This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that
Numerical simulation on laminar convection flow and heat transfer over an iso...eSAT Journals
Abstract A numerical algorithm is presented for studying laminar convection flow and heat transfer over an isothermal vertical horizontal plate embedded in a saturated porous medium. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Velocity and temperature profiles are illustrated graphically. Heat transfer parameters are derived. Keywords
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
Bound State Solution to Schrodinger Equation with Hulthen Plus Exponential Co...ijrap
In this work, we obtained an approximate bound state solution to Schrodinger with Hulthen plus
exponential Coulombic potential with centrifugal potential barrier using parametric Nikiforov-Uvarov
method. We obtained both the eigen energy and the wave functions to non -relativistic wave equations. We
implement Matlab algorithm to obtained the numerical bound state energies for various values of
adjustable screening parameter at various quantum state.. The developed potential reduces to Hulthen
potential and the numerical bound state energy conform to that of existing literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
Numerical simulation on laminar convection flow and heat transfer over an iso...eSAT Journals
Abstract A numerical algorithm is presented for studying laminar convection flow and heat transfer over an isothermal vertical horizontal plate embedded in a saturated porous medium. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Velocity and temperature profiles are illustrated graphically. Heat transfer parameters are derived. Keywords
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
Bound State Solution to Schrodinger Equation with Hulthen Plus Exponential Co...ijrap
In this work, we obtained an approximate bound state solution to Schrodinger with Hulthen plus
exponential Coulombic potential with centrifugal potential barrier using parametric Nikiforov-Uvarov
method. We obtained both the eigen energy and the wave functions to non -relativistic wave equations. We
implement Matlab algorithm to obtained the numerical bound state energies for various values of
adjustable screening parameter at various quantum state.. The developed potential reduces to Hulthen
potential and the numerical bound state energy conform to that of existing literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
Optimization of technological process to decrease dimensions of circuits xor ...ijfcstjournal
The paper describes an approach of increasing of integration rate of elements of integrated circuits. The
approach has been illustrated by example of manufacturing of a circuit XOR. Framework the approach one
should manufacture a heterostructure with specific configuration. After that several special areas of the
heterostructure should be doped by diffusion and/or ion implantation and optimization of annealing of dopant
and/or radiation defects. We analyzed redistribution of dopant with account redistribution of radiation
defects to formulate recommendations to decrease dimensions of integrated circuits by using analytical
approaches of modeling of technological process.
Heat Transfer in the flow of a Non-Newtonian second-order fluid over an enclo...IJMERJOURNAL
ABSTRACT : The problem of the heat transfer in the flow of an incompressible non-Newtonian second-order fluid over an enclosed torsionally oscillating discs in the presence of the magnetic field has been discussed. The obtained differential equations are highly non-linear and contain upto fifth order derivatives of the flow and energy functions. Hence exact or numerical solutions of the differential equations are not possible subject to the given natural boundary conditions; therefore the regular perturbation technique is applied. The flow functions 퐻, 퐺, 퐿 and 푀 are expanded in the powers of the amplitude (taken small) of the oscillations. The behaviour of the temperature distribution at different values of Reynolds number, phase difference, magnetic field and second-order parameters has been studied and shown graphically. The results obtained are compared with those for the infinite torsionally oscillating discs by taking the Reynolds number of out-flow 푅푚 and circulatory flow 푅퐿 equals to zero. Nusselt number at oscillating and stator disc has also been calculated and its behaviour is represented graphically.
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
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.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
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.
The approximate bound state of the nonrelativistic Schrӧdinger equation was
obtained with the modified trigonometric scarf type potential in the framework of
asymptotic iteration method for any arbitrary angular momentum quantum number l
using a suitable approximate scheme to the centrifugal term. The effect of the screening
parameter and potential depth on the eigenvalue was studied numerically. Finally, the
scattering phase shift of the nonrelativistic Schrӧdinger equation with the potential
under consideration was calculated.
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.
FREE CONVECTION HEAT TRANSFER OF NANOFLUIDS FROM A HORIZONTAL PLATE EMBEDDED ...AEIJjournal2
In this paper the natural convection heat transfer from a horizontal plate embedded in a porous medium
saturated with a nanofluid is numerically analyzed. By a similarity approach the partial differential
equations are reduced to a set of two ordinary differential equations. In order to evaluate the influence of
nanoparticles on the heat transfer, Ag and Cuo as the nanoparticles were selected. Results show that heat
transfer rate (Nur) is a decreasing function of volume fraction of nanoparticles.
SUCCESSIVE LINEARIZATION SOLUTION OF A BOUNDARY LAYER CONVECTIVE HEAT TRANSFE...ijcsa
The purpose of this paper is to discuss the flow of forced convection over a flat plate. The governing partial
differential equations are transformed into ordinary differential equations using suitable transformations.
The resulting equations were solved using a recent semi-numerical scheme known as the successive
linearization method (SLM). A comparison between the obtained results with homotopy perturbation method and numerical method (NM) has been included to test the accuracy and convergence of the method.
Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Pot...ijrap
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus
modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy
eigen value and its associated total wave function . This potential with some suitable conditions reduces to
two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical
results for energy eigen value with different values of q as dimensionless parameter. The result shows that
the values of the energies for different quantum number(n) is negative(bound state condition) and increases
with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1)
shows the different energy levels for a particular quantum number.
Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Pot...ijrap
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function . This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions (single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Analytical Solutions of the Modified Coulomb Potential using the Factorizatio...ijrap
We have solved exactly Schrödinger equation with modified Coulomb Potential under the framework of factorization method. Energy levels and the corresponding wave functions in terms of associated Laquerre
function are also obtained. For further guide to interested readers we have computed the energy eigenvalue for some selected elements for various values of n and l .
An Approach to Optimize Regimes of Manufacturing of Complementary Horizontal ...ijrap
In this paper we consider nonlinear model to describe manufacturing complementary horizontal field-effect heterotransistor. Based on analytical solution of the considered boundary problems some recommendations have been formulated to optimize technological processes.
Call for Papers - 8th International Conference on Electrical & Computer Engin...AEIJjournal2
8th International Conference on Electrical & Computer Engineering (E& C 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications impacts and challenges of Electrical & Computer Engineering. The conference documents practical and theoretical results which make a fundamental contribution for the development of Electrical & Computer Engineering. The aim of the conference is to provide a platform to the researchers and practitioners from both academia as well as industry to meet and share cutting-edge development in the field.
