`a`

Analytical approach of one-dimensional solute transport through inhomogeneous semi-infinite porous domain for unsteady flow: Dispersion being proportional to square of velocity

Pages: 457 - 466, Issue special, November 2013

 Abstract        References        Full Text (394.1K)              

Atul Kumar - Department of Mathematics and Astronomy, Lucknow University, Lucknow, 226007, Uttar Pradesh, India (email)
R. R. Yadav - Department of Mathematics and Astronomy, Lucknow University, Lucknow, 226007, Uttar Pradesh, India (email)

Abstract: In this study, we present an analytical solution for solute transport in a semi-infinite inhomogeneous porous domain and a time-varying boundary condition. Dispersion is considered directly proportional to the square of velocity whereas the velocity is time and spatially dependent function. It is expressed in degenerate form. Initially the domain is solute free. The input condition is considered pulse type at the origin and flux type at the other end of the domain. Certain new independent variables are introduced through separate transformation to eliminate the variable coefficients of Advection Diffusion Equation (ADE) into constant coefficient. Laplace transform technique (LTT) is used to get the analytical solution of ADE concentration values are illustrated graphically.

Keywords:  Advection-Diffusion Equation, inhomogeniety, semi-infinite medium, porous domain, unsteady parameter.
Mathematics Subject Classification:  Primary: 37N10, 65L10; Secondary: 44A10.

Received: August 2012;      Revised: December 2012;      Published: November 2013.

 References