This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Dif...IOSR Journals
The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson’s scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.
Magnetic field effect on mixed convection flow in a nanofluid under convectiv...IAEME Publication
An analysis is carried out to investigate the influence of the prominent magnetic effect on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite vertical flat plate in a nanofluid under the convective boundary conditions. The transformed boundary layer,ordinary differential equations are solved numerically using Runge-Kutta Fourth order method.
Convective Heat And Mass Transfer Flow Of A Micropolar Fluid In A Rectangular...IJERA Editor
In this chapter we make an investigation of the convective heat transfer through a porous medium in a Rectangular enclosure with Darcy model. The transport equations of liner momentum, angular momentum and energy are solved by employing Galerkine finite element analysis with linear triangular elements. The computation is carried out for different values of Rayleigh number – Ra micropolar parameter – R, spin gradient parameter, Eckert number Ec and heat source parameter. The rate of heat transfer and couple stress on the side wall is evaluated for different variation of the governing parameters.
The Study of Heat Generation and Viscous Dissipation on Mhd Heat And Mass Dif...IOSR Journals
The present work is devoted to the numerical study of magneto hydrodynamic (MHD) natural convection flow of heat and mass transfer past a plate taking into account viscous dissipation and internal heat generation. The governing equations and the associated boundary conditions for this analysis are made non dimensional forms using a set of dimensionless variables. Thus, the non dimensional governing equations are solved numerically using finite difference method Crank-Nicolson’s scheme. Numerical outcomes are found for different values of the magnetic parameter, Modified Grashof number, Prandtl number, Eckert number, heat generation parameter and Schmidt number for the velocity and the temperature within the boundary layer as well as the skin friction coefficients and the rate of heat and mass transfer along the surface. Results are presented graphically with detailed discussion.
Magnetic field effect on mixed convection flow in a nanofluid under convectiv...IAEME Publication
An analysis is carried out to investigate the influence of the prominent magnetic effect on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite vertical flat plate in a nanofluid under the convective boundary conditions. The transformed boundary layer,ordinary differential equations are solved numerically using Runge-Kutta Fourth order method.
Convective Heat And Mass Transfer Flow Of A Micropolar Fluid In A Rectangular...IJERA Editor
In this chapter we make an investigation of the convective heat transfer through a porous medium in a Rectangular enclosure with Darcy model. The transport equations of liner momentum, angular momentum and energy are solved by employing Galerkine finite element analysis with linear triangular elements. The computation is carried out for different values of Rayleigh number – Ra micropolar parameter – R, spin gradient parameter, Eckert number Ec and heat source parameter. The rate of heat transfer and couple stress on the side wall is evaluated for different variation of the governing parameters.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
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 INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFERFROM SQUARE CYLIND...ijmech
The enhancement of natural convection heat transfer using nanofluids from horizontal square cylinder
placed in a square enclosure is investigated numerically. Water-based Cu is used as the working nanofluid.
The investigation covered a range of Rayleigh numbers of 104
- 106
, nanoparticles volume fraction of
(0<ϕ≤0.2), enclosure width to cylinder height ratio, W/H of 2.5. The investigation includes the solution of
the governing equations in the Vorticity-Stream function space with the aid of a body fitted coordinate
system. Algebraic grid generation is used in the initial transformations, followed by an elliptic
transformation to complete the grid generation to computational domain. The resulting discretized system
of equations is solved using an ADI method. The built code is validated and the results showed an increase
in average Nusselt number with increasing the volume fraction of the nanoparticles for the whole range of
Rayleigh number. The isotherms are nearly similar when the volume fraction of nanoparticles is increased
from 0 to 0.2 for each Rayleigh number but a change in the streamlines is observed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
International journal of engineering and mathematical modelling vol2 no3_2015_1IJEMM
A weak nonlinear stability analysis has been performed for an oscillatory mode of convection, heat and mass transports in terms of
Nusselt, Sherwood numbers are derived and evaluated by a non$-$autonomous complex Ginzburg-Landau equation. The porous layer boundaries are heated sinusoidally with time. The basic state temperature is defined in terms of study and oscillatory parts, where study part show nonlinear throughflow effect on the system and time dependant part show modulation effect. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter $\lambda_1$ has destabilizing effect, while time retardation parameter $\lambda_2$ has stabilizing effect on the system. Three types of modulations have been analyzed, and found that, OPM, LBMO cases are effective on heat and mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat and mass transports have been analyzed and depicted graphically. The study establishes that the heat and mass transports can be controlled effectively by a mechanism that is external to the system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
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.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
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.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
Magnetohydrodynamic mixed convection flow and boundary layer control of a nan...IAEME Publication
This research work is focused on the numerical solution of steady MHD mixed convection boundary layer flow of a nanofluid over a semi-infinite flat plate with heat generation/absorption and viscous dissipation effects in the presence of suction and injection. Gyarmati’s variational principle developed on the thermodynamic theory of irreversible processes is employed to solve the problem
numerically. The governing boundary layer equations are approximated as simple polynomial functions, and the functional of the variational principle is constructed.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
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 INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFERFROM SQUARE CYLIND...ijmech
The enhancement of natural convection heat transfer using nanofluids from horizontal square cylinder
placed in a square enclosure is investigated numerically. Water-based Cu is used as the working nanofluid.