Authors are solicited to contribute to the conference by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the following areas, but are not limited to:
DYNAMICS IN THE HISTORY AND ECONOMIC DEVELOPMENT OF MAN: REFOCUSING ON ECOLOG...AEIJjournal2
Man’s history and development endeavours have beenadvancing alongside a trail of ecological
ramifications and climate change. Since prehistoric times, scientists have not recorded an accelerated shift
in the ecologyof the planet during any other epoch beside that of modern man. The paper seeks to explore
how man’s history and developmentaffects ecologyand climate. It uses desk analysis to recollect data from
global assessment reportsand runs a One paired Sample Means t-Test, 1 tailed, 8 df, at Pearson
Correlation value 0.458 and 0.5 alpha level. Findings show that, there is globalclimate change, seen in
global warming trends; andimbalance in ecological footprint, seen in depletion of air, water and land
sinks. The t-Test reveals significant net loss of global forest cover.The study also,apparently found that,
processes ofdevelopment generally tend to damage ecology. Therefore,the study recommends a refocus to
sustainable means of development.
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ABSTRACT : The problem of the heat transfer in the flow of an incompressible non-Newtonian second-order fluid over an enclosed torsionally oscillating discs in the presence of the magnetic field has been discussed. The obtained differential equations are highly non-linear and contain upto fifth order derivatives of the flow and energy functions. Hence exact or numerical solutions of the differential equations are not possible subject to the given natural boundary conditions; therefore the regular perturbation technique is applied. The flow functions 퐻, 퐺, 퐿 and 푀 are expanded in the powers of the amplitude (taken small) of the oscillations. The behaviour of the temperature distribution at different values of Reynolds number, phase difference, magnetic field and second-order parameters has been studied and shown graphically. The results obtained are compared with those for the infinite torsionally oscillating discs by taking the Reynolds number of out-flow 푅푚 and circulatory flow 푅퐿 equals to zero. Nusselt number at oscillating and stator disc has also been calculated and its behaviour is represented graphically.
On prognozisys of manufacturing doublebaseijaceeejournal
In this paper we introduce a modification of recently introduced analytical approach to model mass- and
heat transport. The approach gives us possibility to model the transport in multilayer structures with account
nonlinearity of the process and time-varing coefficients and without matching the solutions at the
interfaces of the multilayer structures. As an example of using of the approach we consider technological
process to manufacture more compact double base heterobipolar transistor. The technological approach
based on manufacturing a heterostructure with required configuration, doping of required areas of this
heterostructure by diffusion or ion implantation and optimal annealing of dopant and/or radiation defects.
The approach gives us possibility to manufacture p-n- junctions with higher sharpness framework the transistor.
In this situation we have a possibility to obtain smaller switching time of p-n- junctions and higher
compactness of the considered bipolar transistor.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
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MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
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.
Effect of Magnetic Field on Peristaltic Flow of Williamson Fluid in a Symmetr...IOSRJM
This paper deals with the influence of magnetic field on peristaltic flow of an incompressible Williamson fluid in a symmetric channel with heat and mass transfer. Convective conditions of heat and mass transfer are employed. Viscous dissipation and Joule heating are taken into consideration.Channel walls have compliant properties. Analysis has been carried out through long wavelength and low Reynolds number approach. Resulting problems are solved for small Weissenberg number. Impacts of variables reflecting the salient features of wall properties, concentration and heat transfer coefficient are pointed out. Trapping phenomenon is also analyzed.
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The approximate bound state of the nonrelativistic Schrӧdinger equation was
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using a suitable approximate scheme to the centrifugal term. The effect of the screening
parameter and potential depth on the eigenvalue was studied numerically. Finally, the
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under consideration was calculated.
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.
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In this paper the natural convection heat transfer from a horizontal plate embedded in a porous medium
saturated with a nanofluid is numerically analyzed. By a similarity approach the partial differential
equations are reduced to a set of two ordinary differential equations. In order to evaluate the influence of
nanoparticles on the heat transfer, Ag and Cuo as the nanoparticles were selected. Results show that heat
transfer rate (Nur) is a decreasing function of volume fraction of nanoparticles.
SUCCESSIVE LINEARIZATION SOLUTION OF A BOUNDARY LAYER CONVECTIVE HEAT TRANSFE...ijcsa
The purpose of this paper is to discuss the flow of forced convection over a flat plate. The governing partial
differential equations are transformed into ordinary differential equations using suitable transformations.
The resulting equations were solved using a recent semi-numerical scheme known as the successive
linearization method (SLM). A comparison between the obtained results with homotopy perturbation method and numerical method (NM) has been included to test the accuracy and convergence of the method.
Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Pot...ijrap
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus
modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy
eigen value and its associated total wave function . This potential with some suitable conditions reduces to
two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical
results for energy eigen value with different values of q as dimensionless parameter. The result shows that
the values of the energies for different quantum number(n) is negative(bound state condition) and increases
with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1)
shows the different energy levels for a particular quantum number.
Exact Bound State Solution of Qdeformed Woods-Saxon Plus Modified Coulomb Pot...ijrap
In this work, we obtained an exact solution to Schrodinger equation using q-deformed Woods-Saxon plus modified Coulomb potential Using conventional Nikiforov-Uvarov method. We also obtained the energy eigen value and its associated total wave function . This potential with some suitable conditions reduces to two well known potentials namely: the Yukawa and coulomb potential. Finally, we obtained the numerical results for energy eigen value with different values of q as dimensionless parameter. The result shows that the values of the energies for different quantum number(n) is negative(bound state condition) and increases with an increase in the value of the dimensionless parameter(arbitrary constant). The graph in figure (1) shows the different energy levels for a particular quantum number.
MODELING OF REDISTRIBUTION OF INFUSED DOPANT IN A MULTILAYER STRUCTURE DOPANT...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at
the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of
vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by
diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions
(single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
Modeling of Redistribution of Infused Dopant in a Multilayer Structure Dopant...mathsjournal
In this paper we used an analytical approach to model nonlinear diffusion of dopant in a multilayer structure with account nonstationary annealing of the dopant. The approach do without crosslinking solutions at the interface between layers of the multilayer structure. In this paper we analyzed influence of pressure of vapor of infusing dopant during doping of multilayer structure on values of optimal parameters of technological process to manufacture p-n-junctions. It has been shown, that doping of multilayer structures by diffusion and optimization of annealing of dopant gives us possibility to increase sharpness of p-n-junctions (single p-n-junctions and p-n-junctions within transistors) and to increase homogeneity of dopant distribution in doped area.
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8th International Conference on Electrical & Computer Engineering (E& C 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications impacts and challenges of Electrical & Computer Engineering. The conference documents practical and theoretical results which make a fundamental contribution for the development of Electrical & Computer Engineering. The aim of the conference is to provide a platform to the researchers and practitioners from both academia as well as industry to meet and share cutting-edge development in the field.
