A solution of the Burger’s equation arising in the Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media by Sumudu transform Homotopy perturbation Method
1) The document presents a solution to the Burger's equation, which describes the longitudinal dispersion phenomenon that occurs when miscible fluids flow through porous media.
2) The solution is obtained by applying the Sumudu transform to reduce the Burger's equation to a heat equation, which is then solved using the homotopy perturbation method.
3) The final solution obtained for concentration C is expressed as a function of distance x and time t, representing the concentration profile for longitudinal dispersion at any point in the porous media and at any time.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
Numerical analysis is used to examine the unsteady MHD free convection and mass transfer fluid flow through a porous medium in a rotating system. Impulsively started plate moving its individual plane is considered. Similarity equations of the corresponding momentum, energy, and concentration equations are derived by introducing a time dependent length scale which infect plays the role of a resemblance parameter. The velocity component is taken to be inversely proportional to this parameter. The effects on the velocity, temperature, concentration, local skin-friction coefficients, Nusselt number, Prandl number, Dufour, Soret number and the Sherwood number of the various important parameters entering into the problem separately are discussed with the help of graphs.
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.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
MHD convection flow of viscous incompressible fluid over a stretched vertical...IJERA Editor
The effect of thermal radiation, viscous dissipation and hall current of the MHD convection flow of the viscous incompressible fluid over a stretched vertical flat plate has been discussed by using regular perturbation and homotophy perturbation technique with similarity solutions. The influence of various physical parameters on velocity, cross flow velocity and temperature of fluid has been obtained numerically and through graphs.
MHD Natural Convection Flow of an incompressible electrically conducting visc...IJERA Editor
We consider a two-dimensional MHD natural convection flow of an incompressible viscous and electrically
conducting fluid through porous medium past a vertical impermeable flat plate is considered in presence of a
uniform transverse magnetic field. The governing equations of velocity and temperature fields with appropriate
boundary conditions are solved by the ordinary differential equations by introducing appropriate coordinate
transformations. We solve that ordinary differential equations and find the velocity profiles, temperature profile,
the skin friction and nusselt number. The effects of Grashof number (Gr), Hartmann number (M) and Prandtl
number (Pr), Darcy parameter (D-1) on velocity profiles and temperature profiles are shown graphically.
Unsteady Mhd free Convective flow in a Rotating System with Dufour and Soret ...IOSRJM
Numerical analysis is used to examine the unsteady MHD free convection and mass transfer fluid flow through a porous medium in a rotating system. Impulsively started plate moving its individual plane is considered. Similarity equations of the corresponding momentum, energy, and concentration equations are derived by introducing a time dependent length scale which infect plays the role of a resemblance parameter. The velocity component is taken to be inversely proportional to this parameter. The effects on the velocity, temperature, concentration, local skin-friction coefficients, Nusselt number, Prandl number, Dufour, Soret number and the Sherwood number of the various important parameters entering into the problem separately are discussed with the help of graphs.
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.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
MHD convection flow of viscous incompressible fluid over a stretched vertical...IJERA Editor
The effect of thermal radiation, viscous dissipation and hall current of the MHD convection flow of the viscous incompressible fluid over a stretched vertical flat plate has been discussed by using regular perturbation and homotophy perturbation technique with similarity solutions. The influence of various physical parameters on velocity, cross flow velocity and temperature of fluid has been obtained numerically and through graphs.
MHD Natural Convection Flow of an incompressible electrically conducting visc...IJERA Editor
We consider a two-dimensional MHD natural convection flow of an incompressible viscous and electrically
conducting fluid through porous medium past a vertical impermeable flat plate is considered in presence of a
uniform transverse magnetic field. The governing equations of velocity and temperature fields with appropriate
boundary conditions are solved by the ordinary differential equations by introducing appropriate coordinate
transformations. We solve that ordinary differential equations and find the velocity profiles, temperature profile,
the skin friction and nusselt number. The effects of Grashof number (Gr), Hartmann number (M) and Prandtl
number (Pr), Darcy parameter (D-1) on velocity profiles and temperature profiles are shown graphically.
