Closed-Form Solutions of Injection-Driven Flow and Heat Transfer Inside an Inclined Horizontal Filter Chamber

Abstract

The closed-form solutions of models provide operators and designers with a better understanding of how the systems perform practically, thus improving critical industrial production operations. Due to this importance, the case study at hand seeks to find closed-form solutions of the internal momentum and temperature variation during the filtration process to advance fluid purification. Lie group analysis is used to transform a system of equations representing the flow and heat transfer into a solvable system without changing the dynamics of the case study. The transformed solvable system is then integrated to find closed-form solutions of the internal velocity (momentum) and temperature variation. The obtained closed-form solutions are then used to analyse the effects of physical parameters arising from the process dynamics to find combinations of parameters that yield maximum permeates outflow. Graphical representations of the unsteady and steady state regime of the internal velocity and temperature are presented and analysed. The analysis conveys that the internal fluid velocity increases when enhancing the permeation parameter and minimising Reynolds number, wave speed parameter and chamber height.