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.
The steady laminar two dimensional stagnation point flow of an incompressible electrically conducting magneto-micropolar fluid over a permeable stretching surface with heat source/sink and viscous dissipation in the presence of mass transfer and chemical reaction has been studied. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, forth order Runge-Kutta method along with shooting technique has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and Sherwood number as well as the velocity, temperature and concentration profiles for different values of the governing parameters, namely, velocity ratio parameter, boundary parameter, material parameter, magnetic parameter, Prandtl number, Eckert number, heat source/sink parameter, Schmidt number and chemical reaction parameter.
Thermal Energy on Water and Oil placed Squeezed Carreau Nanofluids FlowMOHAMMED FAYYADH
this research work is focused on the numerical study regarding Carreau nanofluids’ squeezed flow via a permeable sensor surface. The nanofluids’ thermal conductivity is considered to be dependent on temperature. A convenient transformation is employed to reorganize governing equations into ordinary differential equations. The Runge–Kutta method and shooting technique are employed to accurately solve the boundary layer momentum as well as heat equations. Graphical and tabular aids are used to evaluate the solutions of applicable parameter with regards to temperature as well as the rate of heat transfer. In this work, a comparison is done from three nanofluids, i.e. copper, oxide aluminum and SWCNTs (nanoparticles) based fluids (water, crude oil and ethylene glycol) to improve heat transfer. It is found that the temperature dimensionless was dropped and dominated with the squeezed flow parameter and nanoparticle volume fraction parameter. That is for all nanomaterials. When compared with water and ethylene glycol, crude oil is cooler and a thinner thermal boundary layer is presented. For the rate of heat transfer (Nusselt number) was higher in: Ethylene glycol- SWCNT with high permeable velocity parameter 0.2, Ethylene glycol- SWCNT with low squeeze flow parameter 0.1 and Ethylene glycol- oxide aluminum with low nanoparticle volume fraction 0.05
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.
The steady laminar two dimensional stagnation point flow of an incompressible electrically conducting magneto-micropolar fluid over a permeable stretching surface with heat source/sink and viscous dissipation in the presence of mass transfer and chemical reaction has been studied. Using the similarity transformations, the governing equations have been transformed into a system of ordinary differential equations. These differential equations are highly nonlinear which cannot be solved analytically. Therefore, forth order Runge-Kutta method along with shooting technique has been used for solving it. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number and Sherwood number as well as the velocity, temperature and concentration profiles for different values of the governing parameters, namely, velocity ratio parameter, boundary parameter, material parameter, magnetic parameter, Prandtl number, Eckert number, heat source/sink parameter, Schmidt number and chemical reaction parameter.
Thermal Energy on Water and Oil placed Squeezed Carreau Nanofluids FlowMOHAMMED FAYYADH
this research work is focused on the numerical study regarding Carreau nanofluids’ squeezed flow via a permeable sensor surface. The nanofluids’ thermal conductivity is considered to be dependent on temperature. A convenient transformation is employed to reorganize governing equations into ordinary differential equations. The Runge–Kutta method and shooting technique are employed to accurately solve the boundary layer momentum as well as heat equations. Graphical and tabular aids are used to evaluate the solutions of applicable parameter with regards to temperature as well as the rate of heat transfer. In this work, a comparison is done from three nanofluids, i.e. copper, oxide aluminum and SWCNTs (nanoparticles) based fluids (water, crude oil and ethylene glycol) to improve heat transfer. It is found that the temperature dimensionless was dropped and dominated with the squeezed flow parameter and nanoparticle volume fraction parameter. That is for all nanomaterials. When compared with water and ethylene glycol, crude oil is cooler and a thinner thermal boundary layer is presented. For the rate of heat transfer (Nusselt number) was higher in: Ethylene glycol- SWCNT with high permeable velocity parameter 0.2, Ethylene glycol- SWCNT with low squeeze flow parameter 0.1 and Ethylene glycol- oxide aluminum with low nanoparticle volume fraction 0.05
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...eSAT Journals
Abstract
The steady boundary layer free convective flow of a dusty fluid past a vertical permeable stretching surface is studied .The governing equations are converted into first order ordinary differential equations using similarity transformations. These equations are solved numerically by using Runge kutta forth order method. The effects of physical parameters like fluid-particle interaction parameter, local Grashof number, suction parameters, Prandtl number, radiation parameter and Eckert number on the flow and heat transfer characteristics are computed and presented graphically. Also the rate of heat transfer at the surface is discussed. The present results are compared with the previous study and there is a good agreement.
AMS classification 76T10, 76T15
Keywords: Volume fraction, Interaction parameter, Dusty fluid, Thermal radiation, suction parameter, steady flow and heat transfer, Boundary layer flow, Numerical solution.
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.
presentation is made with a view to simplify the understanding of fluid mechanics ( fluid kinematics is given more credit ) in civil engineering - mechanical engineering - body science
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.
Numerical study of disk drive rotating flow structure in the cavityeSAT Journals
Abstract
This paper aim in conducting the numerical simulation of laminar flow to explore disk-driven vortical flow structure of a cubical
container subjected to a disk rotation on the roof of the container in different Reynolds numbers to observe the flow structure and
the reason of vortical flow form. For this study, finite difference method with dispersion-relation- preserving (DRP) scheme is
dispersed governing equations space term, but adopt time term with TVD Runge-Kutta method. To add accuracy of numerical,
this thesis also uses topology theory to analyze the characteristic of singular point. Three-dimensional vertical flow is observed
flow structure and move to condition. The result to obtain Reynolds numbers to increase attracting spiral nodes increasingly
approaches the floor of the cavity. We have also depicted the vertical flow structure in terms of cortex cores which provide more
details about how change of the Reynolds number
Keywords: disk-driven, finite difference method, dispersion-relation-preserving (DRP), Runge-Kutta, topology theory
THE EFFECTS OF UNIFORM TRANSVERSE MAGNETIC FIELD ON LOCAL FLOW AND VELOCITY P...IAEME Publication
A numerical model studied the effects of uniform transverse magnetic field for two fluids (pure water and water with electric conductivity), two different non-magnetizable duct and two flow velocities (steady flow for laminar and incompressible) was examined and The results showed an increase in the magnetic field caused a decrease in the local flow and effected on velocity profile. The result also showed that the water with electrical conductivity more affected than pure water.
