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.
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 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.
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.
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
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.
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 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.
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.
Analysis of mhd non darcian boundary layer flow and heat transfer over an exp...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
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.
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a 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 through graphs in detail.
Similarity Solution of an Unsteady Heat and Mass Transfer Boundary Layer Flow...iosrjce
The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting
fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving
surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse
magnetic field. The similarity solution is used to transform the system of partial differential equations,
describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the
parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on
velocity and temperature distributions
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
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.
Acta Mater 57 (2009) 559 Investigation Of The Indentation Size EffectDierk Raabe
Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
The present analysis is made to investigate the effects of heat source and thermal diffusion on an unsteady free convection flow along a porous vertical plate in a rotating system. The plate is subjected to constant heat and mass flux also. The problem is solved analytically and expressions for velocity. Energy and temperature profiles, skin friction and Nusselt number are obtained. The effects of different parameter entered in the problem are discussed on the primary and secondary velocities, temperature and concentration distributions, primary and secondary skin frictions and Nusselt number with the help of tables and graphs.
Numerical study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
Thermal Stress Analysis of a Thin Rectangular Plate With Internal Heat SourceIJLT EMAS
This paper deals with the determination of temperature
distribution, displacement function and thermal stresses of a thin
rectangular plate with internal heat source. A thin rectangular
plate is considered having zero initial temperature and the edges
of the plate are maintained at zero temperature whereas the thin
rectangular plate is subjected to arbitrary heat supply on the
edges y. The governing heat conduction equation has been solved
by the method of integral transform technique. The results are
obtained in a series form in terms of Bessel’s functions.
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
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.
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.
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a 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 through graphs in detail.
Similarity Solution of an Unsteady Heat and Mass Transfer Boundary Layer Flow...iosrjce
The unsteady hydromagnetic boundary layer flow of an incompressible and electrically conducting
fluid through a porous medium bounded by a moving surface has been considered. It is assumed that the moving
surface has a velocity profile with respect to time and fluid flow is taken under the influence of a transverse
magnetic field. The similarity solution is used to transform the system of partial differential equations,
describing the problem under consideration, into a boundary value problem of coupled ordinary differential
equations and an efficient numerical technique is implemented to solve the reduced system. The effects of the
parameters such as Magnetic parameter, Prandtl number and Eckert number are discussed graphically on
velocity and temperature distributions
Effect of Mass Transfer and Hall Current on Unsteady MHD Flow with Thermal Di...IJERA Editor
The paper investigated the effect of mass transfer and Hall current on unsteady MHD flow with Thermal Diffusivity of a viscoelastic fluid in a porous medium. The resultant equations have been solved analytically. The velocity, temperature and concentration distributions are derived, and their profiles for various physical parameters are shown through graphs. The coefficient of Skin friction, Nusselt number and Sherwood number at the plate are derived and their numerical values for various physical parameters are presented through tables. The influence of various parameters such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, viscoelasticity parameter, Hartmann number, Hall parameter, and the frequency of oscillation on the flow field are discussed. It is seen that, the velocity increases with the increase in Gc, Gr, m and K, and it decreases with increase in Sc,M, n and Pr, temperature decreases with increase in Pr and n, Also, the concentration decreases with the increase in Sc and n.
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.
Acta Mater 57 (2009) 559 Investigation Of The Indentation Size EffectDierk Raabe
Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography
Effects Of Heat Source And Thermal Diffusion On An Unsteady Free Convection F...IOSR Journals
The present analysis is made to investigate the effects of heat source and thermal diffusion on an unsteady free convection flow along a porous vertical plate in a rotating system. The plate is subjected to constant heat and mass flux also. The problem is solved analytically and expressions for velocity. Energy and temperature profiles, skin friction and Nusselt number are obtained. The effects of different parameter entered in the problem are discussed on the primary and secondary velocities, temperature and concentration distributions, primary and secondary skin frictions and Nusselt number with the help of tables and graphs.