The investigation covered a range of Rayleigh numbers of 104
- 106
, nanoparticles volume fraction of
(0<ϕ≤0.2), enclosure width to cylinder height ratio, W/H of 2.5. The investigation includes the solution of
the governing equations in the Vorticity-Stream function space with the aid of a body fitted coordinate
system. Algebraic grid generation is used in the initial transformations, followed by an elliptic
transformation to complete the grid generation to computational domain. The resulting discretized system
of equations is solved using an ADI method. The built code is validated and the results showed an increase
in average Nusselt number with increasing the volume fraction of the nanoparticles for the whole range of
Rayleigh number. The isotherms are nearly similar when the volume fraction of nanoparticles is increased
from 0 to 0.2 for each Rayleigh number but a change in the streamlines is observed.
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The present study analyzes the steady boundary layer slip flow of magneto-nanofluid due to an exponentially permeable stretching sheet with heat generation/absorption. In this paper, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique along with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, wall mass suction parameter, Prandtl number, the Lewis number, slip parameter, heat generation/absorption parameter, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction as well as skin friction, local Nusselt number and local Sherwood number has been discussed in detail.
Non-NewtonianFluid Flow and Heat Transfer over a Non- Linearly Stretching Sur...IJERA Editor
This paper investigates the MHD flow and heat transfer of an electrically conducting non-newtonian power-law
fluid over a non-linearly stretching surface along with porous plate in porous medium. The governing equations
are reduced to non-linear ordinary differential equations by means of similarity transformations. These
equations are then solved numerically with the help ofRunge – Kutta shooting method. The effect of various
flow parameters in the form of dimensionless quantities on the flow field are discussed and presented
graphically.
International journal of engineering and mathematical modelling vol2 no3_2015_1IJEMM
A weak nonlinear stability analysis has been performed for an oscillatory mode of convection, heat and mass transports in terms of
Nusselt, Sherwood numbers are derived and evaluated by a non$-$autonomous complex Ginzburg-Landau equation. The porous layer boundaries are heated sinusoidally with time. The basic state temperature is defined in terms of study and oscillatory parts, where study part show nonlinear throughflow effect on the system and time dependant part show modulation effect. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter $\lambda_1$ has destabilizing effect, while time retardation parameter $\lambda_2$ has stabilizing effect on the system. Three types of modulations have been analyzed, and found that, OPM, LBMO cases are effective on heat and mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat and mass transports have been analyzed and depicted graphically. The study establishes that the heat and mass transports can be controlled effectively by a mechanism that is external to the system.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
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.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
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.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
Nanofluid Flow past an Unsteady Permeable Shrinking Sheet with Heat Source or...IJERA Editor
The consideration of nanofluids has been paid a good attention on the forced convection; the analysis focusing
nanofluids in porous media are limited in literature. Thus, the use of nanofluids in porous media would be very
much helpful in heat and mass transfer enhancement. In this paper, the influence of variable suction, Newtonian
heating and heat source or sink heat and mass transfer over a permeable shrinking sheet embedded in a porous
medium filled with a nanofluid is discussed in detail. The solutions of the nonlinear equations governing the
velocɨty, temperature and concentration profiles are solved numerically using Runge-Kutta Gill procedure
together with shooting method and graphical results for the resulting parameters are displayed and discussed.
The influence of the physical parameters on skin-friction coefficient, local Nusselt number and local Sherwood
number are shown in a tabulated form.
Magnetohydrodynamic mixed convection flow and boundary layer control of a nan...IAEME Publication
This research work is focused on the numerical solution of steady MHD mixed convection boundary layer flow of a nanofluid over a semi-infinite flat plate with heat generation/absorption and viscous dissipation effects in the presence of suction and injection. Gyarmati’s variational principle developed on the thermodynamic theory of irreversible processes is employed to solve the problem
numerically. The governing boundary layer equations are approximated as simple polynomial functions, and the functional of the variational principle is constructed.
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel...IJERA Editor
We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
Carbon Nanotubes On Unsteady MHD Non-Darcy Flow Over A Porous Wedge In The Pr...IJERA Editor
Thermal radiation energy technologies are clean sources of energy that have a much lower environmental
impact than conventional energy technologies. The objective of the present work is to investigate theoretically
the effect of copper nanoparticles and carbon nanotubes in the presence of base fluid (water) with variable
stream condition due to thermal radiation energy. Single wall carbon nanotubes (SWCNTs) in the presence of
base fluid flow over a porous wedge plays a significant role compared to that of copper nanoparticles on
absorbs the incident solar radiation and transmits it to the working fluid by convection.