Authors are solicited to contribute to the conference by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the following areas, but are not limited to:
DYNAMICS IN THE HISTORY AND ECONOMIC DEVELOPMENT OF MAN: REFOCUSING ON ECOLOG...AEIJjournal2
Man’s history and development endeavours have beenadvancing alongside a trail of ecological
ramifications and climate change. Since prehistoric times, scientists have not recorded an accelerated shift
in the ecologyof the planet during any other epoch beside that of modern man. The paper seeks to explore
how man’s history and developmentaffects ecologyand climate. It uses desk analysis to recollect data from
global assessment reportsand runs a One paired Sample Means t-Test, 1 tailed, 8 df, at Pearson
Correlation value 0.458 and 0.5 alpha level. Findings show that, there is globalclimate change, seen in
global warming trends; andimbalance in ecological footprint, seen in depletion of air, water and land
sinks. The t-Test reveals significant net loss of global forest cover.The study also,apparently found that,
processes ofdevelopment generally tend to damage ecology. Therefore,the study recommends a refocus to
sustainable means of development.
Direct Alcohol Alkaline Fuel Cell as Future ProspectusAEIJjournal2
Fuel cells are called the fourth electricity power generation after water, nuclear power generation devices.
Fuel cells are widely recognized as very attractive devices to obtain directly electric energy from the
electrochemical combustion of chemical products. When fuel cells are continuously supplied fuel and
oxidant, electricity can be made constantly. According to the different electrolytes, fuel cells can be divided
into different types among them, alkaline fuel cell is best as compared to others ones. Due to the activation
overvoltage at the cathode is generally less than that with an acid electrolyte and there are very few
standard chemicals that are cheaper than potassium hydroxide. These fuel cells have longer lifetimes, and
do not require expensive noble metal catalysts to be used. Noble metal catalysts may be used, but less is
needed to achieve a similar reaction rate. The main objective of the study is to use different kind of
alcohols in alkaline fuel cell and determined the characteristics at different parameter.
COMPARING ECONOMIC FEASIBILITY OF DOMESTIC SOLAR WATER HEATER INSTALLATION IN...AEIJjournal2
Adequate and consistent energy supply is often regarded as a major factor in the development of any
country. To add to this, the depletion of fossil fuels has also emphasised the need for alternate renewable
energy solutions to meet global energy needs without inflicting any serious environmental impacts. Solar
energy is globally acknowledged for its vast potential, as a source of providing most of the heating, cooling
and electricity needs of the world. One of the most effective uses of solar energy is water heating. The use
of solar energy to heat water has been proven to be a very economical, efficient and environmental friendly
option for domestic as well as commercial applications. This study compares the feasibility of domestic
solar water heater installation in three major cities of Pakistan i.e. Lahore, Karachi and Peshawar. The
results show the solar water heater installation is most feasible in Peshawar, among the three selected
cities.
ASSESSING PERCEPTUAL VIDEO QUALITY IN WIMAX NETWORKS AEIJjournal2
This paper presents an approach for assessing the perceptual quality of wireless video networking
applications transmitted via WiMAX, the Worldwide Interoperability for Microwave Access air interface
standard. The Video Quality Model developed by Information Administration’s Video Quality Expert
Group is used to benchmark perceptual video quality.
Layer-Type Power Transformer Thermal Analysis Considering Effective Parameter...AEIJjournal2
Since large power transformers belong to the most valuable assets in electrical power networks it is
suitable to pay higher attention to these operating resources. Thermal impact leads not only to long-term
oil/paper-insulation degradation; it is also a limiting factor for the transformer operation. Therefore, the
knowledge of the temperature, especially the hottest spot (HST) temperature, is of high interest. This paper
presents steady state temperature distribution of a power transformer layer-type winding using conjugated
heat transfer analysis, therefore energy and Navier-Stokes equations are solved using finite difference
method. Meanwhile, the effects of load conditions and type of oil on HST are investigated using the model.
Oil in the transformer is assumed nearly incompressible and oil parameters such as thermal conductivity,
special heat, viscosity, and density vary with temperature. Comparing the results with those obtained from
finite integral transform checks the validity and accuracy of the proposed method
STUDY OF THE EQUIVALENT CIRCUIT OF A DYESENSITIZED SOLAR CELLSAEIJjournal2
The dye-sensitized solar cells (DSSC) have gained the last decades an important place among photovoltaic
technologies due to their low-cost of implementation and their performance, which becomes more efficient.
The experimental data for this type of cells are enriched and accumulated quickly, given the enthusiasm for
this new technology. The present work treats the equivalent circuit of a dye-sensitized solar cell (DSSC) for
a model in an exponential, and by using the results of some works, we shall make a simulation by the
software Scilab to obtain the characteristics (I-V), then we will study the influence of every parameter on
the curve.
TRANSIENT STABILITY IMPROVEMENT OF POWER SYSTEMS BY OPTIMAL SIZING AND ALLOCA...AEIJjournal2
Employing Resistive Superconducting Fault Current Limiters (RSFCL) is one of the practical and effective
methods to improve the transient stability of a power system by limiting the fault current. Regarding
technical and economical constraints, optimal sizing and allocation of RSFCLs in a power system is of
significant importance. It is the purpose of this paper to propose an algorithm based on the Particle Swarm
Optimization (PSO) in order to improve the transient stability of a power system by optimal sizing and
allocation of RSFCLs. The proposed algorithm is next applied to the New England 39-bus test system as a
case study and the results are simulated in Matlab. Simulation results reveal that in the case of employing
RSFCLs with sizes and locations resulted from the optimization algorithm, the transient stability of the
power system under study is improved. Furthermore, it seems that the optimal locations of RSFCLs are to
some extent near the fault location.
A Review on RDB to RDF Mapping for Semantic WebAEIJjournal2
In Databases one of the active research fields is mapping relational databases (RDB) into Resource
Description Framework (RDF). An enormous data is kept in the form of relational databases and accessing
of data is done in the semantic web. The data stored in RDB is to be efficiently mapped to the semantic web
or RDF for data availability to the users. There is a definite need for improvement in technologies for
efficient mapping languages from RDB to RDF in semantic web. This paper presents an up-to-date survey
of different RDB to RDF mapping languages proposed in recent times. It outlines the main features or
characteristics to be considered for efficient mapping in different scenarios. The main objective of this
content, pictures identification of limitations existing in the mapping languages. It also enhances the
comparisons between each language and helps researchers to propose further better proposals in their
future scope of work to improve better mapping techniques.
Dynamics in the History and Economic Development of Man: Refocusing on Ecolog...AEIJjournal2
Man’s history and development endeavours have beenadvancing alongside a trail of ecological
ramifications and climate change. Since prehistoric times, scientists have not recorded an accelerated shift
in the ecologyof the planet during any other epoch beside that of modern man. The paper seeks to explore
how man’s history and developmentaffects ecologyand climate. It uses desk analysis to recollect data from
global assessment reportsand runs a One paired Sample Means t-Test, 1 tailed, 8 df, at Pearson
Correlation value 0.458 and 0.5 alpha level. Findings show that, there is globalclimate change, seen in
global warming trends; andimbalance in ecological footprint, seen in depletion of air, water and land
sinks. The t-Test reveals significant net loss of global forest cover.The study also,apparently found that,
processes ofdevelopment generally tend to damage ecology. Therefore,the study recommends a refocus to
sustainable means of development.