Numerical study of mhd boundary layer stagnation point flow and heat transfer...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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.
Thermal Stress Analysis of a Thin Rectangular Plate With Internal Heat SourceIJLT EMAS
This paper deals with the determination of temperature
distribution, displacement function and thermal stresses of a thin
rectangular plate with internal heat source. A thin rectangular
plate is considered having zero initial temperature and the edges
of the plate are maintained at zero temperature whereas the thin
rectangular plate is subjected to arbitrary heat supply on the
edges y. The governing heat conduction equation has been solved
by the method of integral transform technique. The results are
obtained in a series form in terms of Bessel’s functions.
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
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.
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.
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.
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.
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.
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.
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
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
Magnetohydrodynamic mixed convection flow and boundary layer control of a nan...IAEME Publication
This research work is focused on the numerical solution of steady MHD mixed convection boundary layer flow of a nanofluid over a semi-infinite flat plate with heat generation/absorption and viscous dissipation effects in the presence of suction and injection. Gyarmati’s variational principle developed on the thermodynamic theory of irreversible processes is employed to solve the problem
numerically. The governing boundary layer equations are approximated as simple polynomial functions, and the functional of the variational principle is constructed.
HYDROMAGNETIC MIXED CONVECTION MICRO POLAR FLOW DRIVEN BY A POROUS STRETCHING...IAEME Publication
We analyze a finite element solution for the magneto hydrodynamics mixed convection micro polar flow through a porous medium driven by a porous stretching sheet with uniform suction. The governing partial differential equations are solved numerically by using finite element technique. The
effect of Hartmann number, Darcy parameter and surface condition on velocity, micro rotation and temperature functions has been study.
International Journal of Computational Engineering Research(IJCER)ijceronline
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.
The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Dif...IOSR Journals
The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson’s scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...IJERA Editor
This paper presents a study of MHD free convection flow of an electrically conducting incompressible fluid with
variable viscosity about an isothermal truncated cone in the presence of heat generation or absorption. The fluid
viscosity is assumed to vary as a inverse linear function of temperature. The non-linear coupled partial
differential equations governing the flow and heat transfer have been solved numerically by using an implicit
finite - difference scheme along with quasilinearization technique. The non-similar solutions have been obtained
for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime. Results
indicate that skin friction and heat transfer are strongly affected by, both, viscosity-variation parameter and
magnetic field. In fact, the transverse magnetic field influences the momentum and thermal fields, considerably.
Further, skin friction is found to decrease and heat transfer increases near the leading edge. Also, it is found that
the direction of heat transfer gets reversed during heat generation.
MHD Free Convection from an Isothermal Truncated Cone with Variable Viscosity...IJERA Editor
This paper presents a study of MHD free convection flow of an electrically conducting incompressible fluid with
variable viscosity about an isothermal truncated cone in the presence of heat generation or absorption. The fluid
viscosity is assumed to vary as a inverse linear function of temperature. The non-linear coupled partial
differential equations governing the flow and heat transfer have been solved numerically by using an implicit
finite - difference scheme along with quasilinearization technique. The non-similar solutions have been obtained
for the problem, overcoming numerical difficulties near the leading edge and in the downstream regime. Results
indicate that skin friction and heat transfer are strongly affected by, both, viscosity-variation parameter and
magnetic field. In fact, the transverse magnetic field influences the momentum and thermal fields, considerably.
Further, skin friction is found to decrease and heat transfer increases near the leading edge. Also, it is found that
the direction of heat transfer gets reversed during heat generation.
Radiation and Mass Transfer Effects on MHD Natural Convection Flow over an In...IJMER
A numerical solution for the unsteady, natural convective flow of heat and mass transfer along an inclined plate is presented. The dimensionless unsteady, coupled, and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields have been studied for the effect of Magnetic parameter, buoyancy ratio parameter, Prandtl number, radiation parameter and Schmidt number. The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically.