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.
Moving Lids Direction Effects on MHD Mixed Convection in a Two-Sided Lid-Driv...A Behzadmehr
Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. The obtained results show that for a constant Grashof number (), the rate of heat transfer increases with a decrease in the Richardson and Hartmann numbers. Furthermore, an increase of the volume fraction of nanoparticles may result in enhancement or deterioration of the heat transfer performance depending on the value of the Hartmann and Richardson numbers and the configuration of the moving lids. Also, it is found that in the presence of magnetic field, the nanoparticles have their maximum positive effect when the top lid moves rightward and the bottom one moves leftward.
Fuzzy numbers, Nth - order Fuzzy Initial Value Problems, Runge-Kutta method, ...IOSR Journals
A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics
(MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is
performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and
Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and
insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical
procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl
numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 103 – 105), Hartmann number (Ha = 50) with various
tilt angles Ф = 450, 300 and 00(square).Numerical results are presented in terms of streamlines, isotherms, heat
function (total heat flux) and nusselt numbers.for different Ra and Pr. As Ra increases conduction dominant
region changes for different Pr. Complete heat transfer analysis is performed in terms of local and average
nusselt numbers.
Effect of Rotation on a Layer of Micro-Polar Ferromagnetic Dusty Fluid Heated...IJERA Editor
This paper deals with the theoretical investigation of effect of rotation on micro-polar ferromagnetic dusty fluid
layer heated from below in a porous medium. Linear stability analysis and normal mode analysis methods are
used to find an exact solution for a flat micro-polar ferromagnetic fluid layer contained between two free
boundaries . In case of stationary convection, the effect of various parameters like medium permeability
parameter, non-buoyancy magnetization parameter, micro-polar coupling parameter, spin-diffusion parameter,
micro-polar heat conduction parameter, dust particles parameter and rotation parameter has been analyzed and
results are depicted graphically. In the absence of dust particles, rotation, micro-viscous effect and micro-inertia,
the sufficient condition is obtained for non-oscillatory modes
EFFECT OF SLIP PARAMETER OF A BOUNDARY-LAYER FLOW FOR NANOFLUID OVER A VERTIC...IAEME Publication
In this paper we analyze the effect of momentum slip, thermal slip and solutal slip on stagnation point flow of MHD nanofluid towards stretching sheet .The governing partial differential equation of flow, heat and mass transfer on considered flow are converted into the ordinary differential equations by means of similarity trans formations .The resulting equations are solved by the Runge-Kutta fourth order method with efficient shooting technique. Effects of various governing parameters on flow, heat and mass transfer are studied through the plots. The various numerical tables which are calculated and tabulated. A comparison of our present results with a previous study has been done and we found that an excellent agreement is there with the earlier results and of ours.
Effect of Thermo-Diffusion and Chemical Reaction on Mixed Convective Heat And...IJERA Editor
A finite element study of combined heat and mass transfer flow through a porous medium in a circular cylindrical annulus with Soret and Dufour effects in the presence of heat sources has been analyzed. The coupled velocity, energy, and diffusion equations are solved numerically by using Galerkin- finite element technique. Shear stress, Nusslet number and Sherwood number are evaluated numerically for different values of the governing parameters under consideration and are shown in tabular form.
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.
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
Radiation and magneticfield effects on unsteady natural
1. Chemical and Process Engineering Research www.iiste.org
ISSN 2224-7467 (Paper) ISSN 2225-0913 (Online)
Vol.25, 2014
Radiation and Magneticfield effects on Unsteady Natural
Convection Flow of a Nanofluid Past an Infinite Vertical Plate
with Heat Source
P. Mohan Krishna1 Dr.V.Sugunamma2 Dr.N.Sandeep3
1Resaerch Scholar, Department of Mathematics, S.V.University, Tirupati, A.P., India.
2Associate Professor, Department of Mathematics, S.V.University, Tirupati, A.P., India.
3Assistant Professor, Division of Fluid Dynamics, VIT University, Vellore, T.N., India.
Email:vsugunar@yahoo.co.in
Abstract
In this study, we analyze the effects of thermal radiation and magnetic field on unsteady natural convective flow
of a nanofluid past an impulsively started infinite vertical plate in presence of heat source. The nanofluid
contains Copper, Nikel, Zinc Oxide nanoparticles with water as base fluid. The partial differential equations
governing the flow are solved numerically by Laplace Transform Technique. The effects of various parameters
on velocity and temperature profiles examined and presented graphically .It is found that the increase in
magnetic field causes the decrease in fluid velocity, fluid velocity and temperature profiles are more influenced
by Radiation, Heat source and Volume fraction of the nanoparticles. Shape of nanoparticles does nots hows
effect on the velocity of the fluid.