Control of Suddenly Expanded Flow at Low Supersonic Mach NumbersIJERA Editor
In the present study the experiments were conducted to control the base pressure from a convergent-divergent
nozzle at low supersonic Mach numbers to assess the effectiveness of active control mechanism in the form of
micro jets at different expansion level. The parameters considered in the present study are the diameter ratio,
length to diameter ratio (L/D), Nozzle Pressure Ratio (NPR), and the Mach number. The diameter ratio selected
for the present study are 1.6, 1.8, 2.2, and 2.5. Experiments were conducted for nozzle pressure ratio (NPR)
from 3 to 11. The L/D ratio of the enlarged duct was varied from 10 to 1, and results are presented for L/D 4, 3,
2, and 1. The Mach numbers of the present studies are 1.1, 1.2, 1.4, and 1.5. The results show that the Micro jets
are very effective and are able to raise the base pressure value to a considerable level under the influence of
favorable pressure gradient except at lower NPR 3. At NPRs 5 and 7 for some cases the trends differ due to the
level of expansion, nature of waves present in the base region, relief available to the flow, L/D ratio of the
enlarged duct and the Mach numbers. It is seen that most of the cases exhibit similar behavior for the L/Ds in
the range 4 and 3, which means; that the back pressure has not adversely influenced the flow field in the base
region as well as in the duct. The minimum duct length required for the flow to be attached is L/D = 2, even
though in some cases flow is attached with duct wall. With this it can be stated that the micro jets can be an
alternative for the for base pressure control.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
We follow "Rigorous Publication" model - means that all articles appear on IJERD after full appraisal, effectiveness, legitimacy and reliability of research content. International Journal of Engineering Research and Development publishes papers online as well as provide hard copy of Journal to authors after publication of paper. It is intended to serve as a forum for researchers, practitioners and developers to exchange ideas and results for the advancement of Engineering & Technology.
Prediction of aerodynamic characteristics for slender bluff bodies with nose ...vasishta bhargava
the numerical approach is used to verify the aero/hydrodynamic performance of different
geometries of nose cones. Computational methods predict the flow characteristics fairly accurately in order to validate
the data obtained from experiments. The simulation involves muzzle velocity that range from 5m/s to 25 m/s i.e. 1.69 to
8.4 x 105
and calculated for the different angle of attack, -10 to 20 degrees, to demonstrate the flow behavior around the
shells. Nosecone is the most forward section of any slender moving bodies which are used in rockets, guided missiles,
submarines, aircraft drop tanks and aircraft fuselage to reduce the aerodynamic or hydrodynamic drag. The basic
geometry of bluff body is cylinder with variant nosecone shapes such as flat and tapered head, with moderate to low
taper ratios and conical head.
Numerical Study of Flow Separation Control by Tangential and Perpendicular Bl...CSCJournals
In this study, tangential and perpendicular steady blowing at the trailing edge of NACA 0012 airfoil is investigated numerically to flow separation control and to study the effects of blowing amplitude and blowing coefficient on airfoil aerodynamic characteristics. Flow was fully turbulent with the Reynolds number of 5105 and the turbulent employed model was the Menter’s shear stress model. Blowing on airfoil is modeled in tangential (tangential blowing) and perpendicular (perpendicular blowing) form and length of blowing jet is 3.5 percent of chord length. Considering previous studies, blowing jet is optimum in two distances on the airfoil surface, one around 40 percent and the other around 80 percent of chord length from the leading edge, which in this study blowing jet is placed at 80 percent of the chord length from the leading edge. Blowing velocity from 0.1 to 0.5 is considered of freestream velocity. Results of tangential blowing show that by increasing amplitude of blowing, lift and drag coefficients changes are inconsiderable. Maximum increase of lift to drag ratio in amplitude of 0.5, around 16.5 percent, but in perpendicular blowing lower amplitude of blowing is more appropriate. Also tangential blowing has no effect on stall angle and cause gradual stall of NACA 0012 airfoil, whereas perpendicular blowing improve stall angle from 14 to 16 degrees.
The technologies and people we are designing experiences for are constantly changing, in most cases they are changing at a rate that is difficult keep up with. When we think about how our teams are structured and the design processes we use in light of this challenge, a new design problem (or problem space) emerges, one that requires us to focus inward. How do we structure our teams and processes to be resilient? What would happen if we looked at our teams and design process as IA’s, Designers, Researchers? What strategies would we put in place to help them be successful? This talk will look at challenges we face leading, supporting, or simply being a part of design teams creating experiences for user groups with changing technological needs.
UX, ethnography and possibilities: for Libraries, Museums and ArchivesNed Potter
These slides are adapted from a talk I gave at the Welsh Government's Marketing Awards for the LAM sector, in 2017.
It offers a primer on UX - User Experience - and how ethnography and design might be used in the library, archive and museum worlds to better understand our users. All good marketing starts with audience insight.
The presentation covers the following:
1) An introduction to UX
2) Ethnography, with definitions and examples of 7 ethnographic techniques
3) User-centred design and Design Thinking
4) Examples of UX-led changes made at institutions in the UK and Scandinavia
5) Next Steps - if you'd like to try out UX at your own organisation
Study: The Future of VR, AR and Self-Driving CarsLinkedIn
We asked LinkedIn members worldwide about their levels of interest in the latest wave of technology: whether they’re using wearables, and whether they intend to buy self-driving cars and VR headsets as they become available. We asked them too about their attitudes to technology and to the growing role of Artificial Intelligence (AI) in the devices that they use. The answers were fascinating – and in many cases, surprising.
This SlideShare explores the full results of this study, including detailed market-by-market breakdowns of intention levels for each technology – and how attitudes change with age, location and seniority level. If you’re marketing a tech brand – or planning to use VR and wearables to reach a professional audience – then these are insights you won’t want to miss.
An immersive workshop at General Assembly, SF. I typically teach this workshop at General Assembly, San Francisco. To see a list of my upcoming classes, visit https://generalassemb.ly/instructors/seth-familian/4813
I also teach this workshop as a private lunch-and-learn or half-day immersive session for corporate clients. To learn more about pricing and availability, please contact me at http://familian1.com
Boundary layer flow and heat transfer of a dusty fluid over a vertical permea...eSAT Journals
Abstract
The steady boundary layer free convective flow of a dusty fluid past a vertical permeable stretching surface is studied .The governing equations are converted into first order ordinary differential equations using similarity transformations. These equations are solved numerically by using Runge kutta forth order method. The effects of physical parameters like fluid-particle interaction parameter, local Grashof number, suction parameters, Prandtl number, radiation parameter and Eckert number on the flow and heat transfer characteristics are computed and presented graphically. Also the rate of heat transfer at the surface is discussed. The present results are compared with the previous study and there is a good agreement.
