Effect of Buoyancy and Magnetic Field on Unsteady Convective Diusion of Solute in a Boussinesq Stokes Suspension Bounded by Porous Beds

Hydromagnetic free and forced convection in a parallel plate channel bounded by porous bed and transverse magnetic field has been considered. When there is a uniform axial temperature variation along the walls, the primary flow shows incipient flow reversal at the upper plate for an increase in temperature along that plate. Similarly flow reversal at the lower plate occurs with a decrease in temperature along that plate. The magnetic field, arising as a body couple in the governing equations is shown to increase the axis dispersion coefficient. The effect of various physical parameters such as Hartmann number, Grashof number, porous parameter and couple stress parameter on the velocity, temperature and dispersion coefficient, mean concentration, skin friction coefficient and Nusselt numbers are computed and analyzed through graphs

Analysis of Groundwater Contaminants Using Aris Dispersion Model

The paper presents the study of dispersion of contaminants in unsteady laminar flow of an incompressible fluid (groundwater) bounded by an upper porous layer and lower impermeable layer with interphase mass transfer. An analytical solution of unsteady advection dispersion based on Aris-Barton method of moments is presented up to the second moment about the mean in axial direction

Seir Model of Seasonal Epidemic Diseases using HAM

SEIR mathematical model of childhood diseases measles, chickenpox, mumps, rubella incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. Driven by seasonality these diseases are characterized by annual oscillations with variable contact rate which is a periodic function of time in years. Homotopy Analysis Method (HAM) is considered in this paper to obtain a semi analytic approximate solution of non-linear simultaneous differential equations. Mathematica is used to carry out the computations. Results established through graphs show the validity and potential of HAM for amplitude of variation greater than zero. Also, when it is equal to zero both HAM and Runge-Kutta method graphs are compared

Study of Spilled Oil Behavior on the Topsoil Induced by Thermal Diffusion

The fate and transport of oil spilled in soil has long been a focus for experimental and theoretical research in subsurface hydrology. Oil transport in the soil is affected by a large number of physical, chemical and microbial processes; and the properties of the media. This study is a two layer problem containing horizontal oil layer overlying the subsurface topsoil region saturated with oil and water (native fluid). To explain the method by which the convective flow in the oil region affect the transportation of oil, modeling is carried out in two regions (oil and topsoil). The two dimensional, transient oil flow equations for both the regions include thermal and concentration buoyancy effects. The species equations include the effects of energy flux caused by the temperature gradient on the unsteady advective-diffusion equation. The resulting fluid flow, heat and mass transfer processes are discussed numerically with the aid of graphs. The validity of the results obtained is verified by comparison with available results and good agreement is found

Mathematical model to study The spread of spilled oil in the soil

A mathematical model describing the spread of spilled oil through the soil is discussed. The spread of spilled oil in soil is controlled by the flow of water and is described by multiphase equations. In this context, the two-phase flow characteristics of oil-water flow with varying viscosity in the subsurface coupled to an advective-diffusion equation are examined to study the transport of oil. The terms that model the interaction between the multiple phases are introduced at the boundary, such as the slip condition at the porous-fluid interface, shear stress condition at the fluid-fluid interface, and the continuity of velocity at both the interfaces. The effect of various physical parameters such as Schmidt number, retardation factor, viscosity ratio, porous and slip parameter on the velocity and concentration profiles are discussed in detail with the help of graphs. The surface plots of velocity and concentration of oil against axial distance at different time are also analyzed. The obtained results show that the velocity of oil accelerates linearly with axial length and there is a decrease in the concentration of the spilled oil through the media. The validity of the results obtained is verified by comparison with available experimental result, and good agreement is found