Solitons Solutions to Some Evolution Equations by ExtendedTan-Cot Methodijceronline
The proposed extended Tan-Cot method is applied to obtain new exact travelling wave solutions to evolution equation. The method is applicable to a large variety of nonlinear partial differential equations, the Fifth-order nonlinear integrable equation, the symmetric regularized long wave equation, the higher-order wave equation of Kdv type, and Benney-Luke equation. The Extended Tan-Cot method seems to be powerful tool in dealing with nonlinear physical models
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
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.
Applications of Homotopy perturbation Method and Sumudu Transform for Solving...IJRES Journal
In this paper, we make use of the properties of the Sumudu transform to find the exact solution of
fractional initial-boundary value problem (FIBVP) and fractional KDV equation. The method, namely,
homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the
HPM using He’s polynomials. This method is very powerful and professional techniques for solving different
kinds of linear and nonlinear fractional differential equations arising in different fields of science and
engineering. We also present two different examples to illustrate the preciseness and effectiveness of this
method.
B spline collocation solution for an equation arising in instability phenomenoneSAT Journals
Abstract
In the present paper numerical discusses a theoretical model for instability phenomenon in double phase flow through
homogeneous porous medium. Relation between relative permeability and saturation has been considered based on earlier
experiment. A governing nonlinear partial differential equation is solved by collocation method with cubic B-splines. To obtain
the scheme of the equation the nonlinear term is approximated by Taylor series which leads to tridiagonal system and has been
solved by well-known Thomas Algorithm. The Numerical solution is obtained by using MATLAB coding.
Keywords: Darcy’s law, Taylor series, Saturation, Cubic B-splines
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with S...IJERA Editor
This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized
Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the
no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is
introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete
Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear
stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant
pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition
and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various
parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between
the two cases is also made.
Effect of an Inclined Magnetic Field on Peristaltic Flow of Williamson Fluid ...QUESTJOURNAL
ABSTRACT: This paper deals with the influence ofinclined magnetic field on peristaltic flow of an incompressible Williamson fluid in an inclined channel with heat and mass transfer. 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.
Stability study of stationary solutions of the viscous Burgers equation using Fourier mode stability analysis for the stationary solutions u1 = D , where
D is constant and u1 =u1(x),0≤x≤1, in two cases is analyzed. Firstly when the wave amplitude A is constant and secondly when the wave amplitude A is variable. In the case of constant amplitude, the results found to be: The solution u1 = D is always stable while the solution u1 = u1 (x) is conditionally stable. In the case of variable amplitude, it has been found that the solutions u1 = D and u1 = u1 (x) , 0 ≤ x ≤ 1 are conditionally stable.
A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND DIFFERENTIAL EVOLUTIONijsc
Two modern optimization methods including Particle Swarm Optimization and Differential Evolution are
compared on twelve constrained nonlinear test functions. Generally, the results show that Differential
Evolution is better than Particle Swarm Optimization in terms of high-quality solutions, running time and
robustness.
Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Co...IOSR Journals
Tan-cot method is applied to get exact soliton solutions of non-linear partial differential equations notably generalized Benjamin-Bona-Mahony, Zakharov-Kuznetsov Benjamin-Bona-Mahony, Kadomtsov-Petviashvilli Benjamin-Bona-Mahony and Korteweg-de Vries equations, which are important evolution equations with wide variety of physical applications. Elastic behavior and soliton fusion/fission is shown graphically and discussed physically as far as possible
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The variational iteration method for calculating carbon dioxide absorbed into...iosrjce
In this paper, the variational iteration method (VIM) is used to get an approximate solution for a
system of two coupled nonlinear ordinary differential equations which represent the concentrations of carbon
dioxide 퐶푂2 and phenyl glycidyl ether. In this system there are boundary conditions of Dirichlet type and the
other is a mixed set of Neumann and Dirichlet type. Our calculations evidenced by tables and figures for the
analysis of the maximal error remainder values. The variational iteration method gives approximate solutions
with fast convergence. Comparison with the results obtained by the Adomian decomposition method (ADM)
reveals that the numerical solutions obtained by the VIM converge faster than those of Adomian's method. The
software we used in our study of these calculations is Mathematica®
9.
