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Papers by Dilip Kumar Jaiswal

Research paper thumbnail of Analytical solution for transport of pollutant from time-dependent locations along groundwater

Research paper thumbnail of Analytical solutions of time and spatially dependent one-dimensional advection-diffusion equation

A B ST R A C T Analytical solutions have been obtained for a one-dimensional advection-diffusion ... more A B ST R A C T Analytical solutions have been obtained for a one-dimensional advection-diffusion equation with variable coefficients in a semi-infinite longitudinal domain. Three cases are considered. In the first one the solute dispersion is time dependent along a uniform flow and in the second case the dispersion and the velocity both are considered spatially dependent expressions, while in third case, dispersion and the velocity both have time and spatially dependent expressions in degenerate forms. In first and third cases the solutions may be used for different time dependent expressions. It has become possible by introducing new independent variables with the help of certain transformations.

Research paper thumbnail of One–Dimensional Solute Transport for an Input against the Flow in a Homogeneous Finite Porous Media

International Journal of Engineering, 2019

A theoretical model comprising advection-dispersion equation with temporal seepage velocity, disp... more A theoretical model comprising advection-dispersion equation with temporal seepage velocity, dispersion coefficient and time dependent pulse type input of uniform nature applied against the flow in a finite porous domain. Input concentration is any continuous smooth function of time acts up to some finite time and then eliminated. Concentration gradient at other boundary is proportional to concentration. Dispersion is proportional to seepage velocity. Interpolation method is applied to reduce the input function into a polynomial. Certain transformations are utilized to reduce the variable coefficient into constant coefficient in the advection dispersion equation. The Laplace transform technique is applied to get the solution of advection dispersion equation. Two different functions of input are discussed to understand the utility of the present study. Obtained result is demonstrated graphically with the help of numerical example.

Research paper thumbnail of Study of Specially and Temporally Dependent Adsorption Coefficient in Heterogeneous Porous Medium

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow t... more One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

Research paper thumbnail of Discussion of “Analytical Solutions for Advection-Dispersion Equations with Time-Dependent Coefficients” by Baoqing Deng, Fei Long, and Jing Gao

Journal of Hydrologic Engineering, 2020

Research paper thumbnail of Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

JOURNAL OF ADVANCES IN PHYSICS, 2014

The present paper has been focused mainly towards understanding of the various parameters affecti... more The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Research paper thumbnail of Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

Journal of Engineering Mechanics, 2017

AbstractIn the dispersion theory of solute transport in groundwater flow, the dispersion coeffici... more AbstractIn the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the nth power of groundwater velocity, where n varies from 1 to 2...

Research paper thumbnail of Contaminant Diffusion along uniform flow velocity with pulse type input sources in finite porous medium

International Journal of Applied Mathematics, Electronics and Computers, 2014

Research paper thumbnail of Temporally Dependent Solute Dispersion in One-Dimensional Porous Media

Communications in Computer and Information Science, 2012

Research paper thumbnail of Fuzzy Model: Time Dependent Dispersion in Rivers

Indian International Conference on Artificial Intelligence, 2009

Research paper thumbnail of Analytical solutions for temporally dependent dispersion through homogeneous porous media

International Journal of Hydrology Science and Technology, 2012

Research paper thumbnail of Three-dimensional temporally dependent dispersion through porous media: analytical solution

Environmental Earth Sciences, 2011

Abstract A three-dimensional model for non-reactive solute transport in physically homogeneous su... more Abstract A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model ...

Research paper thumbnail of Analytical Solution to the One-Dimensional Advection-Diffusion Equation with Temporally Dependent Coefficients

Journal of Water Resource and Protection, 2011

Research paper thumbnail of Analytical Solutions of One-Dimensional Temporally Dependent Advection-Diffusion Equation along Longitudinal Semi-Infinite Homogeneous Porous Domain for Uniform Flow

IOSR Journal of Mathematics, 2012

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable ... more Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional to the dispersion coefficient. Retardation factor is also considered in present paper. Analytical solutions are obtained for two cases: former one is for uniform input point source and latter case is for increasing input point source where the solute transport is considered initially solute free. The Laplace transformation technique is used. New space and time variables are introduced to get the analytical solutions. The solutions in all possible combinations of increasing or decreasing temporally dependence dispersion are compared with each other with the help of graph. It is observed that the concentration attenuation with position and time is the fastest in case of decreasing dispersion in accelerating flow field.