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.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Study of Magnetohydrodynamic Fluid Flows and Their Applicationsijtsrd
In this paper a detailed study is presented on magnetohydrodynamic fluid flows with their basic governing equations. Basic concept of magnetohydrodynamic is discussed in detail. The results of various problems done by researchers are presented and addressed properly. The various applications of magnetohydrodynamic fluid flows have been presented. Dr. Vishal Saxena ""Study of Magnetohydrodynamic Fluid Flows and Their Applications"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-2 , February 2020, URL: https://www.ijtsrd.com/papers/ijtsrd29931.pdf
Paper Url : https://www.ijtsrd.com/mathemetics/applied-mathematics/29931/study-of-magnetohydrodynamic-fluid-flows-and-their-applications/dr-vishal-saxena
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
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.
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.
Connector Corner: Automate dynamic content and events by pushing a buttonDianaGray10
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Create a campaign using Mailchimp with merge tags/fields
Send an interactive Slack channel message (using buttons)
Have the message received by managers and peers along with a test email for review
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In a second workflow supporting the same use case, you’ll see:
Your campaign sent to target colleagues for approval
If the “Approve” button is clicked, a Jira/Zendesk ticket is created for the marketing design team
But—if the “Reject” button is pushed, colleagues will be alerted via Slack message
Join us to learn more about this new, human-in-the-loop capability, brought to you by Integration Service connectors.
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1. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
572 | P a g e
Effects Of Radiation On Mhd Mixed Convection Flow Of A
Micropolar Fluid Over A Heated Stretching Surface With Heat
Generation/Absorption
P. Bala Anki Reddy*and D. Vijaya Sekhar**
*Department of Mathematics, Fluid dynamics division, VIT University, Vellore-632014, Tamil Nadu.
**Department of Mathematics, NBKRIST, Vidyanagar, Nellore, A.P., India.
Abstract
A theoretical analysis is performed to
study the flow and heat transfer characteristics
of magnetohydrodynamic mixed convection flow
of a micropolar fluid past a stretching surface
with radiation and heat generation/absorption.
The transformed equations solved numerically
using the shooting method. The effects of the
velocity, the angular velocity, and the
temperature for various values of different
parameters are illustrated graphically. Also, the
effects of various parameters on the local skin-
friction coefficient and the local Nusselt number
are given in tabular form and discussed. The
results show that the mixed convection
parameter has the effect of enhancing both the
velocity and the local Nusselt number and
suppressing both the local skin-friction
coefficient and the temperature. It is found that
local skin-friction coefficient increases while the
local Nusselt number decreases as the magnetic
parameter increases. The results show also that
increasing the heat generation parameter leads to
a rise in both the velocity and the temperature
and a fall in the local skin-friction coefficient and
the local Nusselt number. Furthermore, it is
shown that the local skin-friction coefficient and
the local Nusselt number decrease when the slip
parameter increases.
Keywords: Radiation, stretching surface,
micropolar fluid, heat transfer, heat source.
1.Introduction
The fluid dynamics due to a stretching
surface and by thermal buoyancy is of considerable
interest in several applications such as aerodynamic
extrusion of plastic sheets, the boundary layer along
a liquid film in condensation processes, paper
production, glass blowing, metal spinning and
drawing plastic films. Free and mixed convections
of a micropolar fluid over a moving surface have
been studied by many authors [1–9] under different
situations. Desseaux and Kelson [10] studied the
flow of a micropolar fluid bounded by a linearly
stretching sheet while Bhargava et. al. [11] studied
the same flow of a micropolar flow over a non-
linear stretching sheet. The theory of micropolar
fluid was first introduced and formulated by Eringen
[12]. Later
Eringen [13] generalized the theory to incorporate
thermal effects in the so-called thermo micropolar
fluid. Crane [14] first obtained an elegant analytical
solution to the boundary layer equations for the
problem of steady two dimensional flow due to a
stretching surface in a quiescent incompressible
fluid. Gupta and Gupta [15] extended the problem
posed by Crane [14] to a permeable sheet and
obtained closed-form solution, while Grubka and
Bobba [16] studied the thermal field and presented
the solutions in terms of Kummer’s functions. The
3-dimensional case has been considered by Wang
[17]. Chen [18] studied the case when buoyancy
force is taken into consideration, and Magyari and
Keller [19] considered exponentially stretching
surface. The heat transfer over a stretching surface
with variable surface heat flux has been considered
by Char and Chen [20], Lin and Cheng [21],
Elbashbeshy [22] and very recently by Ishak et al.