Solitons Solutions to Some Evolution Equations by ExtendedTan-Cot Methodijceronline
The proposed extended Tan-Cot method is applied to obtain new exact travelling wave solutions to evolution equation. The method is applicable to a large variety of nonlinear partial differential equations, the Fifth-order nonlinear integrable equation, the symmetric regularized long wave equation, the higher-order wave equation of Kdv type, and Benney-Luke equation. The Extended Tan-Cot method seems to be powerful tool in dealing with nonlinear physical models
Homotopy Analysis to Soret and Dufour Effects on Heat and Mass Transfer of a ...iosrjce
The objective of this paper is to study the Soret and Dufour effects on the free convection boundary
layer flow of an incompressible, viscous and chemically reacting fluid over a vertical plate in the presence of
viscous dissipation. The governing partial differential equations are converted to a set of ordinary differential
equations using suitable similarity transformations. The resulting equations are solved analytically using
homotopy analysis method (HAM). The convergence of obtained analytical solutions is explicitly discussed. The
effects of various parameters on dimensionless velocity, temperature and concentration profiles are discussed
with the help of graphs. The numerical values of skin friction, Nusselt number and Sherwood number for
different parameters are presented in tabular form. Our results are compared with the previously published
results and are found to be in good agreement.
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.
Applications of Homotopy perturbation Method and Sumudu Transform for Solving...IJRES Journal
In this paper, we make use of the properties of the Sumudu transform to find the exact solution of
fractional initial-boundary value problem (FIBVP) and fractional KDV equation. The method, namely,
homotopy perturbation Sumudu transform method, is the combination of the Sumudu transform and the
HPM using He’s polynomials. This method is very powerful and professional techniques for solving different
kinds of linear and nonlinear fractional differential equations arising in different fields of science and
engineering. We also present two different examples to illustrate the preciseness and effectiveness of this
method.
B spline collocation solution for an equation arising in instability phenomenoneSAT Journals
Abstract
In the present paper numerical discusses a theoretical model for instability phenomenon in double phase flow through
homogeneous porous medium. Relation between relative permeability and saturation has been considered based on earlier
experiment. A governing nonlinear partial differential equation is solved by collocation method with cubic B-splines. To obtain
the scheme of the equation the nonlinear term is approximated by Taylor series which leads to tridiagonal system and has been
solved by well-known Thomas Algorithm. The Numerical solution is obtained by using MATLAB coding.
Keywords: Darcy’s law, Taylor series, Saturation, Cubic B-splines
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with S...IJERA Editor
This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized
Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the
no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is
introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete
Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear
stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant
pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition
and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various
parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between
the two cases is also made.
Effect of an Inclined Magnetic Field on Peristaltic Flow of Williamson Fluid ...QUESTJOURNAL
ABSTRACT: This paper deals with the influence ofinclined magnetic field on peristaltic flow of an incompressible Williamson fluid in an inclined channel with heat and mass transfer. 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.
Stability study of stationary solutions of the viscous Burgers equation using Fourier mode stability analysis for the stationary solutions u1 = D , where
D is constant and u1 =u1(x),0≤x≤1, in two cases is analyzed. Firstly when the wave amplitude A is constant and secondly when the wave amplitude A is variable. In the case of constant amplitude, the results found to be: The solution u1 = D is always stable while the solution u1 = u1 (x) is conditionally stable. In the case of variable amplitude, it has been found that the solutions u1 = D and u1 = u1 (x) , 0 ≤ x ≤ 1 are conditionally stable.
A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND DIFFERENTIAL EVOLUTIONijsc
Two modern optimization methods including Particle Swarm Optimization and Differential Evolution are
compared on twelve constrained nonlinear test functions. Generally, the results show that Differential
Evolution is better than Particle Swarm Optimization in terms of high-quality solutions, running time and
robustness.
Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Co...IOSR Journals
Tan-cot method is applied to get exact soliton solutions of non-linear partial differential equations notably generalized Benjamin-Bona-Mahony, Zakharov-Kuznetsov Benjamin-Bona-Mahony, Kadomtsov-Petviashvilli Benjamin-Bona-Mahony and Korteweg-de Vries equations, which are important evolution equations with wide variety of physical applications. Elastic behavior and soliton fusion/fission is shown graphically and discussed physically as far as possible
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The variational iteration method for calculating carbon dioxide absorbed into...iosrjce
In this paper, the variational iteration method (VIM) is used to get an approximate solution for a
system of two coupled nonlinear ordinary differential equations which represent the concentrations of carbon
dioxide 퐶푂2 and phenyl glycidyl ether. In this system there are boundary conditions of Dirichlet type and the
other is a mixed set of Neumann and Dirichlet type. Our calculations evidenced by tables and figures for the
analysis of the maximal error remainder values. The variational iteration method gives approximate solutions
with fast convergence. Comparison with the results obtained by the Adomian decomposition method (ADM)
reveals that the numerical solutions obtained by the VIM converge faster than those of Adomian's method. The
software we used in our study of these calculations is Mathematica®
9.
Reduction of Side Lobes by Using Complementary Codes for Radar ApplicationIOSR Journals
The analysis of new types of Complementary direct sequence complex signals which have synthesized
with well – know code sequences like Barker, Walsh, Golay, and complementary codes. Build on the
autocorrelation function (ACF) and ambiguity function (AF) of signals, the numerical method estimates the
volume of side lobes separately for each signal. The results obtained show that the signals, which have a low
volume of side lobes, means of approximately zero in by using complementary codes with compare to different
codes
Non- Newtonian behavior of blood in very narrow vesselsIOSR Journals
The purpose of the study is to get some qualitative and quantitative insight into the problem of flow in vessels under consideration where the concentration of lubrication film of plasma is present between each red cells and tube wall. This film is potentially important in region to mass transfer and to hydraulic resistance, as well as to the relative resistance times of red cells and plasma in the vessels network.
Multi-Element Determination of Cu, Mn, and Se using Electrothermal Atomic Abs...IOSR Journals
Simultaneous multi-element graphite furnace atomic absorption spectrometer (SIMAA 6000) is used to get a new multi-element determinations methodology for Cu, Mn, and Se. Firstly, the optimum conditions for single-element mode are determined (which include: pyrolysis and atomization temperatures). Secondly, the optimum conditions for multi-element mode are also determined. The conditions in the two modes have been compared in terms of the characteristic masses, detection limits and pyrolysis and atomization temperatures. The effect of the matrix on the determination has been studied using urine standard sample from Seronorm (LOT 0511545). The accuracy of the developing methods has been confirmed by analysis different biological reference materials. Simultaneous multi-element GF-AAS offers a rapid, low cost and sensitive method for the analysis of trace elements
Curative Effect of Parinari curatellifolia Leaf Extract on EpiglottitisIOSR Journals
The curative effect of Parinari curatellifolia leaf extract on epiglottitis was investigated. The air dried leaf of Parinari curatellifolia was extracted using the soxhlet extractor. Crude extract of the plant was found to be rich in phytochemicals of medicinal importance such as alkaloids, tannins, saponins, flavonoids, steroids, and cardiac glycosides. Acetic acid extract had the highest antimicrobial activity with zones of inhibition ranging from 20.0 ± 0.6 to 28.3 ± 0.3 against the test organisms. This activity was not significantly (P<0.05) different from leofloxacin with zones of inhibition ranging from 25.0 ± 0.6 to 29.3 ± 0.3 which was the highest activity among the standard drugs used. The minimum inhibitory concentration (MIC) of the extract was found to be 5mg/ml against Pseudomonas sp and Staphylococcus aureus, indicating broad spectrum activity. Results were discussed in respect to traditional treatment of epiglottitis.