Research paper thumbnail of Analytical solutions to one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media

Journal of Hydrology, 2010

Research paper thumbnail of Solute Transport along Temporally and Spatially Dependent Flows through Horizontal Semi-Infinite Media: Dispersion Proportional to Square of Velocity

Journal of Hydrologic Engineering, 2011

According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a ... more According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a power n of the velocity; the power ranges between 1 and 2. Based on the value n=1, analytical solutions of the dispersion problems along temporally dependent flow domains were obtained in previous works. In the present work, two dispersion problems are addressed for n=2. Using the Laplace transform technique, analytical solutions are obtained for two-dimensional advection-diffusion equations describing the dispersion of pulse-type point source along temporally and spatially dependent flow domains, respectively, through a semi-infinite horizontal isotropic medium. Point sources of a uniform and varying nature are considered. The inhomogeneity of the medium is demonstrated by the linearly interpolated velocity in the space variable. Introduction of new space variables enable one to reduce the advection-diffusion equation in both problems to a one-dimensional equation with constant coefficients. The solutions are...

Research paper thumbnail of Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one-dimensional semi-infinite media

Journal of Hydro-environment Research, 2009

Research paper thumbnail of Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain

Journal of Earth System Science, 2009

Research paper thumbnail of One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

Journal of Earth System Science, 2011

Research paper thumbnail of One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Hydrological Sciences Journal, 2012

This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

Research paper thumbnail of Analytical solution for transport of pollutant from time-dependent locations along groundwater

Research paper thumbnail of Analytical solutions of time and spatially dependent one-dimensional advection-diffusion equation

A B ST R A C T Analytical solutions have been obtained for a one-dimensional advection-diffusion ... more A B ST R A C T Analytical solutions have been obtained for a one-dimensional advection-diffusion equation with variable coefficients in a semi-infinite longitudinal domain. Three cases are considered. In the first one the solute dispersion is time dependent along a uniform flow and in the second case the dispersion and the velocity both are considered spatially dependent expressions, while in third case, dispersion and the velocity both have time and spatially dependent expressions in degenerate forms. In first and third cases the solutions may be used for different time dependent expressions. It has become possible by introducing new independent variables with the help of certain transformations.

Research paper thumbnail of One–Dimensional Solute Transport for an Input against the Flow in a Homogeneous Finite Porous Media

International Journal of Engineering, 2019

A theoretical model comprising advection-dispersion equation with temporal seepage velocity, disp... more A theoretical model comprising advection-dispersion equation with temporal seepage velocity, dispersion coefficient and time dependent pulse type input of uniform nature applied against the flow in a finite porous domain. Input concentration is any continuous smooth function of time acts up to some finite time and then eliminated. Concentration gradient at other boundary is proportional to concentration. Dispersion is proportional to seepage velocity. Interpolation method is applied to reduce the input function into a polynomial. Certain transformations are utilized to reduce the variable coefficient into constant coefficient in the advection dispersion equation. The Laplace transform technique is applied to get the solution of advection dispersion equation. Two different functions of input are discussed to understand the utility of the present study. Obtained result is demonstrated graphically with the help of numerical example.

Research paper thumbnail of Study of Specially and Temporally Dependent Adsorption Coefficient in Heterogeneous Porous Medium

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow t... more One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

Research paper thumbnail of Discussion of “Analytical Solutions for Advection-Dispersion Equations with Time-Dependent Coefficients” by Baoqing Deng, Fei Long, and Jing Gao

Journal of Hydrologic Engineering, 2020

Research paper thumbnail of Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

JOURNAL OF ADVANCES IN PHYSICS, 2014

The present paper has been focused mainly towards understanding of the various parameters affecti... more The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Research paper thumbnail of Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

Journal of Engineering Mechanics, 2017

AbstractIn the dispersion theory of solute transport in groundwater flow, the dispersion coeffici... more AbstractIn the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the nth power of groundwater velocity, where n varies from 1 to 2...

