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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
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.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
A steady two-dimensional MHD free convection and mass transfer flow past an inclined vertical surface in the presence of heat generation and a porous medium have been studied numerically when the fluid viscosity and thermal conductivity are assumed to be vary as inverse linear function of temperature. The governing partial differential equations are reduced to a system of ordinary differential equations by introducing similarity transformations. The non-linear similarity equations are solved numerically by applying the Runge-Kutta method of fourth order with shooting technique. The numerical results are presented graphically to illustrate influence of different values of the parameters on the velocity, temperature and concentration profiles. Skin friction, Nusselt number and Sherwood number are also completed and presented in tabular form.
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.
STEADY FLOW OF A VISCOUS FLUID THROUGH A SATURATED POROUS MEDIUM AT A CONSTAN...Journal For Research
In this paper the Steady flow of a viscous fluid through a porous medium over a fixed horizontal, impermeable and thermally insulated bottom. The flow through the porous medium satisfies the general momentum and energy equations are obtained when the temperature on the fixed bottom and on free surface prescibed. By using Galerkin Method, the expression for Velocity and Drag force are obtained. The Galerkin Method endowed with distinct features that account for its superiority over competing methods. The effect of different parameters on Velocity and Drag force are discussed with the help of graphs.
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.
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
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.
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
Heat and Mass Transfer Hydromagnetic Radiative Casson Fluid Flow over an Expo...inventionjournals
The present paper examines the hydromagnetic two-dimensional boundary layer flow of a nonNewtonian fluid accompanied by heat and mass transfer towards an exponentially stretching sheet in the presence of chemical reaction and thermal radiation. Casson model is used to characterize non-Newtonian fluid behavior. Using the similarity transformations, the governing partial differential equations are transformed into self-similar ordinary differential equations is solved by using Matlab bvp4c package. The effects of pertinent parameters are presented in both graphical and tabular form.
Abstract— A scientific investigation is created to examine the nonlinear unfaltering blended convection limit
layer stream and warmth exchange of an incompressible digression hyperbolicnon-Newtonian liquid from a
non-isothermal wedge in the nearness of attractive field. The changed preservation conditions are understood
numerically subject to physically fitting limit conditions utilizing a second-arrange precise verifiable limited
distinction Keller Box method. The numerical code is accepted with past studies. The impact of various rising
non-dimensional parameters, to be specific Weissenberg number (We), power law record (n), blended
convection parameter, weight angle parameter (m), Prandtl number (Pr), Biot number, attractive parameter
(M)and dimensionless extraneous direction on speed and temperature development in the limit layer
administration are inspected in subtle element. Moreover, the impacts of these parameters on surface warmth
exchange rate and nearby skin erosion are additionally examined. Approval with prior Newtonian studies is
introduced and amazing relationship accomplished. It is found that speed is lessened with expanding We,
while, temperature is increased. Expanding n improves speed yet diminishes temperature, a comparable
pattern was seen. An expanding M is found to decline speed however temperature increments.
Keywords— Magnetic parameter, Mixed Convection parameter, Non-Newtonian digression hyperbolic liquid,
power law index, Weissenberg number, Weight inclination parameter.
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...IJERA Editor
An analysis is made for the two-dimensional laminar boundary layer flow of a viscous, incompressible
fluid,along an infinite porous hot horizontal continuous moving plate. The governing system of partial
differential equations was transformed into ordinary differential equations before being solve by Natural
transformation. The effects of various physical parameters, such as Eckert number Ec , Prandtlnumber Pr ,
plate velocity α and heat source/sink parameter Sare presented and discussed. It is found that the plate velocity
significantly effects the flow and heat transfer.
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.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability
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.
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.
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.
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.
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
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.
Effects of Variable Viscosity and Thermal Conductivity on MHD free Convection...theijes
A steady two-dimensional MHD free convection and mass transfer flow past an inclined vertical surface in the presence of heat generation and a porous medium have been studied numerically when the fluid viscosity and thermal conductivity are assumed to be vary as inverse linear function of temperature. The governing partial differential equations are reduced to a system of ordinary differential equations by introducing similarity transformations. The non-linear similarity equations are solved numerically by applying the Runge-Kutta method of fourth order with shooting technique. The numerical results are presented graphically to illustrate influence of different values of the parameters on the velocity, temperature and concentration profiles. Skin friction, Nusselt number and Sherwood number are also completed and presented in tabular form.