Key Words: Heat transfer, Nanofluids, Thermal radiation, MHD, Heat source, Volume fraction.
Introduction
Unsteady natural convection flow of a nanofluid past an impulsively infinite vertical plate in presence of
radiation and magnetic field have received a lot of attention in the field of several industrial, scientific, and
engineering applications in recent years. Nanofluids have many applications in the industries since materials of
nanometer size have unique chemical and physical properties. With regard to the sundry applications of
nanofluids, the cooling applications of nanofluids include silicon mirror cooling, electronics cooling, vehicle
cooling, transformer cooling, etc. This study is more important in industries such as hot rolling, melt spinning,
extrusion, glass fiber production, wire drawing, and manufacture of plastic and rubber sheets, polymer sheet and
filaments, etc. among the tasks facing by the engineer is the development of ultrahigh-performance cooling in
many industrial technologies. This is where nanotechnology takes important part for further development of high
performance, compact, cost-effective liquid cooling systems.
Researchers Hossain and Takhar (1996) discussed the effect of thermal radiation using the Rosseland diffusion
approximation on mixed convection along a vertical plate with uniform free stream velocity and surface
temperature. Kuznetsov and Nield (2010) presented the natural convective boundary layer flow of a nanofluid
past an infinite vertical plate by considering thermophoresis and Brownian motion of nanoparticles. Boundary
layer flow of a nanofluid over a permeable stretching/shrinking sheet was studied theoretically by Bachok et al
(2012).
Takhar et al. (1996) studied the radiation effects on the MHD free convection flow of a gas past a semi-infinite
vertical plate. Ghaly (2002) considered the thermal radiation effect on a steady flow, whereas Rapits and
Massalas (1998) and El-Aziz (2009) analyzed the unsteady case. Sattar and Alam (1994) presented unsteady free
convection and mass transfer flow of a viscous, incompressible, and electrically conducting fluid past a moving
infinite vertical porous plate with thermal diffusion effect. Radiation convection interaction problems are found
in consideration of the cooling of high temperature components, convection cells and their effect on radiation
from stars, furnace design where heat transfer from surfaces occurs by parallel radiation and convection, the
interaction of incident solar radiation with the earth’s surface to produce complex free convection patterns and
thus to complicate the art of weather forecasting and marine environment studies for predicting free convection
patterns in oceans and lakes this was discussed by Siegel and Howell (1981). Hady (2012) analysed radiation
effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet.
Yao et al. (2011) have recently investigated the heat transfer of a viscous fluid flow over a permeable
stretching/shrinking sheet with a convective boundary condition. Magyari and Weidman (2006) analyzed the
heat transfer characteristics on a semi-infinite flat plate due to a uniform shear flow, both for the prescribed
surface temperature and prescribed surface heat flux. It is worth pointing out that a uniform shear flow is driven
by a viscous outer flow of rotational velocity whereas the classical Blasius flow is driven over the plate by an in
viscid outer flow of irrotational velocity. Sandeep et. al (2013) discussed Radiation effects on an Unsteady
Natural Convective Flow of a EG-Nimonic 80a Nanofluid Past an Infinite Vertical Plate and they concluded that
nanofluid velocity influenced by radiation parameter. Sandeep and Sugunamma (2014) studied Radiation and
39
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Inclined Magnetic Field Effects on Unsteady Hydromagnetic Free Convection Flow past an Impulsively Moving
Vertical Plate in a Porous Medium.
To the author’s knowledge, no studies have been communicated so far with regard to radiation and magneticfield
effects on an unsteady natural convective flow of a nanofluid past an infinite vertical plate. The objective of this
paper is to analyze the effects of radiation and magneticfield on transient natural convective flow of nanofluid
past an infinite vertical plate in presence of heat source. The unsteadiness is caused by the impulsive motion of
the vertical plate. The present study is of immediate application to all those processes which are highly affected
with heat enhancement concept
Fig.1 Physical Model of the problem
40
Mathematical Formulation
Consider an unsteady, incompressible, two dimensional flow of a nanofluid past an impulsively
started infinite vertical plate. The flow is considered along x-axis, which is taken along the plate in the vertically
upward direction and the y-axis is measured normal to the surface of the plate. At time t* £ 0 , the plate and the
fluid are at the same temperature. At time t* > 0 , the plate is given an impulsive motion in the vertically upward
direction with the constant velocity u0. The surface of the plate is maintained at a constant temperature higher
than the temperature of the ambient nanofluid. The fluid is water based nanofluid containing the nano
particles. Zinc Oxide (Zno), Nikel (Ni) and Copper (Cu) .In this study, nanofluids are assumed to behave as
single phase fluids with local thermal equilibrium between the base fluid and the nano particles suspended in
them, so that no slip occurs between them. A schematic representation of physical model and coordinate system
is depicted in Fig. 1. The thermophysical properties of the nanofluids are given in Table 1 .The basic unsteady
momentum and thermal energy equations according to the model for nanofluids in the presence of radiation and
magnetic field along with heat source are as follows:
¶ u 1
¶ 2
= m u
+ ( rb ) ( - )
- s
2
¶ * r nf ¶ 2 nf
¥
0
nf
g T T B u
t y
(1)
¶ T 2
= 1 ¶ T - ¶ q
r
+ - ¶ ¶ ¶
( ) ( )
nf
* 2
p nf
k Q T T
t rc y y ¥
(2)
The boundary conditions for the problem are
*
£ = =
> = = =
® ® ®¥
t u T T for all y
t *
u u T T for y
u T T as y
0, 0, ,
¥
0, , 0,
0
w
0, .
