This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence o...This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.展开更多
In this paper, a finite difference scheme for the linear and nonlinear models of wheezes are given. The stability of the finite difference scheme for the linear model is obtained by using of von Neumann method. Moreov...In this paper, a finite difference scheme for the linear and nonlinear models of wheezes are given. The stability of the finite difference scheme for the linear model is obtained by using of von Neumann method. Moreover, the convergence and stability of the finite difference scheme for the nonlinear model are studied by the energy inequalities method. By some numerical computations, the relationships between angular frequency and wall position, fluid speed and amplitude are discussed. Finally, the author shows that the numerical results are coincided with Grotberg's theoretical results.展开更多
文摘This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.
文摘In this paper, a finite difference scheme for the linear and nonlinear models of wheezes are given. The stability of the finite difference scheme for the linear model is obtained by using of von Neumann method. Moreover, the convergence and stability of the finite difference scheme for the nonlinear model are studied by the energy inequalities method. By some numerical computations, the relationships between angular frequency and wall position, fluid speed and amplitude are discussed. Finally, the author shows that the numerical results are coincided with Grotberg's theoretical results.