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.
STEADY FLOW OF A VISCOUS FLUID THROUGH A SATURATED POROUS MEDIUM AT A CONSTAN...Journal For Research
In this paper the Steady flow of a viscous fluid through a porous medium over a fixed horizontal, impermeable and thermally insulated bottom. The flow through the porous medium satisfies the general momentum and energy equations are obtained when the temperature on the fixed bottom and on free surface prescibed. By using Galerkin Method, the expression for Velocity and Drag force are obtained. The Galerkin Method endowed with distinct features that account for its superiority over competing methods. The effect of different parameters on Velocity and Drag force are discussed with the help of graphs.
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.
The effect of magnetic field on the boundary layer flow over a stretching she...IAEME Publication
The boundary layer flow created due to a linearly stretching sheet in a nanofluid is studied numerically. The boundary value problem consisting of nonlinear partial differential equations are converted into nonlinear ordinary differential equations, using similarity transformation and are solved numerically using Runge-Kutta Fourth order method, with shooting technique. The transport equations include the effects of Brownian motion and thermophoresis.
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.
MHD CASSON FLUID FLOW AND HEAT TRANSFER WITH PST AND PHF HEATING CONDITIONS D...IAEME Publication
In the present paper two-dimensional flow of non-Newtonian MHD flow of Casson fluid heat transfer with PST & PHF is considered. Using Nevier Stoke’s Equations of Motion the momentum and energy equations of Casson fluid are derived. These governing equations of motion and temperature are non-linear partial differential equations which are tedious to solve as they are, hence these partial differential equations are converted into Ordinary differential equations using suitable similarity transformations. These ODE’s are then solved numerically by the efficient Runge Kutta Fehlberg method. Effects of various governing parameters on the flow and heat transfer profiles are analyzed. Further the numerical Values of Wall temperature and Wall temperature Profiles are calculated and discussed in detail through graphs in both the cases of PST and PHF.
Heat and Mass Transfer Hydromagnetic Radiative Casson Fluid Flow over an Expo...inventionjournals
The present paper examines the hydromagnetic two-dimensional boundary layer flow of a nonNewtonian fluid accompanied by heat and mass transfer towards an exponentially stretching sheet in the presence of chemical reaction and thermal radiation. Casson model is used to characterize non-Newtonian fluid behavior. Using the similarity transformations, the governing partial differential equations are transformed into self-similar ordinary differential equations is solved by using Matlab bvp4c package. The effects of pertinent parameters are presented in both graphical and tabular form.
Abstract— A scientific investigation is created to examine the nonlinear unfaltering blended convection limit
layer stream and warmth exchange of an incompressible digression hyperbolicnon-Newtonian liquid from a
non-isothermal wedge in the nearness of attractive field. The changed preservation conditions are understood
numerically subject to physically fitting limit conditions utilizing a second-arrange precise verifiable limited
distinction Keller Box method. The numerical code is accepted with past studies. The impact of various rising
non-dimensional parameters, to be specific Weissenberg number (We), power law record (n), blended
convection parameter, weight angle parameter (m), Prandtl number (Pr), Biot number, attractive parameter
(M)and dimensionless extraneous direction on speed and temperature development in the limit layer
administration are inspected in subtle element. Moreover, the impacts of these parameters on surface warmth
exchange rate and nearby skin erosion are additionally examined. Approval with prior Newtonian studies is
introduced and amazing relationship accomplished. It is found that speed is lessened with expanding We,
while, temperature is increased. Expanding n improves speed yet diminishes temperature, a comparable
pattern was seen. An expanding M is found to decline speed however temperature increments.
Keywords— Magnetic parameter, Mixed Convection parameter, Non-Newtonian digression hyperbolic liquid,
power law index, Weissenberg number, Weight inclination parameter.
Boundry Layer Flow and Heat Transfer along an Infinite Porous Hot Horizontal ...IJERA Editor
An analysis is made for the two-dimensional laminar boundary layer flow of a viscous, incompressible
fluid,along an infinite porous hot horizontal continuous moving plate. The governing system of partial
differential equations was transformed into ordinary differential equations before being solve by Natural
transformation. The effects of various physical parameters, such as Eckert number Ec , Prandtlnumber Pr ,
plate velocity α and heat source/sink parameter Sare presented and discussed. It is found that the plate velocity
significantly effects the flow and heat transfer.