SIMULATION OF THE SOLAR CELLS WITH PC1D, APPLICATION TO CELLS BASED ON SILICONAEIJjournal2
A way of exploiting the solar energy is to use cells photovoltaic which convert the energy conveyed by the
incidental radiation in a continuous electric current. This conversation is based on the photovoltaic effect
engendered by the absorption of photons. A part of the absorbed photons generates pairs electron-hole in
which an electric field created in the zone of load of space of a junction p–n.
Thus, the junction p-n, its characteristics, its components and its dimensions are the parameters
responsible of the efficiency and the performances of a solar cell. To study this, we are going to use a very
known software in the mode of the simulation of solar cells, the PC1D, and we are going, at the end, to
draw a conclusion around the ideal parameters that a good solar cell has to have.
DESIGN AND DEVELOPMENT OF WIND TURBINE EMULATOR TO OPERATE WITH 1.5KW INDUCTI...AEIJjournal2
This paper contributes to design a Wind Emulator coupled to 1.5 kW Induction generator for Wind Energy
Conversion System. A wind turbine emulator (WTE) is important equipment for developing wind energy
conversion systems. It offers a controllable test environment that allows the evaluation and improvement of
control schemes for electric generators that is hard to achieve with an actual wind turbine since the wind
speed varies randomly. In this paper a wind emulator is modelled and simulated using MATLAB.
Verification of the simulation results is done by experimental setup using DC motor-Induction generator
set, LABVIEW and data acquisition card.
EVALUATING MATHEMATICAL HEAT TRANSFER EFFECTIVENESS EQUATIONS USING CFD TECHN...AEIJjournal2
Mathematical heat transfer equations for finned double pipe heat exchangers based on experimental work
carried out in the 1970s can be programmed in a spreadsheet for repetitive use. Thus avoiding CFD
analysis which can be time consuming and costly. However, it is important that such mathematical
equations be evaluated for their accuracy. This paper uses CFD methods in evaluating the accuracy of
mathematical equations. Several models were created with varying; geometry, flue gas entry temperature,
and flow rates. The analysis should provide designers and manufacturers a judgment on the expected level
of accuracy when using mathematical modelling methodology. This paper simultaneously identifies best
practices in carrying out such CFD analysis.
Co integration Relationship Between Economic Growth, Export and Electricity C...AEIJjournal2
Energy dependent small developing island states are besieged to sustain potential rate of growth. This is
due to increase in energy prices and lack of evidence based policy on long term sustainable energy use.
This paper examines the long run relationship between economic growth, export and electricity
consumption in Fiji over the period 1981-2011. Employing Granger causality test it is found that there is
cointegrating relationship between economic growth, export and electricity consumption. The casual
relationship between the variables was investigated within the error correction model framework. We
found that in the long run causality runs from electricity consumption and export to economic growth.
Based on this empirical analysis some important policy implications are suggested.
Effect of Zn Concentration On Structural and Optical Proprieties Of ZNO Thin ...AEIJjournal2
ZnO thin film were deposited by spray pyrolysis on glass substrates, using zinc nitrate as precursor with
different molar concentrations varying from 0.05M to 0.2 M. To study the structural proprieties of the film ,
the different technique was used as the X-ray diffraction, atomic force microscopy (AFM), Raman
scattering , and FTIR . The optical properties were explored by transmission, reflectivity and
Photoluminescence techniques. The ZnO thin films obtained in this paper are polycrystallines, the grain
size increases when the molar concentration of Zn precursor was increasing. The films are transparent in
visible region, this transmission values decreases when the molar concentration increase caused by the
increasing of surface roughness
Split Second Analysis Covering High Pressure Gas Flow Dynamics At Pipe Outlet...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow
analysis can be resolved using established mathematical equations known as the Fanno condition, which
usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what
happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in
high pressure gas flow condition.
In this example air was selected for simulation purposes. In HVAC applications, such gas flow conditions
can occur in typical applications such as; air compressors releasing high pressure air through a pipe, or
compressor over pressure refrigerant gas being released into the atmosphere via a discharge pipe.
Investigation has shown that rather than a steady mass flow rate condition occurring at the pipe outlet,
calculated by the Fanno flow condition, a spiked increase in flow rate occurs at the beginning,and then
stabilizing after a few seconds, with relatively minor ripples in flow rate. Other observations were also
made and commented.
CFD results in mass flow rate were compared with the mathematically derived results, differences were
recorded. The CFD analysis showed how the k-omega turbulence model performed well, with the processor
stabilizing at an early stage.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
Advanced Energy: An International Journal (AEIJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Energy Engineering and allied fields. This multi disciplinary journal is devoted to the publication of high quality papers on theoretical and practical aspects of Energy Engineering.
A MODIFIED ANT COLONY ALGORITHM FOR SOLVING THE UNIT COMMITMENT PROBLEMAEIJjournal2
Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its
exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is
equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the
optimization of the generative units to minimize the full action cost regarding problem constraints. In this
article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in
a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from
local minimums by performing flexible memory system. The efficiency of proposed method in two power
system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed
method with results of the past well-known methods is a proof for suitability of performing the introduced
algorithm in economic input and output of generative units.
Impedance Spectroscopy Analysis of a Liquid Tin Anode Fuel Cell in Voltage Re...AEIJjournal2
A concept of a liquid tin anode-indirect carbon air fuel cell (LTA-ICFC) are described. Experimental
setups for analysis of LTA-ICFC polarisations of an operational electrochemical reactor of the LTA-ICFC
are presented. Results from Electrochemical Impedance Spectroscopy (EIS) Analysis of the electrochemical
reactor of the LTA-ICFC are shown and analysed.The rate-determining step of the system is concluded.
The charge-transfer resistance did not show considerable differences at 700-800 °C. This can be implied
that the charge-transfer resistance is not the rate-limiting step of the transport processes of the fuel cell.
The increase of the Warburg impedance concurrently with the resistance to fit mass-transport loss (R3)
suggests that the rate-limiting step for the LTA-ICFC in voltage recovery mode is the diffusion of the oxide
ions through SnO2 layer. The increment of mass transport lost, R3, of the cell causes the slowly increase of
the cell’s voltage over the voltage from 0.7-0.8 V at 700, 750, and 800 °C.
Impedance Spectroscopy Analysis of a Liquid Tin Anode Fuel Cell in Voltage Re...AEIJjournal2
A concept of a liquid tin anode-indirect carbon air fuel cell (LTA-ICFC) are described. Experimental
setups for analysis of LTA-ICFC polarisations of an operational electrochemical reactor of the LTA-ICFC
are presented. Results from Electrochemical Impedance Spectroscopy (EIS) Analysis of the electrochemical
reactor of the LTA-ICFC are shown and analysed.The rate-determining step of the system is concluded.