Curative Effect of Parinari curatellifolia Leaf Extract on Epiglottitis
Similar to A solution of the Burger’s equation arising in the Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media by Sumudu transform Homotopy perturbation Method
Chemical Reaction on Heat and Mass TransferFlow through an Infinite Inclined ...iosrjce
The numerical studies are performed to examine the mass transfer flow with thermal diffusion and
diffusion thermo effect past an infinite, inclined vertical plate in a porous medium in the presence of chemical
reaction. First of all, the governing equations are transformed to a system of dimensionless coupled partial
equations. Explicit finite difference method has been used to solve these dimensionless equations for momentum,
concentration and energy equations. During the course of discussion, it is found that various parameters related
to the problem influence the calculated result. Finally, the profiles of velocity, concentration and temperature
are analyzed and illustrated with graphs.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq
equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper
approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy
perturbation transform method(HPTM). The solution is compared with the exact solution. The
comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height
of water table. The results resemble well with the physical phenomena.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq
equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper
approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy
perturbation transform method(HPTM). The solution is compared with the exact solution. The
comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height
of water table. The results resemble well with the physical phenomena.
Controlling of Depth of Dopant Diffusion Layer in a Material by Time Modulati...IJCI JOURNAL
In this paper as a development of recently introduced analytical approach for estimation of temporal characteristics of mass and heat transport we present analysis of diffusion depth of dopant in a material with time varying diffusion coefficient. It has been shown, that changing of time dependence of diffusion coefficient gives a possibility to accelerate or decelerate diffusion process. In this situation it is an actual question is control of diffusion depth during manufacturing p-n-junctions. The controlling gives a possibility to obtain required depth of the junctions, but not larger or smaller.
Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Uns...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
Numerical Solution of Diffusion Equation by Finite Difference Methodiosrjce
IOSR Journal of Mathematics(IOSR-JM) is a double blind peer reviewed 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.
Sinc collocation linked with finite differences for Korteweg-de Vries Fraction...IJECEIAES
A novel numerical method is proposed for Korteweg-de Vries Fractional Equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The method combining a finite difference approach in the time-fractional direction, and the Sinc-Collocation in the space direction, where the derivatives are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The numerical results are shown to demonstrate the efficiency of the newly proposed method. Easy and economical implementation is the strength of this method.
A Tau Approach for Solving Fractional Diffusion Equations using Legendre-Cheb...iosrjce
In this paper, a modified numerical algorithm for solving the fractional diffusion equation is
proposed. Based on Tau idea where the shifted Legendre polynomials in time and the shifted Chebyshev
polynomials in space are utilized respectively.
The problem is reduced to the solution of a system of linear algebraic equations. From the computational point
of view, the solution obtained by this approach is tested and the efficiency of the proposed method is confirmed.
STEADY FLOW OF A VISCOUS FLUID THROUGH A SATURATED POROUS MEDIUM AT A CONSTAN...Journal For Research
In this paper the Steady flow of a viscous fluid through a porous medium over a fixed horizontal, impermeable and thermally insulated bottom. The flow through the porous medium satisfies the general momentum and energy equations are obtained when the temperature on the fixed bottom and on free surface prescibed. By using Galerkin Method, the expression for Velocity and Drag force are obtained. The Galerkin Method endowed with distinct features that account for its superiority over competing methods. The effect of different parameters on Velocity and Drag force are discussed with the help of graphs.