¥
(3)
Where u is the velocity along x- axis, r is the effective density of the nanofluid, m is the effective dynamic
nf nf viscosity of the nanofluid, b is the thermal expansion of the nanofluid, g is the acceleration due to gravity
nf , k is the thermal conductivity of the nanofluid, q is the radiative heat flux, s is surface tension and B is
nf r o applied magnetic field. For nanofluids the expressions of density r , thermal expansion coefficient
nf ( rb )and heat capacitance ( r c ) are given by
nf p nf
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41
( )
( )
= - +
= -
= - +
= - +
r 1
j r jr
nf f s
m m 1
j
2.5
nf f
rb j rb j rb
r j r j r
( ) ( 1
)( ) ( )
nf f s
( c ) ( 1
)( c ) ( c
)
p nf p f p s
(4)
The effective thermal conductivity of the nanofluid according to Hamilton and Crosser model is given by
+ - - - -
j
j
( 1) ( 1) ( )
k k n k n k k
k k n k k k
nf s f f s
+ - + -
( 1) ( )
=
f s f f s
(5)
Where n is the empirical shape factor for nanoparticle. In particular n=3 for spherical shaped nanoparticles and
n=3/2 for cylindrical shaped nanoparticles.j is the solid volume fraction of the nanoparticles, k is thermal
conductivity. Here the subscripts nf , f and s represents the thermo physical properties of nanofluid, base fluid
and solid nanoparticles respectively.
By using Rosseland approximation (26) the radiative heat flux leads to
= - s ¶
* 4
*
4
3 r
T
q
¶
k y
(6)
Where s * and k* are Stefan-Boltzmann constant and the mean absorption coefficient respectively.
¶ = - -
¶
q
r 4 a * * ( T 4 T
4 ) y
s ¥
(7)
If the temperature differences are within the flow are sufficiently small such that T 4 may be expressed as a
linear function of temperature, then expanding T 4 in Taylors series about T¥ and neglecting higher order
terms we get
T 4 4T 4T 3T 4 ¥ ¥ @ - (8)
In view of equations (6)-(8) and introducing the following non dimensional variables in equations (1)-(3)
= = =
, , ,
u u
f f
16
s u s u
= - = =
¥ ¥
¥
f f
, ,
w f
( )
* 2
0 0
0
* * 2 3 2
0
2
0 0
2
w f f f
, Pr ,
3 2
0 f f
0
u yu t u
U Y t
u
T T a T B
R M
T T k u u
g T T Q
Gr H
u k u
q
b u u u
a
¥
-
-
= = =
(9)
Governing equations reduces to
¶ U =a ¶ 2
U
+a q -a
¶ ¶
U
3 2 4 5
t Y
(10)
¶q =a ¶ 2
q -a q
¶ t 1 ¶
Y 2 7
(11)
The corresponding dimensionless boundary conditions are
q
q
£ = =
> = = =
® ® ®¥
0, 0, 0 ,
0, 0, 1 0,
t U for all Y
t U for Y
U as Y
q
0, 0 .