Research paper thumbnail of Contaminant Diffusion along uniform flow velocity with pulse type input sources in finite porous medium

International Journal of Applied Mathematics, Electronics and Computers, 2014

Research paper thumbnail of Temporally Dependent Solute Dispersion in One-Dimensional Porous Media

Communications in Computer and Information Science, 2012

Research paper thumbnail of Fuzzy Model: Time Dependent Dispersion in Rivers

Indian International Conference on Artificial Intelligence, 2009

Research paper thumbnail of Analytical solutions for temporally dependent dispersion through homogeneous porous media

International Journal of Hydrology Science and Technology, 2012

Research paper thumbnail of Three-dimensional temporally dependent dispersion through porous media: analytical solution

Environmental Earth Sciences, 2011

Abstract A three-dimensional model for non-reactive solute transport in physically homogeneous su... more Abstract A three-dimensional model for non-reactive solute transport in physically homogeneous subsurface porous media is presented. The model involves solution of the advection-dispersion equation, which additionally considered temporally dependent dispersion. The model ...

Research paper thumbnail of Analytical Solution to the One-Dimensional Advection-Diffusion Equation with Temporally Dependent Coefficients

Journal of Water Resource and Protection, 2011

Research paper thumbnail of Analytical Solutions of One-Dimensional Temporally Dependent Advection-Diffusion Equation along Longitudinal Semi-Infinite Homogeneous Porous Domain for Uniform Flow

IOSR Journal of Mathematics, 2012

Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable ... more Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional to the dispersion coefficient. Retardation factor is also considered in present paper. Analytical solutions are obtained for two cases: former one is for uniform input point source and latter case is for increasing input point source where the solute transport is considered initially solute free. The Laplace transformation technique is used. New space and time variables are introduced to get the analytical solutions. The solutions in all possible combinations of increasing or decreasing temporally dependence dispersion are compared with each other with the help of graph. It is observed that the concentration attenuation with position and time is the fastest in case of decreasing dispersion in accelerating flow field.

Research paper thumbnail of Analytical solutions to one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media

Journal of Hydrology, 2010

Research paper thumbnail of Solute Transport along Temporally and Spatially Dependent Flows through Horizontal Semi-Infinite Media: Dispersion Proportional to Square of Velocity

Journal of Hydrologic Engineering, 2011

According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a ... more According to the hydrodynamic dispersion theories, the dispersion parameter is proportional to a power n of the velocity; the power ranges between 1 and 2. Based on the value n=1, analytical solutions of the dispersion problems along temporally dependent flow domains were obtained in previous works. In the present work, two dispersion problems are addressed for n=2. Using the Laplace transform technique, analytical solutions are obtained for two-dimensional advection-diffusion equations describing the dispersion of pulse-type point source along temporally and spatially dependent flow domains, respectively, through a semi-infinite horizontal isotropic medium. Point sources of a uniform and varying nature are considered. The inhomogeneity of the medium is demonstrated by the linearly interpolated velocity in the space variable. Introduction of new space variables enable one to reduce the advection-diffusion equation in both problems to a one-dimensional equation with constant coefficients. The solutions are...

Research paper thumbnail of Analytical solutions for temporally and spatially dependent solute dispersion of pulse type input concentration in one-dimensional semi-infinite media

Journal of Hydro-environment Research, 2009

Research paper thumbnail of Analytical solutions of one-dimensional advection-diffusion equation with variable coefficients in a finite domain

Journal of Earth System Science, 2009

Research paper thumbnail of One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

Journal of Earth System Science, 2011

Research paper thumbnail of One-dimensional solute dispersion along unsteady flow through a heterogeneous medium, dispersion being proportional to the square of velocity

Hydrological Sciences Journal, 2012

This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.