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.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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 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.
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.
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.
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.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability
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.
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.
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.
Heat and Mass Transfer Hydromagnetic Radiative Casson Fluid Flow over an Expo...inventionjournals
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The International Journal of Engineering and Science (The IJES)
1. The International Journal Of Engineering And Science (IJES)
||Volume||2 ||Issue|| 9 ||Pages|| 51-57||2013||
ISSN(e): 2319 – 1813 ISSN(p): 2319 – 1805
www.theijes.com The IJES Page 51
Free Convective Oscillatory Flow of a Visco-Elastic Fluid Past A
Porous Plate In Presence Of Radiation And Mass Transfer
1
Madhumita Mahanta 2
Rita Choudhury
1
Department of Mathematics, Girijananda Chowdhury Institute of Management and Technology,
Guwahati-781 017, Assam, India
2
Department of Mathematics, Gauhati University, Guwahati-781 014, Assam, India
--------------------------------------------------------ABSTRACT--------------------------------------------------
The effects of heat and mass transfer on unsteady free convective oscillatory flow of an optically thin fluid past
a porous plate in presence of radiation have been investigated. The flow is characterized by the second-order
fluid model. Analytical solutions for velocity, temperature and concentration of the governing equations of fluid
flow are obtained by using perturbation technique. Also, the coefficients of skin friction, rate of heat transfer
and rate of mass transfer at the plate are calculated. The profiles of velocity and skin friction are presented
through graphs for various values of physical parameters to discuss the effects of the visco-elastic parameter
involved in the solution.
KEY WORDS: free convection, mass transfer, radiation, oscillatory flow, visco-elastic fluid.
----------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: 26, August, 2013 Date of Acceptance: 20, September 2013
---------------------------------------------------------------------------------------------------------------------------------------
I. INTRUDUCTION
Heat and mass transfer on unsteady flow past a porous plate in presence of radiation has gained interest
owing to its applications in the fields of plasma physics, geophysics, geohydrology, environmental engineering
etc. Some examples of such areas are gas turbines, various propulsion devices for aircrafts, missiles, satellites,
space vehicles etc. Because of wide applications of such flows, numerous scholars have paid their attention in
this field. Seddeek et al. [1] have studied the effects of thermal diffusivity on heat transfer over a stretching
surface with variable heat flux in the presence of radiation. The effect of radiation on free convective flow of
fluid has been investigated by Hossain et al. [2, 3] and Raptis et al. [4]. Raptis [5], Badruddin et al. [6] and
Mukhopadhyay et al. [7] have considered the flow through a porous medium in presence of radiation. The MHD
flow adjacent to a non-isothermal wedge in the presence of heat source or sink has been analyzed by Chamkha
et al. [8] and Duwairi [9]. England et al. [10] have studied the thermal radiation effects of an optically thin gray
gas bounded by a stationary vertical plate. Bestman et al. [11] have investigated the hydromagnetic free
convection flow with radiation and heat transfer in a rotating and optically thin fluid. The effect of radiation in
an optically thin fluid past a vertical plate (when the induced magnetic field is taken into account) has been
studied by Raptis et al. [12]. The unsteady flow of an optically thin fluid in the presence of convection and mass
transfer has been investigated by Raptis et al. [13]. The free convection one dimensional flow with radiation and
heat transfer for an optically thin fluid past a vertical oscillating plate in the presence of chemical reaction has
been studied by Manivannan et al. [14]. Vijayalakshmi [15] has investigated the effects of radiation on free
convection flow past an impulsively started vertical plate in a rotating fluid. For an optically thin fluid the two-
dimensional free convective oscillatory flow and mass transfer past a porous plate in presence of radiation has
been investigated by Raptis [16].
