Numerical examination of concentration-dependent wastewater sludge ejected into a drinking water source

One of the significant water-related health challenges globally is due to pollutant fate. Contaminants endanger the lives of humans, animals, and even plants. The present mathematical analysis explains reactive wastewater sludge ejected into a drinking water source from wastewater treatment plants. The assumption that wastewater sludge follows a power-law constitutive relation leads to nonlinear momentum and concentration equations. The contaminants are assumed to follow a nonlinear irreversible first-order sorption model. The numerical solution of the coupled problem is solved using the Bivariate Spectral Local Linearization Method and validated with the spectral Chebyshev weighted residual method. Profiles are presented for dimensionless flow velocity and concentration. Comprehensive explanations for the obtained results are provided with relevant applications.