Mathematics

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Mathematics

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    INFLUENCE OF OFF-DIAGONAL DISPERSION ON THE CONCENTRATION OF CONTAMINANT IN A TWO-DIMENSIONAL CONTAMINANT FLOW: A SEMI-ANALYTICAL APPROACH
    (Journal of the Nigerian Association of Mathematical Physics, 2018-03-20) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; JIYA, M.; Bolarin G. A.
    The equation which describes the two-dimensional contaminant flow model is a partial differential equation characterized by advection, dispersion, adsorption, first order decay and zero-order source. In this paper, the off-diagonal dispersion parameter is introduced into the two dimensional contaminant flow model in order to study its effect on the concentration of the contaminant. It is assumed that the adsorption term is modeled by Freudlich isotherm. The parameter expanding method is applied on the equation to obtain a set of differential equations which are then solved successively using the Eigen functions expansion technique to obtain the analytical solution. The results obtained are plotted into graphs to show the effect of change in the parameters on the concentration of the contaminants. Findings from this research show that the contaminant concentration decreases with increase in distance as the off-diagonal dispersion coefficient, zero-order source coefficient and vertical dispersion coefficient increases.
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    Mathematical Analysis of a Contaminant Flow in a Finite Medium using the Weighted Residual Method
    (Ilorin Journal of Science, 2015-02-01) JIMOH, OMANANYI RAZAQ; Aiyesimi, Y. M.; Jiya, M.; Bolarin, G. A.
    In this paper, a Galerkin weighted Residual method is used in providing an analytical solution of two-dimensional contaminant flow problem with non-zero initial concentration. The equation is described by advection, dispersion, adsorption, first order decay and zero-order source. It is assumed that the adsorption term is modeled by Freudlich isotherm. Using Bubnov-Galerkin method, the governing equation was converted to a discrete problem. Thereafter, the approximate solution of the resulting system of initial value problem was obtained. The results obtained are expressed in graphical form to show the effect of change in the parameters on the concentration of the contaminants. From the analysis of the results, it was discovered that the contaminant concentration decreases with increase in the distance from the origin while it increases with increase in the zero-order source coefficient.