AMS classification 76T10, 76T15
Keywords: Volume fraction, Interaction parameter, Dusty fluid, Thermal radiation, suction parameter, steady flow and heat transfer, Boundary layer flow, Numerical solution.
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.
presentation is made with a view to simplify the understanding of fluid mechanics ( fluid kinematics is given more credit ) in civil engineering - mechanical engineering - body science
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.
Numerical study of disk drive rotating flow structure in the cavityeSAT Journals
Abstract
This paper aim in conducting the numerical simulation of laminar flow to explore disk-driven vortical flow structure of a cubical
container subjected to a disk rotation on the roof of the container in different Reynolds numbers to observe the flow structure and
the reason of vortical flow form. For this study, finite difference method with dispersion-relation- preserving (DRP) scheme is
dispersed governing equations space term, but adopt time term with TVD Runge-Kutta method. To add accuracy of numerical,
this thesis also uses topology theory to analyze the characteristic of singular point. Three-dimensional vertical flow is observed
flow structure and move to condition. The result to obtain Reynolds numbers to increase attracting spiral nodes increasingly
approaches the floor of the cavity. We have also depicted the vertical flow structure in terms of cortex cores which provide more
details about how change of the Reynolds number
Keywords: disk-driven, finite difference method, dispersion-relation-preserving (DRP), Runge-Kutta, topology theory
THE EFFECTS OF UNIFORM TRANSVERSE MAGNETIC FIELD ON LOCAL FLOW AND VELOCITY P...IAEME Publication
A numerical model studied the effects of uniform transverse magnetic field for two fluids (pure water and water with electric conductivity), two different non-magnetizable duct and two flow velocities (steady flow for laminar and incompressible) was examined and The results showed an increase in the magnetic field caused a decrease in the local flow and effected on velocity profile. The result also showed that the water with electrical conductivity more affected than pure water.
Control of Suddenly Expanded Flow at Low Supersonic Mach NumbersIJERA Editor
In the present study the experiments were conducted to control the base pressure from a convergent-divergent
nozzle at low supersonic Mach numbers to assess the effectiveness of active control mechanism in the form of
micro jets at different expansion level. The parameters considered in the present study are the diameter ratio,
length to diameter ratio (L/D), Nozzle Pressure Ratio (NPR), and the Mach number. The diameter ratio selected
for the present study are 1.6, 1.8, 2.2, and 2.5. Experiments were conducted for nozzle pressure ratio (NPR)
from 3 to 11. The L/D ratio of the enlarged duct was varied from 10 to 1, and results are presented for L/D 4, 3,
2, and 1. The Mach numbers of the present studies are 1.1, 1.2, 1.4, and 1.5. The results show that the Micro jets
are very effective and are able to raise the base pressure value to a considerable level under the influence of
favorable pressure gradient except at lower NPR 3. At NPRs 5 and 7 for some cases the trends differ due to the
level of expansion, nature of waves present in the base region, relief available to the flow, L/D ratio of the
enlarged duct and the Mach numbers. It is seen that most of the cases exhibit similar behavior for the L/Ds in
the range 4 and 3, which means; that the back pressure has not adversely influenced the flow field in the base
region as well as in the duct. The minimum duct length required for the flow to be attached is L/D = 2, even
though in some cases flow is attached with duct wall. With this it can be stated that the micro jets can be an
alternative for the for base pressure control.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
International Journal of Engineering Research and Development is an international premier peer reviewed open access engineering and technology journal promoting the discovery, innovation, advancement and dissemination of basic and transitional knowledge in engineering, technology and related disciplines.
We follow "Rigorous Publication" model - means that all articles appear on IJERD after full appraisal, effectiveness, legitimacy and reliability of research content. International Journal of Engineering Research and Development publishes papers online as well as provide hard copy of Journal to authors after publication of paper. It is intended to serve as a forum for researchers, practitioners and developers to exchange ideas and results for the advancement of Engineering & Technology.
Prediction of aerodynamic characteristics for slender bluff bodies with nose ...vasishta bhargava
the numerical approach is used to verify the aero/hydrodynamic performance of different
geometries of nose cones. Computational methods predict the flow characteristics fairly accurately in order to validate
the data obtained from experiments. The simulation involves muzzle velocity that range from 5m/s to 25 m/s i.e. 1.69 to
8.4 x 105
and calculated for the different angle of attack, -10 to 20 degrees, to demonstrate the flow behavior around the
shells. Nosecone is the most forward section of any slender moving bodies which are used in rockets, guided missiles,
submarines, aircraft drop tanks and aircraft fuselage to reduce the aerodynamic or hydrodynamic drag. The basic
geometry of bluff body is cylinder with variant nosecone shapes such as flat and tapered head, with moderate to low
taper ratios and conical head.
Numerical Study of Flow Separation Control by Tangential and Perpendicular Bl...CSCJournals
In this study, tangential and perpendicular steady blowing at the trailing edge of NACA 0012 airfoil is investigated numerically to flow separation control and to study the effects of blowing amplitude and blowing coefficient on airfoil aerodynamic characteristics. Flow was fully turbulent with the Reynolds number of 5105 and the turbulent employed model was the Menter’s shear stress model. Blowing on airfoil is modeled in tangential (tangential blowing) and perpendicular (perpendicular blowing) form and length of blowing jet is 3.5 percent of chord length. Considering previous studies, blowing jet is optimum in two distances on the airfoil surface, one around 40 percent and the other around 80 percent of chord length from the leading edge, which in this study blowing jet is placed at 80 percent of the chord length from the leading edge. Blowing velocity from 0.1 to 0.5 is considered of freestream velocity. Results of tangential blowing show that by increasing amplitude of blowing, lift and drag coefficients changes are inconsiderable. Maximum increase of lift to drag ratio in amplitude of 0.5, around 16.5 percent, but in perpendicular blowing lower amplitude of blowing is more appropriate. Also tangential blowing has no effect on stall angle and cause gradual stall of NACA 0012 airfoil, whereas perpendicular blowing improve stall angle from 14 to 16 degrees.
The technologies and people we are designing experiences for are constantly changing, in most cases they are changing at a rate that is difficult keep up with. When we think about how our teams are structured and the design processes we use in light of this challenge, a new design problem (or problem space) emerges, one that requires us to focus inward. How do we structure our teams and processes to be resilient? What would happen if we looked at our teams and design process as IA’s, Designers, Researchers? What strategies would we put in place to help them be successful? This talk will look at challenges we face leading, supporting, or simply being a part of design teams creating experiences for user groups with changing technological needs.
