofluid Over An Exponentially Stretching Permeable Sheet With Heat
www.ijeijournal.com Page | 49
Here the variable magnetic field B(x) is taken the form [17, 25]
2
0( )
x
L
B x B e (2.6)
Where B0 is the constant.
The stretching velocity wU is given by
( )
x
L
wU x ce (2.7)
where 0c is stretching constant. A physical model with the coordinate system of the problem is sketched in
Fig. A.
Here wv is the variable wall mass transfer velocity and is given by
2
0( )
x
L
wv x v e (2.8)
where 0v is a constant with 0 0v formass suction and 0 0v for mass injection.
The continuity equation (2.1) is satisfied by the Cauchy Riemann equations
u
y
and
v
x
(2.9)
where ( , )x y is the stream function.
In order to transform the equations (2.2) to (2.5) into a set of ordinary differential equations, the following
similarity transformations and dimensionless variables are introduced.
2 2
2
/0
0
2 ,
2
( ) , ( )
2 2
Pr , , , ,
( ) ( )
,
x x
L L
w w
x L
B
B w T wp p
f f
c
Lc f e y e
L
T T N N
T T N N
L B qL
Le M q q e
D c c
D c N N D c T T
Nb Nt
c T c
(2.10)
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where ( )f is the dimensionless stream function, θ - the dimensionless temperature, - the dimensionless
nanoparticle volume fraction, η - the similarity variable, M - the magnetic parameter, Le - the Lewis number,
Nb - the Brownian motion parameter, Nt - the thermophoresis parameter, Pr - the Prandtl number..
In view of the equation (2.10), the equations (2.2) to (2.6) transform into
2
''' '' 2 ' ' 0f ff f Mf (2.11)
2
" Pr( ' ' ' ' ' ) 0f f Nb Nt (2.12)
" ( ' ' ) '' 0
Nt
Le f f
Nb
(2.13)
The transformed boundary conditions can be written as
, ' 1 ''(0), 1, 1f S f f at 0
' 0, 0, 0f as (2.14)
where 0 / / 2S v c L is the wall mass transfer parameter. 00( 0)S v corresponds to mass suction
and 00( 0)S v corresponds to mass injection and
2
cL
is the slip parameter.
Physical quantities of interest are Local skin friction coefficient fC , Local Nusselt number Nu and Local
Sherwood number Sh , defined as [24]
2 2 /
0 0 0
, ,f x L
w w wy y y
u x T x N
C Nu Sh
U e y T T y N N y
(2.15)
or by introducing the transformations (2.10), we have
2Re ''(0), ' 0 , ' 0
2 22Re Re
x f
x x
Nu x Sh x
C f
L L
(2.16)
Where Re w
x
U x
is the local Reynolds number
III. Solution Of The Problem
The highly nonlinear coupled ODEs (2.11-2.13) along with the boundary conditions (2.14) form a two-
point boundary value problem (BVP) and those are solved using shooting method [26–27]. The following first-
order system is set:
2
2
' , '
' 2
'
' ( )
'
' ( ) '
f p p q
q p fq Mp
r
r pr fr p Nbrz Ntr
z
Nt
z le fz p r
Nb
(3.1)
with the boundary conditions
(0) , (0) 1 (0), (0) 1, (0) 1f S p q (3.2)
The set of nonlinear first-order ordinary differential equations (3.1) with boundary conditions (3.2) have been
solved by shooting method using the fourth-order Runge-Kutta algorithm with a systematic guessing of (0)q ,
that is, ''(0)f , (0)r , that is, '(0) , and 𝑧(0), that is, '(0) . The step size is taken as Δ𝜂 = 0.01 and the
suitable finite value of 𝜂 → ∞, , is taken as 30 in all cases. The guess values ''(0)f , '(0) , and '(0) are
adjusted using “secant method” to give better approximation for the solution. An asymptotic convergence
criterion of
5
10
level for the boundary conditions '( )f , ( ), ( ) is taken in the computation.
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IV. Results And Discussion
In order to get a clear insight of the physical problem, the velocity, temperature and nanoparticle
volume friction have been discussed by assigning numerical values to the governing parameters encountered in
the problem. Numerical computations are shown from figs.1-13.
The velocity, temperature and nanoparticle volume friction are plotted in Fig. 1(a)-(c) for different
values of the magnetic field parameter (M). As is now well known, the velocity of the fluid decreases with
increases in the magnetic field parameter due to an increase in the Lorentz drag force that opposes the fluid
motion. Also noticed that temperature and nanoparticle volume friction increases with an increasing the
magnetic parameter. Figs. 2(a)-(c) shows the effect of the mass suction parameter on the velocity, temperature
and mass volume fraction profiles. It is observed that the velocity, temperature and concentration of the fluid
decrease with an increase the mass suction parameter. Due to mass suction, the fluid is brought closer to the
sheet and it thins velocity boundary layer thickness as well as the thermal and nanoparticle volume boundary
layer thicknesses. Opposite effect is found for mass injection case; that is, the fluid is taken away from the sheet.
Consequently, the velocity, thermal, and nanoparticle volume boundary layer thicknesses become broader. Figs.
3(a)-(c) shows the effect of the slip parameter on the velocity, temperature and mass volume fraction profiles. It
is observed that the velocity of the fluid decreases with an increase the slip parameter and temperature of the
fluid as well as mass volume friction of the fluid increases the slip parameter.
