Open AccessANALYTICAL SOLUTION OF A NON - HOMOGENEOUS ONE - DIMENSIONAL ADVECTION DIFFUSION EQUATION WITH TEMPORALLY VARYING COEFFICIENTS .
Author(s) -
Constance Atieno Ojwando,
Thomas Onyango,
Mark Kimathi,
Ben Obiero
Publication year - 2020
Publication title -
international journal of engineering, sciences and research technology
Language(s) - English
Resource type - Journals
ISSN - 2277-9655
DOI - 10.29121/ijesrt.v9.i12.2020.7
Subject(s) - advection , dispersion (optics) , partial differential equation , diffusion , mathematical analysis , constant (computer programming) , constant coefficients , mechanics , convection–diffusion equation , diffusion equation , mathematics , physics , thermodynamics , economy , computer science , optics , economics , programming language , service (business)
Advection Diffusion Equation is a partial differential equation that describes the transport of pollutants in rivers. Its coefficients (dispersion and velocity) can be constant, dependent on space or time or both space and time. This study presents an analytical solution of a one dimensional non - homogeneous advection diffusion equation with temporally dependent coefficients, describing one dimensional pollutant transport in a section of a river. Temporal dependence is accounted for by considering a temporally dependent dispersion coefficient along an unsteady flow assuming that dispersion is proportional to the velocity. Transformations are used to convert the time dependent coefficients to constant coefficients and to eliminate the advection term. Analytical solution is obtained using Fourier transform method considering an instantaneous point source. Numerical results are presented. The findings show that concentration monotonically decreases with increasing distance and increasing time.