UX, ethnography and possibilities: for Libraries, Museums and ArchivesNed Potter
These slides are adapted from a talk I gave at the Welsh Government's Marketing Awards for the LAM sector, in 2017.
It offers a primer on UX - User Experience - and how ethnography and design might be used in the library, archive and museum worlds to better understand our users. All good marketing starts with audience insight.
The presentation covers the following:
1) An introduction to UX
2) Ethnography, with definitions and examples of 7 ethnographic techniques
3) User-centred design and Design Thinking
4) Examples of UX-led changes made at institutions in the UK and Scandinavia
5) Next Steps - if you'd like to try out UX at your own organisation
Study: The Future of VR, AR and Self-Driving CarsLinkedIn
We asked LinkedIn members worldwide about their levels of interest in the latest wave of technology: whether they’re using wearables, and whether they intend to buy self-driving cars and VR headsets as they become available. We asked them too about their attitudes to technology and to the growing role of Artificial Intelligence (AI) in the devices that they use. The answers were fascinating – and in many cases, surprising.
This SlideShare explores the full results of this study, including detailed market-by-market breakdowns of intention levels for each technology – and how attitudes change with age, location and seniority level. If you’re marketing a tech brand – or planning to use VR and wearables to reach a professional audience – then these are insights you won’t want to miss.
An immersive workshop at General Assembly, SF. I typically teach this workshop at General Assembly, San Francisco. To see a list of my upcoming classes, visit https://generalassemb.ly/instructors/seth-familian/4813
I also teach this workshop as a private lunch-and-learn or half-day immersive session for corporate clients. To learn more about pricing and availability, please contact me at http://familian1.com
Artificial intelligence (AI) is everywhere, promising self-driving cars, medical breakthroughs, and new ways of working. But how do you separate hype from reality? How can your company apply AI to solve real business problems?
Here’s what AI learnings your business should keep in mind for 2017.
3 Things Every Sales Team Needs to Be Thinking About in 2017Drift
Thinking about your sales team's goals for 2017? Drift's VP of Sales shares 3 things you can do to improve conversion rates and drive more revenue.
Read the full story on the Drift blog here: http://blog.drift.com/sales-team-tips
How to Become a Thought Leader in Your NicheLeslie Samuel
Are bloggers thought leaders? Here are some tips on how you can become one. Provide great value, put awesome content out there on a regular basis, and help others.
The International Journal of Engineering and Science (IJES)theijes
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.
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.
The International Journal of Engineering and Science (The IJES)theijes
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.
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.
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.
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 Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, 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.
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.
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.
The Effect of Radiation on the Convective Heat and Mass Transfer Flow of a Vi...inventionjournals
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FIDO Alliance Osaka Seminar: Passkeys and the Road Ahead.pdf
E0325022040
1. The International Journal Of Engineering And Science (IJES)
||Volume||3 ||Issue|| 2||Pages|| 22-40||2014||
ISSN(e): 2319 – 1813 ISSN(p): 2319 – 1805
www.theijes.com The IJES Page 22
Radiation and Mass Transfer Effects on An Unsteady Mhd
Convection Flow of A Micropolar Fluid Past In Infinite Heated
Vertical Moving Porous Plate In A Porous Medium
T. Sankar Reddy1
, P.Roja2
, N. Bhaskar reddy3
1
Dept. of Mathematics, Annamacharya Institute of Technology and Sciences, C.K Dinne (M&V), KADAPA,
Y.S.R.-516003
2
Dept. of Mathematics, Annamacharya Institute of Technology and Sciences, Rajampeta(M), KADAPA, YSR-
516126
3
Dept. of Mathematics, Sri Venkateswara University, Tirupati, CHITTOOR-517502
--------------------------------------------------------ABSTRACT--------------------------------------------------
An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a
porous medium bounded by an infinite vertical porous plate in an optically thin environment with time
dependent suction in the presence of thermal radiation field in the case of unsteady flow. The plate moves with
constant velocity in the longitudinal direction, and the free steam velocity follows an exponentially small
perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the
micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of
micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. It is observed that,
when the radiation parameter increases the velocity and temperature decrease in the boundary layer, whereas
when Grashof number increases the velocity increases. Also, the results of the skin- friction coefficient, the
couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of
fluid properties and flow conditions.
KEYWORDS: Mass transfer, MHD, Micropolar, Radiation, Sherwood Number, Skin-Friction.
----------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: 06 February 2014 Date of Acceptance: 05 March 2014
---------------------------------------------------------------------------------------------------------------------------------------
NOMENCLATURE:
A Suction velocity parameter
0
B Magnetic flux density.
C Concentration..
f
C Skin friction coefficient.
mC Couple stress coefficient
pC Specific heat at constant pressure .
D Chemical molecular diffusivity
g Acceleration due to gravity.
Gc Modified Grashof number.
Gr Grashof number.
j Microinertia per unit mass.
K Permeability of the porous medium.
k Thermal conductivity
M Magnetic field parameter.
N Model parameter.
n Parameter related to microgyration vector and shear stress.
Nu Nusult number.
R Radiation parameter
Rex Local Reynolds number
p Pressure.
2. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 23
Pr Prandtl number.
rq Radiative heat flux
R Radiation parameter
Sc Schmidt number.
Sh Sherwood number.
t Time.
T Temperature.
,u v Components of velocities along and perpendicular to the
plate.
0U Scale of free stream velocity.
0V Scale of suction velocity.
,x y Distances of along and perpendicular to the plate.
Greek symbols
Fluid thermal diffusivity
1 Absorption coefficient
B Plank’s function
Ratio of vertex viscosity and dynamic viscosity
c Coefficient of volumetric expansion with concentration
f Coefficient of volumetric expansion of the working fluid
Spin gradient viscosity
Scalar constant
Scalar constant 1
Dimensionless temperature
Coefficient of vertex(microrotation) viscosity
Dimensionless heat absorption coefficient
Fluid dynamic viscosity
Fluid density
c Electrical conductivity.
Fluid kinematic viscosity
1 Radiation absorption coefficient
r Fluid dynamic rotational viscosity
Friction coefficient
Angular velocity vector
Frequency
Subscripts
w Wall condition
Free steam condition
Superscripts
'
Differentiation with respect to y.