The charge-transfer resistance did not show considerable differences at 700-800 °C. This can be implied
that the charge-transfer resistance is not the rate-limiting step of the transport processes of the fuel cell.
The increase of the Warburg impedance concurrently with the resistance to fit mass-transport loss (R3)
suggests that the rate-limiting step for the LTA-ICFC in voltage recovery mode is the diffusion of the oxide
ions through SnO2 layer. The increment of mass transport lost, R3, of the cell causes the slowly increase of
the cell’s voltage over the voltage from 0.7-0.8 V at 700, 750, and 800 °C.
Willie Nelson Net Worth: A Journey Through Music, Movies, and Business Venturesgreendigital
Willie Nelson is a name that resonates within the world of music and entertainment. Known for his unique voice, and masterful guitar skills. and an extraordinary career spanning several decades. Nelson has become a legend in the country music scene. But, his influence extends far beyond the realm of music. with ventures in acting, writing, activism, and business. This comprehensive article delves into Willie Nelson net worth. exploring the various facets of his career that have contributed to his large fortune.
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Introduction
Willie Nelson net worth is a testament to his enduring influence and success in many fields. Born on April 29, 1933, in Abbott, Texas. Nelson's journey from a humble beginning to becoming one of the most iconic figures in American music is nothing short of inspirational. His net worth, which estimated to be around $25 million as of 2024. reflects a career that is as diverse as it is prolific.
Early Life and Musical Beginnings
Humble Origins
Willie Hugh Nelson was born during the Great Depression. a time of significant economic hardship in the United States. Raised by his grandparents. Nelson found solace and inspiration in music from an early age. His grandmother taught him to play the guitar. setting the stage for what would become an illustrious career.
First Steps in Music
Nelson's initial foray into the music industry was fraught with challenges. He moved to Nashville, Tennessee, to pursue his dreams, but success did not come . Working as a songwriter, Nelson penned hits for other artists. which helped him gain a foothold in the competitive music scene. His songwriting skills contributed to his early earnings. laying the foundation for his net worth.
Rise to Stardom
Breakthrough Albums
The 1970s marked a turning point in Willie Nelson's career. His albums "Shotgun Willie" (1973), "Red Headed Stranger" (1975). and "Stardust" (1978) received critical acclaim and commercial success. These albums not only solidified his position in the country music genre. but also introduced his music to a broader audience. The success of these albums played a crucial role in boosting Willie Nelson net worth.
Iconic Songs
Willie Nelson net worth is also attributed to his extensive catalog of hit songs. Tracks like "Blue Eyes Crying in the Rain," "On the Road Again," and "Always on My Mind" have become timeless classics. These songs have not only earned Nelson large royalties but have also ensured his continued relevance in the music industry.
Acting and Film Career
Hollywood Ventures
In addition to his music career, Willie Nelson has also made a mark in Hollywood. His distinctive personality and on-screen presence have landed him roles in several films and television shows. Notable appearances include roles in "The Electric Horseman" (1979), "Honeysuckle Rose" (1980), and "Barbarosa" (1982). These acting gigs have added a significant amount to Willie Nelson net worth.
Television Appearances
Nelson's char
WRI’s brand new “Food Service Playbook for Promoting Sustainable Food Choices” gives food service operators the very latest strategies for creating dining environments that empower consumers to choose sustainable, plant-rich dishes. This research builds off our first guide for food service, now with industry experience and insights from nearly 350 academic trials.
Artificial Reefs by Kuddle Life Foundation - May 2024punit537210
Situated in Pondicherry, India, Kuddle Life Foundation is a charitable, non-profit and non-governmental organization (NGO) dedicated to improving the living standards of coastal communities and simultaneously placing a strong emphasis on the protection of marine ecosystems.
One of the key areas we work in is Artificial Reefs. This presentation captures our journey so far and our learnings. We hope you get as excited about marine conservation and artificial reefs as we are.
Please visit our website: https://kuddlelife.org
Our Instagram channel:
@kuddlelifefoundation
Our Linkedin Page:
https://www.linkedin.com/company/kuddlelifefoundation/
and write to us if you have any questions:
info@kuddlelife.org
Micro RNA genes and their likely influence in rice (Oryza sativa L.) dynamic ...Open Access Research Paper
Micro RNAs (miRNAs) are small non-coding RNAs molecules having approximately 18-25 nucleotides, they are present in both plants and animals genomes. MiRNAs have diverse spatial expression patterns and regulate various developmental metabolisms, stress responses and other physiological processes. The dynamic gene expression playing major roles in phenotypic differences in organisms are believed to be controlled by miRNAs. Mutations in regions of regulatory factors, such as miRNA genes or transcription factors (TF) necessitated by dynamic environmental factors or pathogen infections, have tremendous effects on structure and expression of genes. The resultant novel gene products presents potential explanations for constant evolving desirable traits that have long been bred using conventional means, biotechnology or genetic engineering. Rice grain quality, yield, disease tolerance, climate-resilience and palatability properties are not exceptional to miRN Asmutations effects. There are new insights courtesy of high-throughput sequencing and improved proteomic techniques that organisms’ complexity and adaptations are highly contributed by miRNAs containing regulatory networks. This article aims to expound on how rice miRNAs could be driving evolution of traits and highlight the latest miRNA research progress. Moreover, the review accentuates miRNAs grey areas to be addressed and gives recommendations for further studies.
Diabetes is a rapidly and serious health problem in Pakistan. This chronic condition is associated with serious long-term complications, including higher risk of heart disease and stroke. Aggressive treatment of hypertension and hyperlipideamia can result in a substantial reduction in cardiovascular events in patients with diabetes 1. Consequently pharmacist-led diabetes cardiovascular risk (DCVR) clinics have been established in both primary and secondary care sites in NHS Lothian during the past five years. An audit of the pharmaceutical care delivery at the clinics was conducted in order to evaluate practice and to standardize the pharmacists’ documentation of outcomes. Pharmaceutical care issues (PCI) and patient details were collected both prospectively and retrospectively from three DCVR clinics. The PCI`s were categorized according to a triangularised system consisting of multiple categories. These were ‘checks’, ‘changes’ (‘change in drug therapy process’ and ‘change in drug therapy’), ‘drug therapy problems’ and ‘quality assurance descriptors’ (‘timer perspective’ and ‘degree of change’). A verified medication assessment tool (MAT) for patients with chronic cardiovascular disease was applied to the patients from one of the clinics. The tool was used to quantify PCI`s and pharmacist actions that were centered on implementing or enforcing clinical guideline standards. A database was developed to be used as an assessment tool and to standardize the documentation of achievement of outcomes. Feedback on the audit of the pharmaceutical care delivery and the database was received from the DCVR clinic pharmacist at a focus group meeting.