[23], Mostaffa Mahmoud and Shimaa Waheed [24].
All of the above mentioned studies dealt with
stretching sheet where the flows were assumed to be
steady.
The aim of this work is to investigate the
effect of radiation on the flow and heat transfer of a
micropolar fluid over a vertical stretching surface in
the presence of heat generation (absorption) and
magnetic field, where numerical solutions are
obtained using shooting method.
2. Formulation of the Problem
Consider a steady, two-dimensional
hydromagnetic laminar convective flow of an
incompressible, viscous, micropolar fluid with a
heat generation (absorption) on a stretching vertical
surface with a velocity ( )wv x . The flow is assumed
to be in the x-direction, which is taken along the
vertical surface in upward direction and y-axis
normal to it. A uniform magnetic field of strength B0
is imposed along y-axis. The magnetic Reynolds
number of the flow is taken to be small enough so
that the induced magnetic field is assumed to be
negligible. The gravitational acceleration g acts in
the downward direction.
2. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
573 | P a g e
The temperature of the micropolar fluid far away
from the plate is T∞, whereas the surface
temperature of the plate is maintained at Tw, where
( )wT x T ax , a > 0 is constant, and Tw > T∞.
The temperature difference between the body
surface and the surrounding micropolar fluid
generates a buoyancy force, which results in an
upward convective flow. Under usual boundary
layer and Boussinesq approximations, the flow and
heat transfer in the presence of heat generation
(absorption) are governed by the following
equations:
0
u v
x y
(1)
22
0
2
Bu u k u k N
u v g T T u
x y y y
(2)
2
0
2
2
N N N k u
u v N
x y j y j y
(3)
2
0
2
1 r
p p p
QqT T k T
u v T T
x y c y c y c
(4)
Subject to the boundary conditions:
( )wu u x cx , 00,
u
v N m
y
, ( ) 0wT T x at y
0, 0,u N T T as y (5)
where u and v are the velocity components in the x
and y directions respectively, T is the fluid
temperature, N is the component of the
microrotation vector normal to the x-y plane, ρis the
density, j is the microinertia density, μ is the
dynamic viscosity, k is the gyro-viscosity (or vortex
viscosity), β is the thermal expansion coefficient, σ
is the electrical conductivity, pc is the specific heat
at constant pressure, κ is the thermal conductivity, c
is a positive constant of proportionality, x measures
the distance from the leading edge along the surface
of the plate, and 0 is the spin-gradient viscosity.
Thermal radiation is simulated using the Rosseland
diffusion approximation and in accordance with this,
the radiative heat flux rq is given by:
* 4
*
1
4
3
r
T
q
k y
Where
*
is the Stefan–Boltzman constant and
*
1k
is the Rosseland mean absorption coefficient.