(12)
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h a h
+ a
a a
=
+ - -
42
Where
1 1
( )
( )
( )
( )
( )
1
2
3 2.5
,
Pr
1
,
1
1 1
,
1
1
nf
p s f
p f
p s
p f
s
f
k
c k
c
R
c
c
a
r
j j
r
a
r
j j
r
a
j r j j
r
=
- +
=
- +
=
-
- +
( )
( )
1
- +
=
- +
=
rb
( - ) ( - +
)
( )
( )
4
5 2.5
6
=
- +
= -
7 2 6
,
1
1
,
1 (1 )
,
1
s
f
s
f
f s
p s
p f
Gr
M
H
c
c
j j
rb
a r j j
r
a
j j r jr
a
r
j j
r
a a a
(13)
Equations (10) and (11) subjected to boundary conditions in equation (12) are solved using Laplace transform
technique and the solutions are given by
7
7
1 1
7
7
1 1
e x p 2
1
( , )
2
e x p 2
t
e r f c t
y t
t
e r f c t
q
h a h a
a a
(14)
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1 e x p 2 h a h a h 5 + a + e x p - 2
h 5
- a
= a 5 5
3 a a 3 a
3 3
h a h a h
5 a h 5
a
a a a a
+ + - -
+
+ +
-
+
+ - - +
h
e r f c + z + a
t
a a
+ - h + a h - + a
p c
JKg- K-
43
5 5
3 3 3 3
7
1
1 4
( , )
2
1
e x p 2 e x p 2
2
1
e x p 2
2
t t
e r f c t e r f c t
U y t
t t
e r f c t e r f c t
t
h a
a
a a
+ + - -
-
+
7
7 7
1 1 1
5
5
3 3
5
5
3 3
e x p 2
( )
e x p 2 ( )
z t
2 ( )
e x p 2 ( )
(
e x p 2
z t
2
t
e r fc t e r f c t
z t
e r f c z t
e
z t
e r f c z t
z
e
h a h a h a
a a a
h a h a
a a
h a h a
a a
+
h a
+
7
7
t
1 1
z t
7
7
1 1
)
( )
( )
e x p 2 ( )
e r f c z t
a a
(15)
Where 1 5 3 7
3 1
,
Y
2
z
t
a a a a h
a a
= - =
-
Results and Discussion
The partial differential equations (10) and (11) subjects to the boundary conditions (12) were solved numerically
by using Laplace Transform Technique. We considerCu , Ni and Zno nanoparticles with water as the base
fluid. Table 1 shows the thermo physical Properties of water and nanoparticles.
r
-
(Kgm 3)
( 1 1)
k
Wm- K-
( 1 1)
b -
5
´
10
-
1
(K )
2 H O
997.1 4179 0.613 21
Cu
8933 385 401 1.67
Ni
8890 456 702 1.33
Zno
5600 514 147 3.02
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
44
5
4
3
2
1
0
-1
h
v e lo c ity
M = 1, 2, 3, 4
Fig.1 Effect of Magnetic parameterM on the velocity of Cu water nanofluid when Gr =5,
H =2, Pr =6.2, R =1, t =0.5, j =0.04.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
5
4
3
2
1
0
-1
h
velocity
M = 0.5, 1.0, 1.5, 2.0
Fig.2 Effect of Magnetic parameter M on the velocity of Ni water nanofluid when Gr 5, Pr =6.2, R =1,
t =0.5, j =0.04, H =2.
5
4
3
2
1
0
-1
-2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
h
v e lo c ity
M = 0.5, 1.0, 1.5, 2.0
Fig.3 Effects of Magnetic parameterM on the velocity of Zno water nanofluid when Gr =5, Pr =6.2, R =1,
t =0.5, j =0.04, H =2.
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Pr = 6.2, Gr = 2, H = 2, R = 1, t = 0.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
45
2
1.5
1
0.5
0
-0.5
h
velocity
Cu, Ni, Zno
Fig.4 Comparison of velocity profiles of nanofluids in the presence of magnetic field
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
120
100
80
60
40
20
0
-20
-40
-60
-80
h
v e lo c ity
H = 0.2, 0.4, 0.6, 0.8
H = 0.2, 0.4, 0.6, 0.8
Fig.5. Effects of Heat source parameter H on the velocity field of Cu water nanofluid when Gr =5, Pr =6.2,
M = 1, R = 1, t =0.5, j =0.04.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
h
v e lo c ity
H =0.2, 0.4, 0.6, 0.8
Fig: 6. Effects of Heat source parameter H on the velocity of Ni water nanofluid when Gr =5, Pr =6.2,
M =1, R =1, t =0.5, j =0.04.
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Pr = 6.2, Gr = 2, M = 1, R = 1, t = 0.5
46
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
h
v e lo c ity
H = 0.2, 0.4, 0.6, 0.8
Fig: 7 Effects of Heat source parameter H on the velocity of Zno water nanofluid when Gr =5, Pr =6.2,
M =1, R =1, t =0.5, j =0.04.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
h
velocity
Cu, Zno, Ni
Fig.8 Comparison of velocity profiles of water and nanofluids in the presence of heat source (H=0.2)
f = 0.01, 0.02, 0.03, 0.04
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2
1.5
1
0.5
0
-0.5
h
v e lo c ity
f = 0.01, 0.02, 0.03, 0.04
f = 0.01, 0.02, 0.03, 0.04
Fig: 9. Effects of volume fraction j on the velocity of Cu water nanofluid when Gr =2,
Pr =6.2, M =1, R =2, t =0.6, H =3.
