One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is ...One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is considered. Due to heterogeneity velocity and dispersivity coefficient of the advection dispersion equation are considered functions of space variable and time variable. Analytical solution is obtained using Laplace transform technique when dispersivity depended on velocity. The effects of first order decay term and adsorption are studied. The graphical representations are made using展开更多
This paper presents non-Darcy mixed convective flow of an incompressible and viscous fluid in a differentially heated vertical channel filled with a porous material in the presence of a temperature dependent source/si...This paper presents non-Darcy mixed convective flow of an incompressible and viscous fluid in a differentially heated vertical channel filled with a porous material in the presence of a temperature dependent source/sink. The analytical solution of fourth order non-linear ordinary differential equation for temperature field, which is formed by eliminating velocity field from system of governing equations in non-dimensional form, is obtained by using new modified Adomian decomposition method (NMADM) in terms of various parameters. In order to illustrate the interactive influences of governing parameters on the temperature and velocity fields, a numerical study of the analytical solution is performed with respect to three categories of transport processes i) when forced convection is dominated, ii) when forced and natural convection are equal and iii) when natural convection is dominated. Analysis of all categories has revealed that the temperature and velocity profiles are increasing function of modified Darcy number while decreasing function of Forchheimer number.展开更多
Analytical solution is obtained to predict the contaminant concentration with presence and absence of pollution source in finite aquifer subject to constant point source concentration. A longitudinal dispersion along ...Analytical solution is obtained to predict the contaminant concentration with presence and absence of pollution source in finite aquifer subject to constant point source concentration. A longitudinal dispersion along unsteady groundwater flow in homogeneous and finite aquifer is considered which is initially solute free that is, aquifer is supposed to be clean. The constant source concentration in intermediate portion of the aquifer system is considered with pulse type boundary condition and at the other end of the aquifer, concentration gradient is supposed to be zero. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution of the formulated solute transport model with suitable initial and boundary conditions. The time varying velocities are considered. Analytical solutions are perhaps most useful for benchmarking the numerical codes and models. It may be used as the preliminary predictive tools for groundwater management.展开更多
文摘One dimensional advection dispersion equation is analytically solved initially in solute free domain by considering uniform exponential decay input condition at origin. Heterogeneous medium of semi infinite extent is considered. Due to heterogeneity velocity and dispersivity coefficient of the advection dispersion equation are considered functions of space variable and time variable. Analytical solution is obtained using Laplace transform technique when dispersivity depended on velocity. The effects of first order decay term and adsorption are studied. The graphical representations are made using
文摘This paper presents non-Darcy mixed convective flow of an incompressible and viscous fluid in a differentially heated vertical channel filled with a porous material in the presence of a temperature dependent source/sink. The analytical solution of fourth order non-linear ordinary differential equation for temperature field, which is formed by eliminating velocity field from system of governing equations in non-dimensional form, is obtained by using new modified Adomian decomposition method (NMADM) in terms of various parameters. In order to illustrate the interactive influences of governing parameters on the temperature and velocity fields, a numerical study of the analytical solution is performed with respect to three categories of transport processes i) when forced convection is dominated, ii) when forced and natural convection are equal and iii) when natural convection is dominated. Analysis of all categories has revealed that the temperature and velocity profiles are increasing function of modified Darcy number while decreasing function of Forchheimer number.
文摘Analytical solution is obtained to predict the contaminant concentration with presence and absence of pollution source in finite aquifer subject to constant point source concentration. A longitudinal dispersion along unsteady groundwater flow in homogeneous and finite aquifer is considered which is initially solute free that is, aquifer is supposed to be clean. The constant source concentration in intermediate portion of the aquifer system is considered with pulse type boundary condition and at the other end of the aquifer, concentration gradient is supposed to be zero. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution of the formulated solute transport model with suitable initial and boundary conditions. The time varying velocities are considered. Analytical solutions are perhaps most useful for benchmarking the numerical codes and models. It may be used as the preliminary predictive tools for groundwater management.