We follow the recent work of the authors [25, 26] by
assuming that 0 is given by
0 1
2 2
k K
j j
(6)
This equation gives a relation between the
coefficient of viscosity and micro inertia, where K =
k/μ (> 0) is the material parameter, j = ν/c, j is
the reference length, and m0 (0 ≤ m0 ≤ 1) is the
boundary parameter. When the boundary parameter
m0 = 0, we obtain N = 0 which is the no-spin
condition, that is, the microelements in a
concentrated particle flow close to the wall are not
able to rotate (as stipulated by Jena and Mathur
(27)). The case m0 = 1/2 represents the weak
concentration of microelements. The case
corresponding to m0 = 1 is used for the modelling of
turbulent boundary layer flow (see Peddieson
andMcnitt (28)).
We introduce the following dimensionless
variables:
1 1 22 2 1
02
, , ', , , ,
w
BT Tc c
y N cx g u cxf v c f M
T T c
* *
01 1 1
2 * 3 * 3
3 3
, ,Pr , , ,
16 16
p
p
c Qk k k kg a k
R K R
c T k cc T
(7)
Through (7), the continuity (1) is automatically
satisfied and (2) – (4) will give then
2
''' '' ' '
1 ' 0K f ff f Kg Mf
(8)
'' ' '
1 2 '' 0
2
K
g fg f g K g f
(9)
'' ' '1 1
1 0
Pr
f f
R
(10)
The corresponding boundary conditions are
'
0
'
1, 0, '', 1 at 0
0, 0, 0 as
f f g m f
f g
(11)
where the primes denote the differentiation with
respect to , M is the magnetic parameter, λ is the
buoyancy parameter, γ is the heat generation (> 0)
or absorption (<0) and R is the radiation parameter.
The physical quantities of interest are the local skin-
friction coefficient Cfx and the local Nusselt number
Nux , which are respectively proportional to
'' '
0 , 0f are worked out and their
numerical values presented in a tabular form.
3. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
574 | P a g e
3. Solution of the problem
The governing boundary layer equations
(8) - (10) subject to boundary conditions (11) are
solved numerically by using shooting method. First
of all higher order non-linear differential equations
(8) - (10) are converted into simultaneous linear
differential equations of first order and they are
further transformed into initial value problem by
applying the shooting technique. From the process
of numerical computation, the skin-friction
coefficient, the Nusselt number and Sherwood
number which are respectively proportional to
''
0f and '
0 are also sorted out and their
numerical values are presented in a tabular form.
4. Results and Discussion
To study the behavior of the velocity, the
angular velocity, and the temperature profiles,
curves are drawn in Figures 1–18. The effect of
various parameters, namely, the magnetic parameter
M, the material parameter K, the radiation parameter
R, the buoyancy parameter λ, the heat generation
(absorption) parameter γ, and the Prandtl number Pr
have been studied over these profiles.
Figures 1–3 illustrate the variation of the
velocity 'f , the angular velocity g, and the
temperature θ profiles with the magnetic parameter
M. Figure 1 depict the variation of 'f with M. It is
observed that 'f decreases with the increase in M
along the surface. This indicates that the fluid
velocity is reduced by increasing the magnetic field
and confines the fact that application of a magnetic
field to an electrically conducting fluid produces a
drag like force which causes reduction in the fluid
velocity. The profile of the angular velocity g with
the variation of M is shown in Figure 2. It is clear
from this figure that g increases with an increase in
M near the surface and the reverse is true away from
the surface. Figure 3 shows the resulting
temperature profile θ for various values of M. It is
noted that an increase of M leads to an increase of θ.
Figure 4 illustrates the effects of the
material parameter K on 'f . It can be seen from this
figure that the velocity decreases as the material
parameter K rises near the surface and the opposite
is true away from it. Also, it is noticed that the
material parameter has no effect on the boundary
layer thickness. The effect of K on g is shown in
Figure 5. It is observed that initially g decreases by
increasing K near the surface and the reverse is true
away from the surface. Figure 6 demonstrates the
variation of θ with K. From this figure it is clear that
θ decreases with an increase in K.
