Analyzing the impact of boundary slip and absorption effects on the dispersion of solute in a pulsatile channel flow of Casson fluid under magnetic field

In this work, the main focus is to analyze the transport of solute in non-Newtonian Casson fluid flow in a channel with suction/injection effects in the presence transverse magnetic field. The impact of Navier’s slip and boundary absorption effects are also examined for some practical utility of the proposed problem. At the beginning, the non-dimensional velocity distribution for a periodic pressure gradient is obtained from the Navier–Stokes equation of motion. Later, the analytical expression for the non-dimensional velocity is used in the convection–diffusion equation of the contaminants to find the concentration distribution for different flow influential parameters. To do this, initially, the method of moments is employed, and later, the finite difference implicit method is applied to find the solution of the convective–diffusion equation. Further, employing the Hermite polynomial, the profiles of mean concentration are described. The dispersion coefficient with time and mean concentration distribution is investigated for three cases, namely steady, purely oscillatory, and periodic flows with nonzero mean. Finally, the influence of important parameters like the Casson parameter, suction/injection parameter, transverse magnetic field, slip parameter, and boundary absorption is elaborated for steady, oscillatory, and combined flow (combination of steady and purely oscillatory flow) separately. The outcome of this examination reveals a positive correlation between the Casson parameter and the dispersion of solutes in the flow, whereas a negative correlation is seen in the mean concentration profile with the Casson parameter. In addition, the impact of skewness is shown for periodic flow with or without nonzero mean. This investigation correlates ample important biomedical and engineering applications, precisely in analyzing blood samples and drug delivery through blood flows.