Dimensional properties
I. INTRODUCTION
Eringen [1] has proposed the theory of micropolar fluids which takes into account the inertial
characteristics of the microstructure particles which are allowed to undergo rotation. This theory may be applied
to explain the phenomenon of the flow of colloidal fluids, liquid crystals, fluids with additives, animal blood,
etc. The theory of thermomicropolar fluids has been developed by Eringen [2] by extending the theory of
micropolar fluids. The boundary layer flow of a micropolar fluid past a semi-infinite plate has been studied by
Peddieson and Mcnitt [3]. The flow characteristics of the boundary layer flow of a micropolar fluid over a semi-
3. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 24
infinite plate was studied by Ahmadi [4] by taking into account the gyration vector normal to the xy - plane and
the micro-inertia effects.Flow and heat transfer for a micropolar fluid through porous media have several
practical engineering applications such as transpiration cooling, packed-bed chemical reactors, geothermal
systems, crude oil extraction, ground water hydrology and building thermal insulation [5]. Sharma and Gupta
[6] considered thermal convection in micropolar fluids in porous medium. Kim [7] presented an analysis of an
unsteady convection flow of a micropolar fluid past a vertical porous plate embedded in a porous medium.
We know that the radiation effect is important under many non-isothermal situations. If the entire system
involving the polymer extrusion process is placed in a thermally controlled environment, then radiation could
become important. The knowledge of radiation heat transfer in the system can perhaps lead to a desired product
with sought characteristic. Recently, the effects of radiation on the flow and heat transfer of a micropolar fluid
past a continuously moving plate have been studied by many authors [8-12]. The study of flow and mass
transfer for an electrically conducting micropolar fluid past a porous plate under the influence of magnetic field
has attracted the interest of many investigators in view of its applications in many engineering problems such as
magnetohydrodynamic generators, plasma studies, nuclear reactors, oil exploration, geothermal energy
extractions and boundary layer in the field of aerodynamics. Mohammadien and Gorla [13] analyzed the effects
of magnetic field on the laminar boundary layer mixed convection flow of a micropolar fluid over a horizontal
plate. Chamkha et al. [14] considered the effect of radiation on free convection flow past a semi-infinite vertical
plate with mass transfer. El-Hakiem [15] analyzed the effects of magnetic field on natural convection with
temperature dependent viscosity in micropolar fluids. Effects of joule heating on the magnetohydrodynamic free
convection flow of a micropolar fluid were studied by El-Hakiem et al. [16]. El-Amin [17] solved the problem
of MHD free convection and mass transfer flow in micropolar fluid with constant suction. Kim [18] analyzed an
unsteady MHD mixed convection with mass transfer flow of a micropolar fluid past a vertical moving porous
plate via a porous medium. Raptis et al. [19] investigated a steady MHD asymmetric flow of an electrically
conducting fluid past a semi-infinite stationary plate in the presence of radiation. Mahmoud [20] studied the
radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal
conductivity. But the effect of thermal radiation and mass transfer on the non- Newtonian fluids with magnetic
field has not received any attention.
The objective of the present chapter is to analyze the radiation effects on hydrodynamic heat and mass
transfer flow of an incompressible micropolar fluid past a moving semi-infinite heated vertical porous plate in a
porous medium with time-dependent suction. It is assumed that the free stream to consist of a mean velocity
over which is superimposed an exponentially varying with time. The equations of continuity, linear momentum,
angular momentum, energy and diffusion, which govern the flow field, are solved by using a regular
perturbation method. The behavior of the velocity, microrotation, temperature, concentration, skin-friction,
Nusselt number and Sherwood number has been discussed for variations in the physical parameters.
II. MATHEMATICAL ANALYSIS
We consider a two-dimensional unsteady flow of a laminar, incompressible, electrically conducting and
micropolar fluid in an optically thin environment past a semi- infinite heated vertical moving porous plate
embedded in a uniform porous medium in the presence of thermal radiation is considered. The *
x - axis is taken
along the vertical porous plate in an upward direction and
*
y - axis is taken normal to the plate. The applied
magnetic field is considered in the direction perpendicular to the plate. It is assumed that there is no applied
voltage of which implies the absence of an electric field. The transversely applied magnetic field and magnetic
Reynolds number are very small and hence the induced magnetic field is negligible [21]. Viscous and Darcy
resistance terms are taken into account the constant permeability porous medium. The MHD term is derived
from an order-of-magnitude analysis of the full Navier-Stokes equations. It is assumed here that the hole size of
the porous plate is significantly larger than a characteristic microscopic length scale of the porous medium.
Following Yamamoto and Iwamura [22], the porous medium is regarded as an assemblage of small identical
spherical particles fixed in space. Due to the semi-infinite plane surface assumption, the flow variables are
functions of *
y and the time
*
t only. Now under the usual Boussinesq’s approximation, the equation of mass,
linear momentum, micro-rotation, energy and diffusion can be written as
Continuity:
*
*
0,
v
y
(1)
4. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 25
Linear momentum:
2* * * 2 * * *
* * * 2 *
0* * * *2 * *
1
2 ,
u u p u u cv g T T g C C B ur c rf
t y x y K y
(2)
Angular momentum:
* * 2 *
*
* * *2
*
,j v
t y y
(3)
Energy:
** * *
*
* * *2 *
2
1 rqT T T
v
kt y y y
, (4)
*
* 3
1* *
2
3 16 01 s
q T
q Tr
y y
(5)
Diffusion:
* * 2 *
* * *2
* *
,
C C u
v D
t y y
(6)
where
*
x , *
y and
*
t are the dimensional distances along and perpendicular to the plate and dimensional time
respectively.
**
,vu are the components of dimensional velocities along
*
x and
*
y directions, respectively, is
the density, is the kinematic viscosity, r is the kinematic rotational viscosity, g is the acceleration of
gravity, f and c is the coefficients of volumetric thermal and concentration expansion of the fluid , pc is
the specific heat at constant pressure, c is the fluid electrical conductivity, 0 is the magnetic induction, *
K is
the permeability of the porous medium, *
j is the micro inertia density,
*
is the component of the angular
velocity vector normal to the
* *
x y -plane, is the spin gradient viscosity, is the effective thermal diffusivity
of the fluid, k is the effective thermal conductivity, rq is the radiative heat flux, T is the dimensional
temperature, *
C is the dimensional concentration of the fluid and *
D is the chemical molecular diffusivity.
The third term on the right hand side of the momentum equation (2) denotes thermal and concentration
buoyancy effects, the fifth is the bulk matrix linear resistance, that is, Darcy term and the sixth is the MHD term.
Also, the second term on the right hand side of the energy equation (4) represents the radiative heat flux.