The effect of thermophoresis parameter on temperature and mass volume friction is shown in figs. 4(a)
& (b). An increase in Nt the temperature of the fluid is increases as well as mass volume friction. The effect of
Brownian motion parameter Nb on the dimensionless temperature and the dimensionless nanoparticle volume
fraction is plotted in Figure 5(a) & 5(b). The figure reveals that the temperature of the fluid increases and the
nanoparticle volume fraction decreases with increasing values of Nb. In nanofluid system, due to the presence of
nanoparticles, the Brownian motion takes place and for the increase in Nb the Brownianmotion is affected and
consequently the heat transfer characteristic of the fluid changes. Also, when the value of Nb increases, the
nanoparticle volume boundary layer thickness decreases. The effect of heat generation/absorption parameter on
the dimensionless temperature and the dimensionless nanoparticle volume fraction is plotted in Figure 6(a) &
6(b). The figure reveals that the temperature and the nanoparticle volume fraction with increasing values of heat
generation/absorption. The effect of the Prandtl number (Pr) on temperature is shown in fig.7. Since the Prandtl
number is the ratio of momentum diffusivity to the nanofluid thermal diffusivity. It is noticed that temperature
of the fluid decreases with an increases the Prandtl number. From fig. 8 show that the effect of Lewis number
(Le) on temperature. Since Lewis number is the ratio of nanoparticle thermal diffusivity to Brownian diffusivity.
It is observe that the temperature of the fluid decreases with an increase in the Lewis number.
Fig.9 shows the effects of S, γ, and M on skin friction. From fig.9 it is seen that the skin friction
increases with an increase M or S and decrease with an increase γ. The variations of S, γ and M on reduced
Nusselt number is shown in fig.10. It is observed that the reduced Nusselt number increases with an increase the
parameter S and decrease with an increasing the parameters γ or M. The effect of S, γ and M on Sherwood
number is shown in fig.11. It is found that the Sherwood number enhances with a decrease in the parameters γ or
M whereas increases with S. The variations of Nt and Nb on reduced Nusselt number is shown in fig.12. It is
observed that the reduced Nusselt number decrease with an increasing the parameters Nt or Nb. The effect of Nt
and Nb on Sherwood number is shown in fig.13. It is found that the Sherwood number enhances with a increase
in the parameter Nb whereas decreases with Nt. Table 1 is shows to compare our results for the viscous case in
the absence of the parameter M, γ and S. These results are found to be in good agreement.
V. Conclusions
In this paper numerically investigated the nanoparticle effect on magnetohydrodynamic boundary layer
flow of Williamson fluid over a stretching surface with slip effect. The important findings of the paper are:
The velocity of the fluid decreases with an increase of the magnetic field.
The fluid temperature increases with the influence of magnetic field parameter or slip parameter or heat
generation/absorption parameter.
The nanoparticle volume friction enhances the magnetic field or thermophoresis parameter or
Brownian parameter.
Due to mass suction, the velocity boundary layer thickness as well as the thermal and nanoparticle
volume boundary layer thicknesses becomes thinner, whereas mass injectionmakes those thicker.
The skin friction coefficient and local Nusselt number and local Sherwood number enhances the mass
suction parameter.
The skin friction coefficient and local Nusselt number and local Sherwood number reduces the slip
parameter.
The local Nusselt number and local Sherwood number reduces the Brownian parameter.
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Fig.1 (a) Velocity for different values of M
Fig.1 (b) Temperature for different values of M
Fig.1(c) Nan particle volume fraction for different values of M
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Fig.2 (a) Velocity for different values of S
Fig.2 (b) Temperature for different values of S
Fig.2(c) Nanoparticle volume fraction for different values of S
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Fig.3 (a) Velocity for different values of γ
Fig.3 (b) Temperature for different values of γ
Fig.3(c) Nanoparticle volume fraction for different values of γ
0 1 2 3 4 5 6
0.0
0.2
0.4
0.6
0.8
1.0
=0.0
=0.2
=0.4
=0.6
M=1, Le=Pr=6, Nb=Nt==0.1, S=0.25
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Fig.4 (a) Temperature for different values of Nt
Fig.4 (b) Nanoparticle volume fraction for different values of Nt
Fig.5 (a) Temperature for different values of Nb
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Fig.5 (b) Concentration for different values of Nb
Fig.6 (a) Temperature for different values of β
Fig.6 (b) Concentration for different values of β
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Fig.7 Temperature for different values of Pr
Fig.8 Nanoparticle volume fraction for different values of Le
Fig.9 Effect of S, γ and M on the reduced skin friction
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Fig.10 Effect of S, γ and M on the reduced Nusselt number
Fig.11 Effect of S, γ and M on the reduced Sherwood number
Fig.12 Effect of Nb and Nt on the reduced Nusselt number
0.0 0.1 0.2 0.3 0.4 0.5
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
M=0, 0.5, 1
M=0, 0.5, 1
-'(0)
S=-0.25
S=0
S=0.25
M=0, 0.5, 1
0.0 0.1 0.2 0.3 0.4 0.5
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
M=0, 0.5, 1
M=0, 0.5, 1
-'(0)
S=-0.25
S=0
S=0.25
M=0, 0.5, 1
0.0 0.2 0.4 0.6 0.8 1.0
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
-'(0)
Nt
Nb=0.1, 0.4, 0.7
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Fig.13 Effect of Nb and Nt on the reduced Sherwood number
Table 1 Comparison for ''(0)f and ( )f for M=S=γ=0 and β=0
''(0)f
( )f
Present Study Magyari and Keller [28] Bhattacharyya and Layek [18]
1.28181
0.905641
1.281808
0.905639
0.905639
0.90564328
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