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f = 0.01, 0.02, 0.03, 0.04
f = 0.01, 0.02, 0.03, 0.04
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Pr = 6.2, Gr = 2, M = 1, H = 3, R = 2, t = 0.6
47
2
1.5
1
0.5
0
-0.5
h
v elo c ity
f = 0.01, 0.02, 0.03, 0.04
Fig: 11. Effects of volume fractionj on the velocity of Niwater nano fluid when Gr 2, Pr =6.2,M =1, R =2,
t =0.6, H =3.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2
1.5
1
0.5
0
-0.5
-1
h
velocity
f = 0.01, 0.02, 0.03, 0.04
f = 0.01, 0.02, 0.03, 0.04
Fig: 10. Effects of volume fractionj on the velocity of Znowater nanofluid when Gr =2, Pr =6.2, M =1,
R =2, t =0.6, H =3.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2
1.5
1
0.5
0
-0.5
h
velocity
Zno, Cu, Ni
Fig.12 Comparison of velocity profiles of water and nanofluids in the presence of volume fraction (p=0.2)
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48
.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
10
8
6
4
2
0
-2
-4
h
tempe ra tur e
R= 0.1, 0.2, 0.3, 0.4
R= 0.1, 0.2, 0.3, 0.4
Fig: 13. Effects of Radiation parameter R on the temperature of Cu water nanofluid when Pr =6.2, t =0.6,
j =0.04, H =2.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
14
12
10
8
6
4
2
0
-2
-4
h
tempe r a tur e
R = 0.1, 0.2, 0.3, 0.4
R = 0.1, 0.2, 0.3, 0.4
Fig: 14. Effects of Radiation parameter R on the temperature of Ni water nanofluid when Pr =6.2, t =0.6,
j =0.04, H =2.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
6
4
2
0
-2
-4
-6
-8
-10
-12
h
tempe r a tur e
R= 0.1, 0.2, 0.3, 0.4
R= 0.1, 0.2, 0.3, 0.4
Fig: 15. Effects of Radiation parameter R on the temperature of Zno water nanofluid when Pr =6.2, t =0.6,
j =0.04, H =2.
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10
8
6
4
2
0
-2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
49
-4
h
tempera ture
Pr = 6.2, H = 2, t = 0.6
Cu, Ni, Zno
Fig.16 Comparison of temperature profiles of nanofluids in presence of radiation
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
h
tempe ra tur e
H = 0.5, 1.0, 1.5, 2.0
Fig: 17. Effects of Heat source parameter H on the temperature of Cu water nano fluid when Pr =6.2, R =6,
t =0.1, j =0.04.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
h
tempe r a tur e
H = 0.5, 1.0, 1.5, 2.0
Fig: 18. Effects of Heat source parameter H on the temperature of Ni water nanofluid when Pr =6.2, R =6,
t =0.1, j =0.04.
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
f = 0.1, 0.2, 0.3, 0.4
50
0.25
0.2
0.15
0.1
0.05
0
h
tempe r a tur e
H= 0.5, 1.0, 1.5, 2.0
Fig: 19. Effects of Heat source parameter H on the temperature of Zno water nanofluid when Pr =6.2, R =6,
t =0.6, j =0.04.
0.25
0.2
0.15
0.1
0.05
Fig.20 Comparison of temperature profiles nanofluids in the presence of heat source
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.25
0.2
0.15
0.1
0.05
0
h
temperature
f = 0.1, 0.2, 0.3, 0.4
Fig: 21. Effects of volume fractionj on the temperature of Cu water nanofluid when Pr =6.2, R =4, t =0.6,
H =2.
0
h
tempe r a ture
Zno, Cu, Ni
Pr = 6.2, N = 3, t = 0.5
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
51
0.25
0.2
0.15
0.1
0.05
0
h
temperature
f =0.1, 0.2, 0.3, 0.4
f =0.1, 0.2, 0.3, 0.4
Fig: 22. Effects of volume fractionj on the temperature of Ni water nanofluid
when Pr =6.2, R =4, t =0.6, H =2.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.25
0.2
0.15
0.1
0.05
0
h
t em pe r a tur e
f = 0.1, 0.2, 0.3, 0.4
Fig: 23. Effects of volume fractionj on the temperature field of Zno water nanofluid when Pr =6.2, R =4, t =0.6, H =2.
Figs. 1, 2 and 3 shows the effect of Magnetic field on Cu water, Ni water and Zno water nanofluids
respectively. Here we observed that increase in magnetic field causes the decrease in fluid velocity.These may
happen due to the magnetic field pull of the Lorentz force acting on the flow field. From Fig. 4 it is clear that
magnetic field effect is more on Cu water nanofluid .
Figs.5, 6 and 7 depicts the effect of Heat source parameter on Cu water, Ni water and Zno water nanofluids
respectively. Here we observed that increase in Heat source parameter causes the increase in fluid velocity .Here
heat is generated the buoyancy force , which induces the flow rate to increase giving rise to the increase in the
velocity profiles .From fig.8 we found that increase in heat source parameter shows much effect on increasing in
fluid velocity in Cu water nanofluid.
Figures 9, 10 and 11 depict the effect of Volume fraction parameter on Cu water, Ni water and Zno water
nanofluids respectively. Here we observed that decrease in Volume faction parameter causes the increase in fluid
velocity. These may happen due to the number of surface atoms per unit of interior atoms of nanoparticles is
very large when we reduce the volume fraction. From figure 12 it is clear that variation of volume fraction shows
much effect to increase the fluid velocity of Znowater nanofluid .