It was observed from Figure 7 that the
velocity increases for large values of λ while the
boundary layer thickness is the same for all values
of λ. Figure 8 depicts the effects of λ on g. The
angular velocity g is a decreasing function of λ near
the surface and the reverse is true at larger distance
from the surface. Figure 9 shows the variations of λ
on θ. It is found that θ decreases with an increase in
λ.
Figure 10 shows the effect of the heat
generation parameter (γ > 0) or the heat absorption
parameter (γ < 0) on 'f . It is observed that 'f
increases as the heat generation parameter (γ > 0)
increases, but the effect of the absolute value of heat
absorption parameter (γ < 0) is the opposite. The
effect of the heat generation parameter (γ > 0) or the
heat absorption parameter (γ < 0) on g within the
boundary layer region is observed in Figure 11. It is
apparent from this figure that g increases as the heat
generation parameter (γ > 0) decreases, while g
increases as the absolute value of heat absorption
parameter (γ < 0) increases near the surface and the
reverse is true away from the surface. Figure 12
displays the effect of the heat generation parameter
(γ > 0) or the heat absorption parameter (γ < 0) on θ.
It is shown that as the heat generation parameter (γ
> 0) increases, the thermal boundary layer thickness
increases. For the case of the absolute value of the
heat absorption parameter (γ < 0), one sees that the
thermal boundary layer thickness decreases as γ
increases.
The effect of the Prandtl number Pr on the
velocity, the angular velocity, and the temperature
profiles is illustrated in Figures 13, 14, and 15. From
these figures, it can be seen that 'f decrease with
increasing Pr, while g increases as the Prandtl
number Pr increases near the surface and the reverse
is true away from the surface. The temperature θ of
the fluid decreases with an increase of the Prandtl
number Pr as shown in Figure 15. This is in
agreement with the fact that the thermal boundary
layer thickness decreases with increasing Pr. Figures
16, 17, and 18 depict the effect of the radiation
parameter on 'f , g, and θ, respectively. It is seen
that 'f and θ decrease as α increases, while g
increases as α increases.
The local skin-friction coefficient in terms
of − ''(0)f and the local Nusselt number in terms
of − '(0) for various values of M, λ, K, γ, R and
Pr are tabulated in Table 1. It is obvious from this
table that local skin-friction coefficient and the local
Nusselt number increases with the increase of the
magnetic parameter M. It is noticed that as K or λ
increases, the local skin-friction coefficient as well
as the local Nusselt number decreases. It is found
that the local Nusselt number decreases with the
increase of the heat generation parameter (γ > 0),
while it increased with the increase of the absolute
value of the heat absorption parameter (γ < 0). It is
found that both the local skin friction coefficient and
the local Nusselt number increase with increasing Pr
or R
4. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
575 | P a g e
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
M = 0.5
M = 1.0
M = 1.5
Fig. 1. Velocity profiles for various
values of M.
0 1 2 3 4 5
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
M = 0.5
M = 1.0
M = 1.5
Fig. 2. Angular Velocity profiles for
various values of M.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
M = 0.5
M = 1.0
M = 1.5
Fig. 3. Temperature profiles for various values of M.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
K = 0.5
K = 1.2
K = 2.5
Fig. 4. Velocity profiles for various values of K.
5. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
576 | P a g e
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
K = 0.5
K = 1.2
K = 2.5
Fig. 5. Angular velocity profiles for various values
of K.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
K = 0.5
K = 1.2
K = 2.5
Fig. 6. Temperature profiles for various values of K.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
= 0.1
= 0.5
= 1.0
Fig. 7. Velocity profiles for various values of .
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
= 0.1
= 0.5
= 1.0
Fig. 8. Angular velocity profiles for various values
of .
6. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
577 | P a g e
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
= 0.1
= 0.5
= 1.0
Fig. 9. Temperature profiles for various values of
.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
Fig. 10. Velocity profiles for various values of .
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
= - 0.3
= 0.3
= 0.6
Fig. 11. Angular velocity profiles for various values
of .