Basics of Contaminant Transport in Aquifers (Lecture)Amro Elfeki
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Elzaki transform homotopy perturbation method for solving porous medium equat...eSAT Journals
Abstract In this paper, the ELzaki transform homotopy perturbation method (ETHPM) has been successfully applied to obtain the approximate analytical solution of the nonlinear homogeneous and non-homogeneous gas dynamics equations. The proposed method is an elegant combination of the new integral transform “ELzaki Transform” and the homotopy perturbation method. The method is really capable of reducing the size of the computational work besides being effective and convenient for solving nonlinear equations. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. A clear advantage of this technique over the decomposition method is that no calculation of Adomian’s polynomials is needed. Keywords: ELzaki transform, Homotopy perturbation method, non linear partial differential equation, and nonlinear gas dynamics equation
Elzaki transform homotopy perturbation method for solving porous medium equat...eSAT Journals
Abstract In this paper, we apply a new method called ELzaki transform homotopy perturbation method (ETHPM) to solve porous medium equation. This method is a combination of the new integral transform “ELzaki transform” and the homotopy perturbation method. The nonlinear term can be easily handled by homotopy perturbation method. The porous medium equations have importance in engineering and sciences and constitute a good model for many systems in various fields. Some cases of the porous medium equation are solved as examples to illustrate ability and reliability of mixture of ELzaki transform and homotopy perturbation method. The results reveal that the combination of ELzaki transform and homotopy perturbation method is quite capable, practically well appropriate for use in such problems and can be applied to other nonlinear problems. This method is seen as a better alternative method to some existing techniques for such realistic problems. Key words: ELzaki transform, Homotopy perturbation method, non linear partial differential equation, and porous medium equation
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.
Similar to A solution of the Burger’s equation arising in the Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media by Sumudu transform Homotopy perturbation Method (20)
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
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THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
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Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
A solution of the Burger’s equation arising in the Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media by Sumudu transform Homotopy perturbation Method
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 11, Issue 1 Ver. V (Jan - Feb. 2015), PP 42-45
www.iosrjournals.org
DOI: 10.9790/5728-11154245 www.iosrjournals.org 42 | Page
A solution of the Burger’s equation arising in the Longitudinal
Dispersion Phenomena in Fluid Flow through Porous Media by
Sumudu transform Homotopy perturbation Method
Twinkle Singh1
, Bhumika G. Choksi2
, M.N.Mehta3
, Shreekant Pathak4
Applied Mathematics and Humanities Department, SaradarVallabhbhai National Institute of Technology,
Surat-395007
Abstract: The goal of the paper is to examine the concentration of the longitudinal dispersion phenomenon
arising in fluid flow through porous media. The solution of the Burger’s equation for the dispersion problem is
presented by approach to Sumudu transformation. The solution is obtained by using suitable conditions and is
more simplified under the standard assumptions.
Keywords: Longitudinal Dispersion phenomenon, porous media, Sumudu transform.
I. Introduction
The present paper discusses the solution of Burger’s equation [7] which represents longitudinal
dispersion of miscible fluid flow through porous media.
Miscible displacement is one type of poly-phase flow in porous media, where both of the phases are
completely soluble in each other. Hence the capillary forces between these two fluids do not come into effect.
The miscible displacement could be described in a very simple form as follows:
The mixture of the fluids, under the conditions of complete miscibility, could be thought to behave as a
single-phase fluid. Therefore it will obey the Darcy’s law.
The change of connection would be caused by diffusion along the flow channels and thus be governed
by diffusion of one fluid into the other.
The problem is to find the concentration as a function of time t and position x, as two miscible fluids
flow through porous media on either sides of the mixed region, the single fluid equation describes the motion of
the fluid. The problem becomes more complicated in one dimension with fluids of equal properties. Hence the
mixing takes place longitudinally as well as transversely at time t = 0, a dot of fluid having C0concentration is
injected over the phase. It is shown in figure-1. The dot moves in the direction of flow as well as perpendicular
to the flow. Finally, it takes the shape of ellipse with a different concentration Cn.
Figure-1 Longitudinal Dispersion Phenomenon
Many researchers have contributed in various physical phenomena. Patel and Mehta [14] have worked
on Burger’s equation for longitudinal dispersion of miscible fluid flow through porous media. Meher and Mehta
[13] have discussed on a new approach to Backlund transformation to solve Burger’s equation in longitudinal
dispersion phenomenon. Borana, Pradhan and Mehta [12] have discussed numerical solution of Burger’s
equation.