"Understanding the Carbon Cycle: Processes, Human Impacts, and Strategies for...MMariSelvam4
The carbon cycle is a critical component of Earth's environmental system, governing the movement and transformation of carbon through various reservoirs, including the atmosphere, oceans, soil, and living organisms. This complex cycle involves several key processes such as photosynthesis, respiration, decomposition, and carbon sequestration, each contributing to the regulation of carbon levels on the planet.
Human activities, particularly fossil fuel combustion and deforestation, have significantly altered the natural carbon cycle, leading to increased atmospheric carbon dioxide concentrations and driving climate change. Understanding the intricacies of the carbon cycle is essential for assessing the impacts of these changes and developing effective mitigation strategies.
By studying the carbon cycle, scientists can identify carbon sources and sinks, measure carbon fluxes, and predict future trends. This knowledge is crucial for crafting policies aimed at reducing carbon emissions, enhancing carbon storage, and promoting sustainable practices. The carbon cycle's interplay with climate systems, ecosystems, and human activities underscores its importance in maintaining a stable and healthy planet.
In-depth exploration of the carbon cycle reveals the delicate balance required to sustain life and the urgent need to address anthropogenic influences. Through research, education, and policy, we can work towards restoring equilibrium in the carbon cycle and ensuring a sustainable future for generations to come.
Natural farming @ Dr. Siddhartha S. Jena.pptxsidjena70
A brief about organic farming/ Natural farming/ Zero budget natural farming/ Subash Palekar Natural farming which keeps us and environment safe and healthy. Next gen Agricultural practices of chemical free farming.
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER OF A NANOFLUID OVER A NONLINEARLY STRETCHING SHEET
1. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
13
GDQ SIMULATION FOR FLOW AND HEAT TRANSFER
OF A NANOFLUID OVER A NONLINEARLY
STRETCHING SHEET
Delara Soltani1
and M. Gorji-Bandpy2
Department of Mechanical Engineering, Mazandaran Institute of Technology, Babol,
Iran1
Department of Mechanical Engineering, Babol University of Technology, Babol,Iran2
ABSTRACT
This paper presents the generalized differential quadrature (GDQ) simulation for analysis of a nanofluid
over a nonlinearly stretching sheet. The obtained governing equations of flow and heat transfer are
discretized by GDQ method and then are solved by Newton-Raphson method. The effects of stretching
parameter, Brownian motion number (Nb), Thermophoresis number (Nt) and Lewis number (Le), on the
concentration distribution and temperature distribution are evaluated. The obtained results exhibit that the
heat transfer rate can be controlled by choosing different nanoparticles and stretching parameter.
KEYWORDS
GDQ, Nonlinear stretching sheet, Nanofluid, Brownian motion, Thermophoresis
1 . INTRODUCTION
Boundary layer behaviour over a stretching surface has important industrial applications and
considerable role on many technological processes. Sakiadis [1] presented his work as a
pioneering study about boundary layer flow over a continuous solid surface moving with constant
velocity, then many researchers attention to this, and published many papers about that. The flow
created by the stretching of a sheet is obtained by Crane [2]. Many researchers such as Gupta and
Gupta [3], Dutta et al. [4], Chen and Char [5], Andersson [6] developed the work of Crane [2] by
adding the effects of heat and mass transfer analysis under different physical conditions. Wang
[7] found the closed form similarity solution of a full Navier–Stoke’s equations for the flow due
to a stretching sheet with partial slip. Furthermore, Wang [8] investigated stagnation slip flow and
heat transfer on a moving plate. Kelson and Desseaux [9, 10] investigated the effect of surface
conditions on the micropolar flow driven by a porous stretching sheet and the flow of a
micropolar fluid bounded by a linearly stretching sheet, and then Bhargava et al. [11] developed
that work by using nonlinear stretching sheet.
Meanwhile, Choi [12] proposed nanofluid for the first time and after that studies related to the
nanofluid dynamics have increased greatly due to its wide applications in industrial and
engineering systems [13-17]. Nanofluid is a suspension of a nanometer size solid particles and
fibres in convectional base fluids. Commonly used base fluids are water, toluene, oil and ethylene
glycol mixture and etc. Usually, the nanoparticles are constructed of metals such as Aluminum
and Copper, metal oxides (Al2O3), carbides (SiC), nitrides (AlN, SiN) or nonmetals such as
Graphite and Carbon nanotubes. Khan and Pop [18] obtained the flow of a nanofluid caused by
2. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
14
stretching sheet. After that, Khan and Aziz [19] used the same model to earn the boundary layer
flow of a nanofluid with a heat flux. Kuznetsov and Nield [20] studied the influence of
nanoparticles on natural convection boundary layer flow past a vertical plate by taking Brownian
motion and thermophoresis into account. Rana and Bhargava [21] extended the work of Khan and
Pop [18] by nonlinearly stretching sheet with finite element method (FEM).
The most numerical methods such as finite difference method (FDM) and finite element method
(FEM) should be applied to large number of grid points for having a good accuracy. Therefore,
these methods require to high calculations volume. But some new methods such as the
generalized differential quadrature method can have an exact response with a few chosen grid
point. The technique of differential quadrature (DQ) was proposed by Bellman et al [22]. The DQ
method is based on determination of weighting coefficients for any order derivative
discretization. Bellman et al. [22] suggested two approaches to determine the weighting
coefficients of the first order derivative. Shu [23] proposed the generalized differential quadrature
(GDQ), which can calculates the weighting coefficients of the first order derivative by a simple
algebraic formulation without any limitation in choice of nodes, and the weighting coefficients of
the second and higher order derivatives by a recurrence relation [24]. Now, this method is applied
to solve many engineering problems with many researchers [25-28].
In this paper, GDQ method is used to discrete the governing equations of flow and heat transfer
of nanofluid over nonlinearly stretching sheet. The discretized equations are solved by Newton-
Raphson method. The effects of stretching parameter ( ), Brownian motion number (Nb),
thermophoresis number (Nt) and Lewis number (Le), on the concentration distribution and
temperature distribution are evaluated.
2. FORMULATION OF PROBLEM
Consider laminar, steady, two dimensional boundary layer flow of an incompressible viscous
nanofluid over a nonlinearly stretching sheet. This geometry is shown in Fig.1, the sheet
stretching non-linearly that caused by applying two equal and opposite forces along x-axis and
this force makes the flow. Velocity of stretching isu ax
= , where, a is constant and is non-
linearly parameter. The pressure gradient and external force are neglected.
3. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
15
Figure 1. Physical model
The basic equations of nanoparticles and conservation of mass, momentum, thermal energy for
this geometry and flow can be expressed as [18,21];
0
u v
x y
∂ ∂
+ =
∂ ∂
(1)
2
2
u u u
u v v
x y y
∂ ∂ ∂
+ =
∂ ∂ ∂
(2)
2 2
[ . ( / )( ) ]
m B T
T T C T T
u v T D D T
x y y y y
∞
∂ ∂ ∂ ∂ ∂
+ = ∇ + +
∂ ∂ ∂ ∂ ∂
(3)
2 2
2 2
( / )
B T
C C C T
u v D D T
x y y y
∞
∂ ∂ ∂ ∂
+ = +
∂ ∂ ∂ ∂
(4)
Where
( )
m
m
f
k
c
= ,
( )
( )
p
f
c
c
=
Here, m
is the thermal diffusivity and is the proportion of the effective heat capacity of the
nanoparticle to heat capacity of the fluid. Also, B
D and T
D are the Brownian diffusion and the
thermophoretic diffusion coefficients, respectively.