In view of the above, the unsteady free convective flow of a visco-elastic fluid past an infinite vertical
porous plate in the presence of radiation has been considered in this paper. The constitutive equation for second-
order fluid [Coleman & Noll1 (1960)] is
kjikijijijij
AAAAp )1()1(3)2(2)1(1
(1.1)
where ij
are the stress tensor, p the hydrostatic pressure, )( i
A are kinematic Rivlin-Erickson
tensors; 321
,, are material constants describing viscosity, elasticity and cross-viscosity where
02
from thermodynamic consideration [Coleman and Markovitz (1964)]. Equation (1.1) is valid for low
rates of shear.
2. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 52
II. MATHEMATICAL FORMULATION
We consider the unsteady two-dimensional flow past an infinite vertical porous plate through which
suction occurs with constant velocity. Let -axis be taken along the direction of the plate and -axis be normal
to it. All the fluid properties are considered constant except that the influence of density variations with
temperature and concentration. The radiation to the -direction is considered negligible as compared to the -
direction. The governing equations of flow are
Equation of Continuity:
0
y
v
(2.1)
i.e. 0
vv ( 0
v >0) (2.2)
Equation of motion:
])([
)()(
3
3
02
2
22
2
1
0
y
u
v
t
u
yy
u
CCgTTg
td
Ud
y
u
v
t
u
(2.3)
Equation of energy:
)(
16
3
2
2
0
TT
C
Td
y
T
Cy
T
v
t
T
pp
(2.4)
Equation of concentration:
2
2
0
y
C
D
y
C
v
t
C
(2.5)
subject to boundary conditions
(2.6)
Here and are components of the velocity in the directions of and -axis, is the time, is the free stream
velocity, g is the acceleration due to gravity, are the coefficients of volume expansion for heat and mass
transfer, and are the fluid temperature and concentration, ν1, ν2 are the kinematic coefficients of viscosity
and elasticity, ρ is the density of the fluid, Cp is the specific heat at constant pressure, κ is the thermal
conductivity, d is the absorption coefficient, is the Stefan-Boltzman constant, is the fluid temperature far
away from the plate, and are the molar concentration at the plate and far away from the plate, D is the
chemical diffusivity, is the radiative heat flux, is the mean free stream velocity, is the frequency of
vibration of the fluid and is the constant suction velocity.
Let us introduce the following non-dimensional quantities
(2.7)
Introducing the non-dimensional quantities (2.7), the equations (2.3) to (2.5) reduce to
])(
4
1
[
4
1
4
1
3
3
2
2
2
2
y
u
t
u
y
y
u
CGTG
dt
dU
y
u
t
u
cr
(2.8)
3. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 53
ST
y
T
y
T
t
T
Pr
2
2
)
4
1
( (2.9)
2
2
)
4
1
(
y
C
y
C
t
C
S c
(2.10)
subject to boundary conditions
(2.11)
where is the Grashof number for heat transfer, is the Grashof number for mass
transfer, is the Prandtl number, is the radiation parameter, is the Schmidt
number and is the visco-elastic parameter.
III. METHOD OF SOLUTION
To solve the equations (2.8) to (2.10) subject to boundary conditions (2.11), we assume the solutions for
as follows
ti
c
ti
c
ti
c
eyCyCtyC
eyTyTtyT
eyuyutyu
)()(),(
)()(),(
,)()(),(
10
10
10
(3.1)
Substituting (3.1) into equations (2.8) to (2.10) and equating the harmonic and non-harmonic terms, we get
00000
CGTGuuu cr
(3.2)
4
4
)
4
1(
11
1111
i
CGTG
u
i
uu
i
u
cr
(3.3)
000
STTPT r
(3.4)
1111
4
STTP
i
TPT rr
(3.5)
000
CSC c
(3.6)
0
4
111
CS
i
CSC cc
(3.7)
where the primes denote the differentiation with respect to y.
The corresponding boundary conditions are
(3.8)
Substituting the solutions of equations (3.2) to (3.7) under the boundary conditions (3.8), we obtain
ya
e
a
tyT 1
1
1
),(
(3.9)
yS c
etyC
),( (3.10)
4. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 54
where ]4[
2
1 2
1
SPPa rr
and
(3.11)
where and .