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
= - 0.3
= 0.3
= - 0.6
Fig. 12. Temperature profiles for various values of
.
7. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
578 | P a g e
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
Pr = 0.72
Pr = 1.0
Pr = 2.0
Fig. 13. Velocity profiles for various values of Pr.
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
Pr = 0.72
Pr = 1.0
Pr = 2.0
Fig. 14. Angular velocity profiles for various values
of Pr.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
Pr = 0.72
Pr = 1.0
Pr = 2.0
Fig. 15. Temperature profiles for various values of
Pr.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
f'
R = 0.5
R = 1.0
R = 1.5
Fig. 16. Velocity profiles for various values of R.
8. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
579 | P a g e
0 1 2 3 4 5
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
g
R = 0.5
R = 1.0
R = 1.5
Fig. 17. Angular velocity profiles for various values
of R.
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
R = 0.5
R = 1.0
R = 1.5
Fig. 18. Temperature profiles for various values of
R.
Table 1.
M K R Pr ''(0)f '(0)
0.
5
0.
5
1.
2
0.
3
0.
5
0.7
2
0.74840
2
0.29762
3
1.
0
0.
5
1.
2
0.
3
0.
5
0.7
2
0.90297 0.37795
3
0.
5
1.
0
1.
2
0.
3
0.
5
0.7
2
0.55662
4
0.20054
8
0.
5
0.
5
2.
5
0.
3
0.
5
0.7
2
0.64895
4
0.21511
1
0.
5
0.
5
1.
2
-
0.
3
0.
5
0.7
2
0.76828
4
0.30402
7
0.
5
0.
5
1.
2
0.
6
0.
5
0.7
2
0.74539
7
0.29662
6
0.
5
0.
5
1.
2
0.
3
1.
0
0.7
2
0.76345
4
0.30236
9
0.
5
0.
5
1.
2
0.
3
0.
5
1.0 0.76036
3
0.30138
4
5. Conclusions
In the present work, the effects of heat
generation (absorption) and a transverse magnetic
field on the flow and heat transfer of a micropolar
fluid over a vertical stretching surface with radiation
have been studied. The governing fundamental
equations are transformed to a system of nonlinear
ordinary differential equations which are solved by
using shooting technique. The velocity, the angular
velocity, and the temperature fields as well as the
local skin-friction coefficient and the local Nusselt
number are presented for various values of the
parameters governing the problem. From the results,
we can observe that, the velocity decreases with
increasing the magnetic parameter, and the absolute
value of the heat absorption parameter, while it
increases with increasing the buoyancy parameter,
the heat generation parameter, and the Prandtl
number. Also, it is found that near the surface the
velocity decreases as the slip parameter and the
material parameter increase, while the reverse
happens as one moves away from the surface. The
angular velocity decreases with increasing the
material parameter, the slip parameter, the buoyancy
parameter, and the heat generation parameter, while
it increases with increasing the magnetic parameter,
the absolute value of the heat absorption parameter,
and the Prandtl number near the surface and the
reverse is true away from the surface. In addition the
temperature distribution increases with increasing
the slip parameter, the heat generation parameter,
and the magnetic parameter, but it decreases with
increasing the Prandtl number, the buoyancy
parameter, the material parameter, and the absolute
value of the heat absorption parameter. Moreover,
the local skin-friction coefficient increases with
increasing the magnetic parameter and the absolute
value of the heat absorption parameter, while the
local skin-friction decreases with increasing the
9. P. Bala Anki Reddy, D. Vijaya Sekhar / International Journal of Engineering Research and
Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 3, May-Jun 2013, pp.572-581
580 | P a g e
buoyancy parameter, the slip parameter, and the heat
generation parameter. Finally, the local Nusselt
number increases with increasing the buoyancy
parameter, and the absolute value of the heat
absorption parameter, and decreases with increasing
the magnetic parameter, the slip parameter, and the
heat generation parameter.
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