The boundary condition for this problem are given by;
0,
v = , ,
w w w
u ax T T C C
= = = at y=0 (5a)
0, ,
u v T T C C as y
∞ ∞
= = = = → ∞ (5b)
Introducing the suitable transformations as;
1 1
2 2
( 1) ( 1) 1
, ( ), ( ( ) )
2 2 1
a a
y x u ax f v x f f
− −
+ + −
′ ′
= = = − +
+
( ) , ( )
W w
T T C C
T T C C
∞ ∞
∞ ∞
− −
= =
− − (6)
By substituting Eq. (6) into Eqs. (1-4) and Eqs. (5a, 5b), the governing equations and boundary
condition transform to;
2
2
( ) 0
1
f ff f
′′′ ′′ ′
+ − =
+
(7)
4. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
16
2
1
( ) 0
Pr
f Nb Nt
′′ ′ ′ ′ ′
+ + + = (8)
1
0
2
Nt
Lef
Nb
′′ ′ ′′
+ + = (9)
And
0, 1, 1, 1 0
0, 0, 0
f f at
f
′
= = = = =
′ = = = → ∞
(10)
where Pr
= and
B
Le
D
= are the Prandtl number and the Lewis number, respectively. Also
the Brownian motion and the thermophoresis parameters are introduced as follow:
( ) ( )
( )
( ) ( )
( )
p B w
f
p T w
f
c D C C
Nb
c
c D T T
Nt
c T
∞
∞
∞
−
=
−
=
(11)
To solve the high nonlinear Eqs. (7-9), a powerful method is used that describes in the next
section.
3. METHOD OF SOLUTION
3.1. Generalized differential quadrature
The GDQ method is based on the finding of weight coefficients and discretization derivation of
equations. The weighting coefficients for the first-order and higher-order derivatives are
calculated by the simple algebraic formulation and the recurrence relation, repectively. The
details of GDQM can be found in [24].
n-th order derivative with respect to x, at the grid point i
x as;
( ) ( )
1
( ) ( ), 1,..., 1
N
n n
x i ik k
k
f x C f x n N
=
= = −
∑ (12)
Weighting coefficients for the first order derivative;
(1)
(1)
(1)
( )
, , 1,..., ,
( ) ( )
i
ij
i j j
A x
C i j N i j
x x A x
= = ≠
−
(13)
Where
(1)
1
( ) ( )
N
i i j
j
j i
A x x x
=
≠
= −
∏ (14)
5. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
17
Weighting coefficients for the second and higher order derivatives;
( 1)
( ) ( 1) (1)
, , 1,2,..., ; 2,3,..., 1
n
ij
n n
ij ii ij
i j
C
C n C C i j N n N
x x
−
−
= − = = −
−
(15)
When i=j, the weighting coefficients given by;
( ) ( )
1
, 1,..., 1; 1,2,..., 1
N
n n
ii ij
j
j i
C C i N n N
=
≠
= − = − = −
∑ (16)
The sample points are obtained from the Chebyshev-Gauss-Lobatto as follows:
1 ( 1)
(1 cos( ))
2 1
i
i
X
N
−
= −
−
(17)
3.2. Discretization of the governing equations
Now Eqs. (7-9) are discreted with GDQ method:
(3) (2) (1) 2
1 1 1
2
( ) 0
1
N N N
ik k i ik k ik k
k k k
n
C f f C f C f
n
= = =
+ − =
+
∑ ∑ ∑ (18)
(2) (1) (1) 2 (1) (1)
1 1 1 1 1
1
( ) ( )( ) 0
Pr
N N N N N
ik k i ik k ik k ik k ik k
k k k k k
C f C Nt C Nb C C
= = = = =
+ + + =
∑ ∑ ∑ ∑ ∑ (19)
(1) (1) (2)
1 1 1
1
0
2
N N N
ik k i ik k ik k
k k k
Nt
C Lef C C
Nb
= = =
+ + =
∑ ∑ ∑ (20)
Also, discreted boundary conditions are
1 1 1
(1) (1)
1
1 1
0, 1, 0
1, 0
N N
N N
k k Nk k
k k
f
C f C f
= =
= = = = =
= =
∑ ∑
(21)
After that, the set of equations are solved by Newton-Raphson method.
4. RESULTS AND DISCUSSION
Numerical results are demonstrated for different values of Lewis number ( Le ), Brownian motion
parameter ( Nb ), thermophoresis parameter ( Nt ) and non-linearly parameter ( ). Also, Prandtl
number is assumed equal to Pr=2.
6. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
18
The obtained results by GDQ method are compared with presented results in Ref [29], where the
present problem is solved without Brownian motion parameter ( Nb ) and thermophoresis
parameter ( Nt ). This comparison is shown in Table 1 for reduced Nusselt number (0)
′
− .
Table 1. Comparison of results for reduced Nusselt number (0)
′
− and Pr=1.
Ref [29] Present results
0.2 0.610262 0.6112
0.5 0.595277 0.5953
1.5 0.574537 0.5755
3.0 0.564472 0.5643
10 0.554960 0.55510
7. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
19
Figure 2. Effect of Lewis number (Le) on concentration distribution and temperature distribution for Nb =
0.5, Nt = 0.5, Pr= 2.0, = 2.
Effects of Lewis number (Le) on concentration distribution and temperature distribution are
shown in Figures 2. These figures show that by increasing the Lewis number increases the
temperature distribution and decreases the concentration distribution. Figures 3 show variations
of concentration and temperature distribution by stretching parameter.
Effects of Brownian motion parameter (Nb) on concentration distribution and temperature
distributions are displayed in Figures 4. These figures prove that by increasing the Brownian
motion increases the temperature distribution and decreases the concentration distribution.
Figure 3. Effect of stretching parameter ( ) on concentration distribution and and temperature distribution
for Nb = 0.5, Nt = 0.5, Pr = 2.0, Le = 10.
Figure 4. Effect of Brownian motion parameter (Nb) on concentration distribution and temperature
distribution for Nt = 0.5, Pr = 2.0, Le = 2.0, 2
= .
8. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
20
Figure 5. Effect of thermophoresis parameter (Nt) on concentration distribution and temperature
distribution for Nb = 0.5, Pr = 2.0, Le = 2.0, 2
=
.
Also, curves of concentration and temperature distributions versus variations of thermophoresis
parameter (Nt) are presented in Figures 5. The results indicate that, increasing the thermophoresis
parameter increases the temperature distribution and decreases the concentration distribution.