Equation (5) is the differential approximation for radiation under fairly broad realistic assumptions. In one space
coordinate *
y , the radiative heat flux *
q satisfies this nonlinear differential Eq. [5]. It is assumed that the porous
plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an
exponentially small perturbation law.
Under these assumptions, the appropriate boundary conditions for the velocity, microrotation, temperature and
concentration fields are
*
* * * ** * * * * * * *
,
*
( ) , , ( ) 0w
t t
p w w
u
u u T T T T e n C C C C e atw
y
y
(7)
* ** *
0
* * * *
(1 ), , 0,
t
u U U e T T C C as y
where
*
pu , wC and wT are the wall dimensional velocity, concentration and temperature, respectively, C and
T are the free stream dimensional concentration and temperature, respectively,
*
is a constant, is small less
5. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 26
than unity and 0U is a scale of free steam velocity. The boundary condition for microrotation variable
*
describes its relationship with the surface stress. In this equation, the parameter n is a number between 0
and 1 that relates the microgyration vector to the shear stress. The value 0n corresponds to the case where the
particle density is sufficiently large so that microelements close to the wall are unable to rotate. The value
0.5n is indicative of weak concentrations, and when 1n flows believed to represent turbulent boundary
layers (Rees and Bassom, [24]).
From the continuity Eq. (1), the suction velocity normal to the plate can be written as following form:
0
* **
(1 ),
t
v V Ae
(8)
where A is a real constant, and A are small less than unity, and 0V is the scale of suction velocity which is a
non-zero positive constant . The negative sign indicates that the suction is towards the plate. Outside the
boundary layer, Equation (2) gives
.
1 *2
0
*
**
*
*
*
UBU
Kdt
dU
dx
dp
(9)
Since the medium is optically thin with relatively low density and ( 1 absorption coefficient) <<1, the relative
heat flux given by Equation (4), in the spirit of Cogley et al. [23], becomes
*
2 *
4 1*
qr T T
y
(10)
where
0
*1
2
1
T
B
(11)
where B is plank’s function.
On the introducing the non-dimensional quantities
*
0
,
u
u
U
*
0
,
v
v
V
*
0
,
V y
y
*
0
,
U
U
U
*
0
,
p
p
u
U
U
*
0 0
,
U V
2
*0
,
4
V
t t
,
w
T T
T T
* *
* *
,w
w w
C C
C
C C
*
2
0
4
,
V
2
*0
2
,
V
j j
2
2
0
,K
kV
0
2
0
c B
M
V
,
2
2
2
0
4
w
p
R T T
C kV
, Pr
p pC C
k k
, (12)
2
0 0
( )f wg T T
Gr
U V
,
* *
( )
2
0 0
g C Cc wGc
U V
*
Sc
D
Furthermore, the spin-gradient viscosity which gives some relationship between the coefficients of viscosity
and micro-inertia, is defined as
1* *
( ) 1
2 2
j j
;
(13)
where denotes the dimensionless viscosity ratio, in which is the coefficient of gyro-viscosity (or vertex
viscosity).
In view of Equations (5) and (8)-(13), the governing Equations (2)-(4) and (6) reduce to the following non-
dimensional form:
2
2
1 1
1 1 2 .
4 4
t
r c
dUu u u
Ae G G C N U u
t y dt y y
(14)
,
1
1
4
1
2
2
yy
Ae
t
t
(15)
2
2
2
1 1
1
4 Pr
t
Ae R
t y y
, (16)
.
1
1
4
1
2
2
y
C
Scy
C
Ae
t
C t
(17)
6. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 27
where 1
,N M
K
*
2
2
j
and Gr , Gc , Pr , K, M , R and Sc denote the Grashof number, solutal Grashof number, prandtl number,
permeability of the porous medium, magnetic field parameter, Radiation parameter and the Schmidt number,
respectively.
The boundary conditions (8) are than given by the following dimensionless equations:
,pUu 1 ,t
e
y
u
n
, 1
t
C e
at 0y ,
,1 t
eu
0 , 0w , 0C as y (18)
III. SOLUTION OF THE PROBLEM
In order to reduce the above system of partial differential equations to a system of ordinary differential
equations in dimensionless form, we may represent the velocity, microrotation, temperature and concentration in
the neighbourhood of the porous plate as
10
2t
u u y e u y O
...
10
2t
y e y O
...
10
2t
y e y O
… (19)
10
2t
C C y e C y O
…
By Substituting Equation (19) into Equations (13)-(16), and equating the harmonic and non-harmonic
terms, and neglecting the higher-order terms of 2
0 , we obtain the following pairs of equations for
0000 ,,, Cu and 1111 ,,, Cu .
0 0 0 0 0 0
" ' '
(1 ) 2cu u Nu N G G Cr (20)
" ' ' '
(1 ) ( ) ( ) 21 1 1 0 1 1 1
4 4
u u N u N Au G G Cr c
(22)
1 1 1 0
" ' '
4
A
(23)
2
0 0 0
'' '
Pr 0R (24)
1 1 1 0
2'' '
Pr Pr Pr
4
R A
(25)
0 0
'' '
0C ScC (26)
1 1 1 0
'' ' '
4
C ScC Sc AScC
(27)
where the prime denote differentiation with respect to y . The corresponding boundary conditions can be written
as
0 ,pu U 1 0,u
'
,0 0nu
'
,1 1nu 1,0 11 , 0 1,C 1,1C at 0y
0 1,u 1 1u , 0 0 , 1 0, 0 0,C 0,1C 0 0, 1 0, as y (30)
Without going into details, the solutions of Eqs. (20)-(27) subject to Eq. (30) can be shown to be
3 5 61 2 4
1 2 3 4 5 6 7 8
31, 1 1 2 3 4
1
m y m y m ym y m y m yt Scy y
m ym y Scy y
u y t a e a e a e a e
e b e b e b e b e b e b e b e b e
(31)
1 2 1
5
4
,
m yy t yA
y t c e e c e c e
(32)
7. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 28
33 34 4
4
,
t Amm y m ym y m y
y t e e e e e
(33)
6 6
4
,
m yScy t ScyAScm y
C y t e e e e e
(34)
The skin-friction, the couple stress coefficient, the Nusselt number and the Sherwood number are
important physical parameters for this type of boundary layer flow. These parameters can be defined and
determined as follows.