To solve the differential equations, the integral transform is extensively applied and thus there are
several works on the theory and application of integral transforms. In the sequence of these transforms,
Watugala [4] introduced a new integral transform, named the Sumudu transform, and further applied it to the
solution of ordinary differential equation in control engineering problems; see [4]. For further details and
properties of Sumudu transform see [1,3,5,8-10]. The Sumudu transform is defined over the set of the functions
A = f(t)/∃M,τ1, τ2 > 0, f t < Me
t
τj , if tϵ −1 j
× 0, ∞ (1)
by the following formula:
2. A Solution of the Burger’s Equation arising in the Longitudinal Dispersion Phenomena…
DOI: 10.9790/5728-11154245 www.iosrjournals.org 43 | Page
f u = S f t ; u = f ut e−t
dt,
∞
0
u ∈ −τ1, τ2 (2)
II. Mathematical Formulation Of The Problem
According to Darcy’s law, the equation of continuity for the mixture, in the case of compressible fluids
is given by
∂ρ
∂t
+ ∇ ∙ ρv = 0 3
whereρ is the density for the mixture and v is the pore seepage velocity.
The equation of diffusion for a fluid flow through a homogeneous porous medium, without increasing or
decreasing the dispersing material is given by
∂C
∂t
+ ∇ ∙ Cv = ∇ ∙ ρD∇
C
ρ
4
Where C is the concentration of the fluid, D is the tensor coefficient of dispersion with nine components Dij .
In a laminar flow through homogeneous porous medium at a constant temperature,ρ is constant.
Then∇ ∙ v = 0 5
Thus equation (4) becomes
∂C
∂t
+ v ∙ ∇C = ∇ ∙ D∇C (6)
When the seepage velocity is the along x-axis, the non-zero components are D11 = DL ≅ x2
(coefficient of longitudinal dispersion, is a function of x along the x-axis) and other Dij are zero. In this case
equation (6) becomes
∂C
∂t
+ u
∂C
∂x
= x2
∂2
C
∂x2
7
where u is the component of velocity along the x-axis, which is time dependent, as well as concentration along
the x-axis in x > 0 direction, and it is cross-sectional flow velocity of porous medium.
∴ u =
C x, t
C0
, for x > 0 (8)
The boundary and initial conditions in longitudinal direction are
C 0, t = C1 t > 0 9
C x, 0 = C0 x > 0 10
where C0 is the initial concentration of the tracer (one fluid A) and C1 is the concentration of the tracer (of the
same fluid) at x = 0.
Hence equation (7) becomes
∂C
∂t
+
C
C0
∂C
∂x
= x2
∂2
C
∂x2
11
Consider the dimensionless variables
X =
C0
L
x, T =
t
L
; 0 ≤ x ≤
L
C0
and t ≥ 0 12
Thus equation (11) becomes
∂C
∂T
+ C
∂C
∂X
= LX2
∂2
C
∂X2
∴
∂C
∂T
+ C
∂C
∂X
= ε
∂2
C
∂X2
where ε = LX2
13
where C 0, T = C1 T > 0
C X, 0 = C0′ X > 0
Equation (13) is the non-linear Burger’s equation for longitudinal dispersion arising in fluid flow through porous
media.
Choose the transformation [2, 6,14]
C = ΨX , Ψ = −2εlogξ 14
which reduces equation (13) to the diffusion type Heat equation as
3. A Solution of the Burger’s Equation arising in the Longitudinal Dispersion Phenomena…
DOI: 10.9790/5728-11154245 www.iosrjournals.org 44 | Page
ξT = εξXX 15
whereε = LX2
∴
∂ξ
∂T
= LX2
∂2
ξ
∂X2
16
where ξ 0, T = 0
ξ X, 0 = X2
Applying Sumudu transform to equation (16), we get
S
∂ξ
∂T
= LX2
S
∂2
ξ
∂X2
∴
1
u
S ξ X, T −
1
u
ξ X, 0 = LX2
S ξXX
∴ S ξ X, T = X2
+ LuX2
S ξXX 17
Applying inverse Sumudu transform on equation (17), we get
ξ X, T = X2
+ 𝐿𝑋2
𝑆−1
𝑢𝑆 𝜉 𝑋𝑋 18
Now applying Homotopy Perturbation method, we get
𝑝 𝑛
𝜉 𝑛 𝑋, 𝑇
∞
𝑛=0
= 𝑋2
+ 𝑝 𝐿𝑋2
𝑆−1
𝑢𝑆 𝜉 𝑋𝑋 19
Comparing the coefficient of like powers of p, we get
𝑝0
: 𝜉0 𝑋, 𝑇 = 𝑋2
20
𝑝1
: 𝜉1 𝑋, 𝑇 = 𝐿𝑋2
𝑆−1
𝑢𝑆 (𝜉0) 𝑋𝑋 = 2𝐿𝑋2
𝑇 21
𝑝2
: 𝜉2 𝑋, 𝑇 = 𝐿𝑋2
𝑆−1
𝑢𝑆 (𝜉1) 𝑋𝑋 = 22
𝐿2
𝑋2
𝑇2
2!