5. CONCLUSIONS
In this paper, a powerful method (GDQ) was used to solve set of nonlinear equations for
nanofluid flow which are created by nonlinear stretching sheet. The GDQ method can be solved
this problem with few grid points and its results are accurate with minimum volume of
calculations. This study shows effects of different parameters on concentration distribution and
temperature distribution. As can be seen, increasing the Lewis number (Le) decrease both
temperature and concentration profiles and increasing the Brownian motion parameter (Nb)
increases temperature profile and decreases concentration profile. Therefore, the heat transfer rate
can be controlled by choosing different nano-particles for nanofluid. Also, increasing
9. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
21
thermophoresis parameter (Nt) increases concentration profile and decreases temperature profile.
The heat transfer rate and the concentration profile can be changed by decreasing or increasing
stretching parameter (n).
REFERENCES
[1] Sakiadis BC, (1961) "Boundary layer behaviour on continuous moving solid surfaces" Am Inst Chem
Eng J, Vol. 7, pp 26–28.
[2] Crane LJ, (1970) "Flow past a stretching plate", Z Angrew Math Phys, Vol. 21, pp 645–7.
[3] P.S. Gupta, A.S. Gupta, (1977) "Heat and mass transfer on a stretching sheet with suction or
blowing", Can. J. Chem. Eng. Vol. 55, pp 744–746
[4] B.K. Dutta, P. Roy, A.S. Gupta, (1985) "Temperature field in the flow over a stretching sheet with
uniform heat flux", Int. Commun.Heat Mass Transfer, Vol. 12, pp 89–94.
[5] C.K. Chen, M.I. Char (1988) "Heat transfer of a continuous stretching surface with suction or
blowing", J. Math. Anal. Appl.Vol. 135, pp 568–580.
[6] H.I. Andersson, (2002) " Slip flow past a stretching surface", Acta Mech, Vol. 158, pp 121–125.
[7] Wang CY, (2002) "Flow due to a stretching boundary with partial slip-an exact solution of the
Navier–Stokes equation", Chem Eng Sci, Vol. 57, pp 3745–3747.
[8] Wang CY, (2006) "Stagnation slip flow and heat transfer on a moving plate", Chem Eng Sci, Vol. 61,
pp 7668–7672.
[9] Kelson NA, Desseaux A, (2001) "Effect of surface condition on flow of micropolar fluid driven by a
porous stretching sheet", Int J Eng Sci, Vol. 39, pp 1881–1897.
[10] Desseaux A, Kelson NA, (2003) "Flow of a micropolar fluid bounded by a stretching sheet",
ANZIAM J., Vol. 42, pp 536–560.
[11] Bhargava R, Sharma S, Takhar HS, Beg OA, Bhargava P, (2007) "Numerical solutions for micropolar
transport phenomena over a nonlinear stretching sheet", Nonlinear Anal: Model Cont, Vol. 12, pp 45–
63.
[12] S. Choi, (1995) "Enhancing thermal conductivity of fluids with nanoparticle, development and
applications of non-Newtonian flow", ASME FED 231/MD, Vol. 66, pp 99–105.
[13] O.D. Makinde, A. Aziz, (2011) "Boundary layer flow of a nanofluid past a stretching sheet with
convective boundary condition", Int. J. Therm. Sci., Vol. 50, pp 1326–1332.
[14] T.G. Motsumi, O.D. Makinde, (2012) "Effects of thermal radiation and viscous dissipation on
boundary layer flow of nanofluids over a permeable moving flat plate", Phys. Sci., Vol. 86, 045003
(8pp).
[15] O.D. Makinde, (2012) "Analysis of Sakiadis flow of nanofluids with viscous dissipation and
Newtonian heating", Appl. Math. Mech., Vol. 33, No. 12, pp 1545–1554 (English Edition).
[16] Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ, (2001) "Anomalously increased effective thermal
conductivity of ethylene glycol-based nanofluids containing copper nanoparticles". Appl Phys Lett.,
Vol. 78, No. 6, pp 718–720.
[17] Choi SUS, Zhang ZG, Yu W, Lockwoow FE, Grulke EA, (2001) "Anomalous thermal conductivities
enhancement on nanotube suspension". Appl Phys Lett, Vol. 79, pp 2252–2254.
[18] W.A. Khan, I. Pop, (2010) "Boundary-layer flow of a nanofluid past a stretching sheet", Int. J. Heat
Mass Transfer, Vol. 53, pp 2477–2483.
[19] W.A. Khan, A. Aziz, (2011) "Natural convection flow of a nanofluid over a vertical plate with
uniform surface heat flux", Int. J. Therm. Sci., Vol. 50, pp 1207–1214.
[20] Kuznetsov AV, Nield DA, (2010) "Natural convection boundary-layer of a nanofluid past a vertical
plate", Int J Them Sci, Vol. 49, pp 243–247.
[21] P. Rana, R. Bhargava, (2012) "Flow and heat transfer of a nanofluid over a nonlinearly stretching
sheet: numerically", Commun Nonlinear Sci Numer Simulat, Vol. 17, pp 212–226.
[22] R. Bellman, B.G. Kashef, J. Casti, (1972) "Differential quadrature: a technique for the rapid solution
of nonlinear partial differential equations", J. Comput. Phys., Vol. 10, pp 40-52.
[23] C. Shu, (1991) "Generalized differential integral quadrature and application to the simulation of
incompressible viscous flows including parallel computation", Ph.D. Thesis, University of Glasgow.
[24] C. Shu, H. Xue, (1998) "Comparison of two approaches for implementing stream function boundary
conditions in DQ simulation of natural convection in a square cavity", Int J Heat and Fluid Flow, Vol.
19, pp 59-68.
10. Advanced Energy: An International Journal (AEIJ), Vol. 1, No. 1, January 2014
22
[25] C. Shu, BE Richards, (1992) "Parallel simulation of incompressible viscous flows by generalized
differential quadrature", Comput. Sys. Eng, Vol. 3, Nos 1-4, pp 271-281.
[26] J.O, Mingle, (1977) "The method of differential quadrature for transient nonlinear diffusion", J. Math.
Anal. Appl., Vol. 60, pp 559-569.
[27] M. Akbarzadeh. Kh, (2013) "Postbuckling analysis of cracked layered beam with piezoelectric
layers", M.Sc. Thesis, University of Tehran.
[28] M. Akbarzadeh. Kh, D. Soltani, (2013) "Diagnosis of type, location and size of cracks by using
generalized differential quadrature and Rayleigh quotient methods", J. Theoretical Appl. Mech., Vol.
43, No. 1, pp 61-70.
[29] Cortell R, (1994) "Similarity solutions for flow and heat transfer of a viscoelastic fluid over a
stretching sheet", Int J Non-Linear Mech, Vol. 29, pp 155–161.