*
* *
**
* 0
( ) ,
0w
y
u
yy
0 0
0
*
2
2 1 (1 )
y
w
C f
U V
u
n
y
= 1 1 2 2 3 3 4 4 5 6 6 6 7 82 1 (1 ) ( 1 1 2 3 3 4
t
n a m a m a Sc a e b m b m b m b m b m b m b Sc b
(35)
,
0
*
*
*
y
w
y
M
0
1
1
2 0
2
41 11 51 2
2
MwCm
jU
y y
A kt
k e c m
(36)
*
* 0
,
T y
y
Nu xx
T Tw
1
Re
0
2
4 43 313 4
Nux x
y y
Am Amt
m e m
(37)
,
* * *
( )
j xwShx
D C Cw
where
*
*
,
*
* 0
C
j Dw
y
y
6
2
1
Re
0
4 4
1
t
C
Shx x
y y
ASc ASc
Sc e m
(38)
where 0
Re V xx is the Reynolds number.
8. Radiation and Mass Transfer Effects On An…
www.theijes.com The IJES Page 29
IV. RESULTS AND DISCUSSION
The formulation of MHD free convection flow and mass transfer of an incompressible electrically
conducting micropolar fluid along a semi-infinite heated vertical porous moving plate in a porous medium in the
presence of thermal radiation field has been performed in the preceding sections. This enables us to carry out the
numerical computations for the distribution of translational velocity, microrotation, temperature and
concentration across the boundary layer for various values of the parameters. In the present study we have
chosen 1t , 0.01 , 0.001 and 0.5A , while , n , Gr , Gc , P
U , M , K , Pr , R and Sc ,are varied over
a range, which are listed in the figure legends.
The effect of viscosity ratio on the translational velocity and microrotation profiles across the
boundary layer are presented in Fig. 1. It is noteworthy that the velocity distribution greater for a Newtonian
fluid ( 0 ) with given parameters, as compared with micropolar fluids until its peak value reaches. The
translational velocity shows a decelerating nature near the porous plate as -parameter increases, and then
decays to the relevant free stream velocity. In addition, the magnitude of microrotation at the wall is decreased
as -parameter increases. However, the distributions of microrotation across the boundary layer do not show
consistent variations with increment of -parameter. The translational velocity and the microrotation profiles
against spanwise coordinate y for different values of Grashof number Gr and modified Grashof number Gc are
described in Figs. 2 and 3 respectively. It is observed that the velocity increases as Gr or Gc increase, but
decreases due to microrotation. Here the positive values of Gr corresponds to a cooling of the surface by natural
convection. In addition, the curves observed that the peak value of velocity increases rapidly near the wall of the
porous plate as Gr or Gc increases, and then decays to the free stream velocity.
Fig. 4 illustrates the variation of velocity and microrotation distribution across the boundary layer for
various values of the plate velocity pU in the direction of the fluid flow. It is obvious that the values of
translational velocity and microrotation on the porous plate are increased as the plate velocity increases, and
then decayed to the free stream velocity. For different values of the magnetic field parameter M , the
translational velocity and microrotation profiles are plotted in Fig. 5. It is obvious that the effect of increasing
values of M -parameter results in a decreasing velocity distribution across the boundary layer. Further-more, the
results shows the magnitude of microrotation on the porous plate is decreased as M -parameter increases. For
different values of the Schmidt number Sc , translational velocity and the microrotation profiles are plotted in
Fig. 6. It is obvious that the effect of increasing values of Sc results in a decreasing velocity distribution across
the boundary layer. Furthermore, the results show that the magnitude of microrotation on the porous plate is
decreased as Sc increases. For different values of the radiation parameter R, the velocity and temperature
profiles are plotted in Fig. 7. It is obvious that an increase in the radiation parameter R results in decreasing
velocity and temperature within the boundary layer, as well as a decreased thickness of the velocity and
temperature boundary layers. This is because the large R-values correspond to an increased dominance of
conduction over radiation thereby decreasing buoyancy force (thus, vertical velocity) and thickness of the
thermal and momentum boundary layers.
Typical variations in the temperature profiles along the spanwise coordinate are shown in Fig. 8 for
different values of Prandtl number Pr . The results show that an increase of Prandtl number results in a
decreasing temperature distribution across the boundary layer. Fig. 9 shows the concentration profiles across
the boundary layer for various values of Schmidt number Sc . The Figure shows that an increase in Sc results in a
decreasing the concentration distribution, because the smaller values of Sc are equivalent to increasing the
chemical molecular diffusivity. Numerical values for functions proportional to shear stress fC , wall couple
stress mC , heat and mass transfer rates are given in Tables 1-3. It is note that both the skin–friction coefficient
and the wall couple stress coefficient decrease, as Sc increases. In addition, it is interesting to note for
micropolar fluids that the skin-friction coefficient decreases as the n-parameter increases, while, an increase in n
results in a decrease of the wall couple stress coefficient. From the analytical results, it can be seen that the rates
of heat transfer and mass transfer depend only on Prandtl number and Schmidt number, respectively. Therefore,
concentration gradient at the porous plate increases as Schmidt number increases. From Tables 2 and 3 it can be
seen that f
C and m
C decrease as Pr or R increases, but increases due to the absolute values of the heat transfer
rate.
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0 1 2 3 4 5 6 7 8
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
y
u
=0.0, 0.1, 0.5, 1.0, 3.0
=0.001 =0.01 Sc=0.4 t=1.0
Gr=2.0 Gc=2.0 R=0.5
Up=0.5 n=0.5 A=0.0
Pr=0.71 M=2.0 K=1.0
(a)
0 1 2 3 4 5 6 7 8
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
y
=3.0
=1.0
=0.5
=0.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.01 Sc=0.4
Gr=2.0 Gc=2.0 R=0.5
Pr=0.71 M=2.0 K=1.0
(b)
Fig. 1 Velocity and microrotation profiles for various values of .
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0 1 2 3 4 5 6 7 8
0.5
1
1.5
2
y
u
Gr=1.0, 2.0, 4.0, 6.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
M=2.0 Gc=2.0 R=0.5
Pr=0.71 K=1.0 Sc=0.4
(a)
0 1 2 3 4 5 6 7 8
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
y
Gr= 6.0, 4.0, 2.0, 1.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
M=2.0 Gc=2.0 R=0.5
Pr=0.71 K=1.0 Sc=0.4
(b)
Fig. 2 Velocity and microrotation profiles for various values of Gr.
