SAMS Subject Classification Number: 20

Physical model exact solutions improve crucial industrial production processes by giving operators and designers a greater grasp of how systems operate in practice. The current case study aims to find exact momentum and pressure variation solutions during the unsteady-state filtration process to advance fluid purification. Lie symmetry analysis is used to transform a system of PDEs representing the flow and pressure variation into solvable ODEs without changing the dynamics of the case study. The velocity (momentum) and pressure solutions are then determined by integrating the obtained solvable ODEs. The effects of physical parameters resulting from the process dynamics are examined using the exact solutions acquired to identify the parameter combination that results in the maximum permeates outflow. Graphical representations of the flow velocity and pressure are presented and analysed as well as the skin friction tabular. The results indicate that as time evolves, permeate outflow decreases because internal momentum, work done, and pressure diminish over time due to the clustering of particles. In addition, low wave speed, small porosity, more chamber space, high injection rate, and stronger magnetic effects are ideal for minimising the effects of no-slip condition at the bottom wall during operation.