Figs. 13, 14 and 15 shows the effect of Radiation parameter on Cu water, Ni water and Zno water nanofluids
respectively. Here we observed that increase in Radiation parameter causes the decrease in fluid temperature,
these may happen due to Rosseland radiation absorptiveness. From Fig. 16 it is clear that effect of Radiation
parameter is more on Znowater nanofluid .
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Figures 17, 18 and 19 Shows the effect of Heat source parameter on Cu water, Ni water and Zno water
nanofluids respectively. Here we observed that increase in Heat source parameter causes the increase in fluid
temperature. From figure 20 it is clear that effect of Heat source parameter is more on Ni water nanofluid .
Figures 21, 22 and 23 Shows the effect of Volume fraction parameter on Cu water, Ni water and Zno water
nanofluids respectively. Here we observed that increase in Volume fraction initially decrease the fluid
temperature after certain period it is reversed. But in case of Zno water nanofluids increase in volume fraction
of nanoparticles causes the increase in fluid temperature. These may happen dute to the reason that the decrease
in volume fraction improves the heat transfer rate.
Conclusions
The effects of radiation and magnetic field on unsteady natural convective flow of nanofluids past an infinite
vertical plate with heat source using Rosseland approximation for the radiative heat flux are analyzed. The
governing partial differential equations are solved by Laplace Transform Technique. The effects of the
nanoparticle volume fraction, thermal radiation, magneticfield and heat source on fluid velocity and temperature
determined for Cu water, Ni water and Zno water nanofluids.
The conclusions are as follows
1. Velocity of water nanofluid is more influenced by magnetic field parameter
2. The effect of radiation on water nanofluid velocity is less compared to water, water nanofluids.
3. Heat sores parameter improves the velocity of water, water nanofluids.
4. Decrease in Volume fraction of all nanoparticles causes the increase in fluid velocity.
5. The increase in thermal radiation is causes the decrease in temperature of the fluid and it is more influenced
the water nanofluid.
6. Increase in heat source parameter causes the increase in fluid temperature. Water nanofluid is much
influenced by heat source parameter.
7. Decrease in volume fraction of the nanoparticles causes the increase in fluid temperature.
References
Bachok L, Ishak A and Pop I(2012) Boundary layer flow of a nanofluid over a permeable stretching/shrinking
52
sheet.Int J Heat Mass Transf. 55: 642-648 .
El-Aziz MA (2009) Radiation effect on the flow and heat transfer over an unsteady stretching surface. Int
Commu Heat and Mass Transf. 36: 521–524.
Ghaly AY (2002) Radiation effect on a certain MHD free convection flow. Chasos Solitons Fractal 13:1843–
1850.
Hady FM Ibrahim FS, Abdel-Gaied SM, Mohamed Eid R (2012) Radiation effect on viscous flow of a nanofluid
and heat transfer over a nonlinearly stretching sheet. NanoscaleResLett7:229.
Hossain MA, Takhar HS (1996) Radiation effects on mixed convection along a vertical plate with uniform
surface temperature. Heat Mass Transfer 31:243–248.
Kuznetsov AV and Nield DA (2010) Natural convective boundary layer flow of a nanofluid past an infinite
vertical plate. Int J Therm Sci 49:243.
Magyari E, Weidman PD (2006) Heat transfer on a plate beneath an external uniform shear flow. Int J Therm Sci
45:110-115.
Rapits A, Massalas CV (1998) Magnetohydrodynamic flow past a plate by the presence of radiation. Heat and
Mass Transf 34:107–109.
Sandeep N, Sugunamma V and Mohan Krishna P (2013) Effects of Radiation on an Unsteady
Natural Convective Flow of a EG-Nimonic 80a Nanofluid past an Infinite Vertical Plate. Advances in Physics
Theories and Applications 23:36-43.
Sandeep N, Sugunamma V (2014) Radiation and Inclined Magnetic Field Effects on Unsteady
Hydromagnetic Free Convection Flow past an Impulsively Moving Vertical Plate in a Porous Medium. Journal
of Applied Fluid Mechanics, 7: 275-286.
Sattar MA, Alam MM (1994) Thermal diffusion as well as transpiration effects on MHD free convection and
mass transfer flow past an accelerated vertical porous plate. Indian J Pure App Math 25:679–688.
Siegel R and Howell JR (1981) Thermal radiation heat transfer, Series in thermal and fluid engineering.
Hemisphere Publishing Corporation. United State of America.
Takhar HS, Gorla RSR and Soundelgekar VM (1996) Non-linear one-step method for initial value problems. Int
Num Meth Heat Fluid Flow 6:22–83.
Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective
boundary conditions. Communication in Nonlinear Sci Numer Simul 16: 752-760.
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