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0 1 2 3 4 5 6 7 8
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
y
u
Gc=1.0, 2.0, 4.0, 6.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
M=2.0 Gr=2.0 R=0.5
Pr=0.71 K=1.0 Sc=0.4
(a)
0 1 2 3 4 5 6 7 8
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
y
Gc= 6.0, 4.0, 2.0, 1.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
M=2.0 Gr=2.0 R=0.5
Pr=0.71 K=1.0 Sc=0.4
(b)
Fig. 3 Velocity and microrotation profiles for various values of Gc.
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0 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
y
u
Up=1.0, 0.5, 0.0
=0.001 =0.1 =0.01 t=1.0
Gr=2.0 n=0.5 A=0.0
Gc=2.0 R=0.5 K =1.0
Sc=0.4 M=2.0 Pr=0.71
(a)
0 1 2 3 4 5 6
-2.5
-2
-1.5
-1
-0.5
0
y
=0.001 =0.1 =0.01 t=1.0
Gr=2.0 n=0.5 A=0.0
Gc=2.0 Pr=0.71 R =0.5
Sc=0.4 M=2.0 K =1.0
Up=1.0, 0.5, 0.0
(b)
Fig. 4 Velocity and microrotation profiles for various values of Up.
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0 1 2 3 4 5 6 7 8
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
y
u
M=0.0, 1.0, 2.0, 5.0
=0.001 =0.1 =0.01 t=1.0
Gr=2.0 Gc=2.0 R=0.5
Up=0.5 n=0.5 A=0.0
Pr=0.71 K=1.0 Sc=0.4
(a)
0 1 2 3 4 5 6 7 8
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
y
M=5.0, 2.0, 1.0, 0.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
Gr=2.0 Gc=2.0 R =0.5
Pr=0.71 K =1.0 Sc=0.4
(b)
Fig. 5 Velocity and microrotation profiles for various values of M.
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0 1 2 3 4 5 6 7 8 9 10
0.4
0.6
0.8
1
1.2
1.4
1.6
y
u
Sc=0.7, 0.6, 0.4, 0.2
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
Gr=2.0 Gc=2.0 R=0.5
Pr=0.71 M=2.0 K=1.0
(a)
0 1 2 3 4 5 6
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
y
Sc=0.7, 0.6, 0.4, 0.2
Up=0.5 =0.001 =0.1 t=1.0
Gr=2.0 Gc=2.0 =0.01
K=1.0 A=0.0 Pr=0.71
M=2.0 n=0.5 R=0.5
(b)
Fig. 6 Velocity and microrotation profiles for various values of Sc.
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0 1 2 3 4 5 6 7 8
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
y
u
R=2.0, 1.0, 0.5, 0.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
Gr=2.0 Gc=2.0 Sc=0.4
Pr=0.71 M=2.0 K=1.0
(a)
0 1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
R=0.0, 0.5, 1.0, 2.0
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
Gr=2.0 Gc=2.0 Pr=0.71
Sc=0.4 M=2.0 K=1.0
(b)
Fig. 7 Velocity and temperature profiles for various values of R.
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0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
Pr= 5.0, 2.0, 1.0, 0.71
Up=0.5 n=0.5 A=0.0 t=1.0
=0.001 =0.1 =0.01
Gr=2.0 Gc=2.0 R=0.5
Sc=0.4 M=2.0 =1.0
Fig. 8 Temperature profiles for different values of Pr.
0 1 2 3 4 5 6 7 8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
y
C
=0.001 =0.1 =0.01 t=1.0
Gr=2.0 Gc=2.0 R=0.5
Up=0.5 n=0.5 A=0.0
Pr=0.71 M=2.0 K=1.0
Sc=0.2
Sc=0.4
Sc=0.6
Sc=0.8
Fig. 9 Concentration profiles for various values of Sc.
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TABLE IIII: Value of fC , mC ,
1
(0) and
1
(0)C for various values of R with 1.0t , 0.001 , 0.1 ,
0.01 , 0.0A , 0.5n , 2.0M , 0.4Sc , Pr 0.71 , 1.0K , 2.0Gr , 2.0Gc , and 0.5pU .
R f
C m
C
1
(0)
1
(0)C
0.0 6.7795 1.6173 0.7112 0.4004
0.5 6.5454 1.5615 0.9695 0.4004
1.0 6.2466 1.4903 1.4178 0.4004
2.0 5.8512 1.3961 2.3888 0.4004
V. CONCLUSIONS
In this work the problem of combined heat and mass transfer flow of a viscous incompressible
electrically conducting micropolar fluid past a steadily moving infinite vertical plate under the action of a
uniform magnetic field with thermal radiation field is investigated. The resulting governing equations are solved
by perturbation scheme. Numerical results are presented to illustrate the details of the MHD convective flow and
mass transfer characteristics and their dependence on the fluid properties and flow conditions. We may conclude
that the translational velocity across the boundary layer and the magnitude of microrotation at the wall are
decreased with increasing values of M , Sc and Pr , while they show opposite trends with increasing values of
n , Gr and Gc . Also, we found that f
C and m
C decreased as R increases, but it increased due to the absolute
values of the heat transfer rate.
APPENDIX
1
1 1 4 (1 )1
2 1
m N
,
1
1 1 4( )(1 )2
2 1 4
m N
,
2
2
Pr 4
1 13
2 Pr
R
m
,
2 2
2
Pr 4( Pr )
1 14
2 Pr
R
m
,
1 15
2
m
, 6 1 1
2
Sc
m
Sc
11 2 3 4a U a a ap ,
2 2
1 3 3
Gr
a
m m N
,
3 2
1
Gc
a
Sc Sc N
,
2
4 1 1 12
1
a k k
N
,
1 1
1
2
1 ( )1 1
4
Am a
b
m m N
,
(1 )5 72 1 3 4 6 8b b b b b b b b ,
4
3 2
3
2
1 ( )3 3
4
Gr
Am a
b
m m N
,
4 31
4
2
1 ( )4 4
4
Am
Gr
b
m m N
,
19. Radiation and Mass Transfer Effects On An…
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2 5
5 2 2 2
2
1 ( )5 5
4
m
b k k
m m N
,
4
1
6
2
1 ( )6 6
4
ASc
Gc
b
m m N
,
4
3
7
2
1 ( )
4
Gc
ASc a
b
Sc Sc N
,
2
8 1
3
8
2
1 ( )
4
k
A a
b
N
,
1 1 2 3 1 3 1
1 1
1
1
p
n
k U m a m m a Sc m
n m
3 4 2
2
1 52 2
k nk m
k
n m m
,
73 1 1 1 3 3 4 4 6 6 8
A
k k n b m b m b m b m b Sc b
(1 )5 74 1 4 6 8k b b b b b b .
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