Separating real and imaginary parts and taking only the real part, we obtain the velocity field for t in the
form
IV. SKIN FRICTION, RATE OF HEAT AND MASS TRANSFER
The non-dimensional skin friction w
at the plate (y=0) is given by
)]0()0()1[(
)]0()0([
11
00
uuie
uu
ti
(4.1)
The dimensionless heat transfer co-efficient at the plate is given by
1
0
y
u
y
T
N (4.2)
Similarly, the mass transfer co-efficient h
S at the plate is given by
c
y
h
S
y
C
S
0
(4.3)
V. RESULTS AND DISCUSSION
The aim of the problem is to bring out the effects of the visco-elastic parameter on the flow
characteristics. The visco-elastic effect is exhibited through the non-dimensional parameter α. The
corresponding results for Newtonian fluid can be deduced from the above results by setting 0 . Figures 1 to
3 illustrate the variations of velocity profile against y for various values of visco-elastic parameter
along with various values of Prandtl number (Pr), Grashof number for heat transfer (Gr),
Grashof number for mass transfer (Gc), radiation parameter (S), Schmidt number (Sc) and some fixed values
ω=0.1, ε=0.02 and ωt=π. It is noticed from the figures that the velocity of the fluid enhances at each point of the
flow field in both Newtonian and non-Newtonian cases. Again, the velocity profile accelerates with the increase
of the absolute values of visco-elastic parameter in comparison with that of Newtonian fluid flow phenomenon.
Also, it is seen that the velocity increases during the rising behaviour of the Grashof number for mass transfer
5. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 55
(Fig. 1 and Fig. 2) but reverse behaviour is observed in case of Schmidt number (Fig. 1 and Fig. 3) in both
Newtonian and non-Newtonian cases.The variations of shearing stress at the plate (y=0) against various values
of flow parameters are presented in figures 4, 5 and 6. The figures reveal that the shearing stress at the plate
decreases due to the increase of the absolute values of visco-elastic parameter along with the increase of the
Prandtl number (Fig. 4), Grashof number for heat transfer (Fig. 5) and frequency of oscillation (Fig. 6).
The temperature and concentration fields are not significantly affected by visco-elastic parameter.
VI. CONCLUSION
The problem of unsteady two-dimensional free convective flow past an infinite vertical porous plate is
studied analytically. The results of investigation may be summarized in the following conclusions:
The velocity distribution accelerates and then decelerates in both Newtonian and non-Newtonian cases.
The rising trend of the absolute values of the visco-elastic parameter depicts the increase of velocity profile
in comparison to that of Newtonian fluid.
The growth of the absolute values of the visco-elastic parameter diminishes the nature of the skin friction at
each point of the fluid region with the increase of the Prandtl number, Grashof number for heat transfer and
frequency of oscillation respectively.
The temperature and the concentration fields are unaffected due to the variation of visco-elastic parameter.
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
u
y
u(α=0)
u(α=-0.25)
u(α=-0.4)
Fig. 1 Variation of velocity u against y for
Pr=5, Gr=5, Gc=2, Sc=0.22, S=0.2, ω=0.1, ε=0.02
0
2
4
6
8
10
12
14
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
u
y
u(α=0)
u(α=-0.25)
u(α=-0.4)
Fig. 2 Variation of velocity u against y for
Pr=5, Gr=5, Gc=4, Sc=0.22, S=0.2, ω =0.1, ε=0.02
6. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 56
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
u
y
u(α=0)
u(α=-0.25)
u(α=-0.4)
Fig. 3 Variation of velocity u against y for
Pr=5, Gr=5, Gc=2, Sc=0.44, S=0.2, ω =0.1, ε=0.02
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10
τω
Pr
(α=0)
(α=-0.25)
(α=-0.4)
Fig. 4 Variation of skin friction τω against Pr for
Gr=5, Gc=2, Sc=0.44, S=0.2, ω =0.1, ε=0.02
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9 10
τω
Gr
(α=0)
(α=-0.25)
(α=-0.4)
Fig. 5 Variation of skin friction τω against Gr for
Pr=5, Gc=2, Sc=0.44, S=0.2, ω =0.1, ε=0.02
7. Free Convective Oscillatory Flow Of…
www.theijes.com The IJES Page 57
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9 10
τω
ω
(α=0)
(α=-0.25)
(α=-0.4)
Fig. 6 Variation of skin friction τω against ω for
Pr=5, Gr =5, Gc=2, Sc=0.44, S=0.2, ε=0.02
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