22
Proceeding in a similar manner, we get
𝑝3
: 𝜉3 𝑋, 𝑇 = 23
𝐿3
𝑋2
𝑇3
3!
,
𝑝4
: 𝜉4 𝑋, 𝑇 = 24
𝐿4
𝑋2
𝑇4
4!
, 23
Thus the solution 𝜉(𝑋, 𝑇) is given by
𝜉 X, T = X2
1 + 2LT+ 22
L2
T2
2!
+ 23
L3
T3
3!
+ 24
L4
T4
4!
+ ⋯
ξ X, T = X2
e2LT
24
Now to find C, using equation (14), we get
C =
∂
∂X
−2εlogξ
∴ C =
∂
∂X
−2LX2
log X2
e2LT
∴ C = −4LX 1 + log X2
e2LT
25
OR C = −4C0x 1 + 2 log
C0
L
x + 2t
The solution (25) represents the concentration of the longitudinal dispersion phenomenon for any value of x
and for any time t.
III. Concluding Remark
Expression (25) represents the solution of Burger’s equation arising in longitudinal dispersion phenomenon in
fluid flow through porous media which is the concentration for any time
= 0.1, 0.2,0.3,0.4, 0.5, 0.6, 0.7,0.8,0.9 and 1.0. The graph shows the concentration versus distance x when time
t is fixed, and it is observed over here is that after distance 0.01, concentration was increased scatterely.
x
t
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.1 0.3204 0.5299 0.6976 0.8380 0.9583 1.0624 1.1532 1.2325 1.3017 1.3621
0.2 0.3124 0.5139 0.6736 0.8060 0.9183 1.0144 1.0972 1.1685 1.2297 1.2821
0.3 0.3044 0.4979 0.6496 0.7740 0.8783 0.9664 1.0412 1.1045 1.1577 1.2021
4. A Solution of the Burger’s Equation arising in the Longitudinal Dispersion Phenomena…
DOI: 10.9790/5728-11154245 www.iosrjournals.org 45 | Page
0.4 0.2964 0.4819 0.6256 0.7420 0.8383 0.9184 0.9852 1.0405 1.0857 1.1221
0.5 0.2884 0.4659 0.6016 0.7100 0.7983 0.8704 0.9282 0.9765 1.0137 1.0421
0.6 0.2804 0.4499 0.5776 0.6780 0.7583 0.8224 0.8732 0.9125 0.9417 0.9621
0.7 0.2724 0.4339 0.5536 0.6460 0.7183 0.7744 0.8172 0.8485 0.8697 0.8821
0.8 0.2644 0.4179 0.5296 0.6140 0.6783 0.7264 0.7612 0.7845 0.7977 0.8021
0.9 0.2564 0.4019 0.5056 0.5820 0.6383 0.6784 0.7052 0.7205 0.7257 0.7221
1.0 0.2484 0.3859 0.4816 0.5520 0.5983 0.6304 0.6492 0.6565 0.6537 0.6421
Table-1 The value of concentration for different values of distance, x and time, t
Graph-1: Concentration, C versus distance, x.
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