The analytical solutions of squeezing flow and heat transfer in an horizontal filtering channel

Abstract

Flow and heat transfer dynamics inside different industrial chambers play a vital role in understanding momentum and heat transfer during industrial operations. Analysis of such flow and heat transfer helps operators to know how the system works. To better understand the filtration process, the current study analytically investigated the internal flow and heat transfer through a porous horizontal filter channel under the influence of a uniform magnetic field while removing unwanted contaminations from the fluid inside the filter chamber. Thus, the novelty of the current study is to advance the filtration process by investigating how the top moving wall, which aims to minimise filter cake formation, affects permeates outflow (the current design). The partial differential equations (PDEs) model representing the internal flow and heat transfer during filtration is transformed into a system of ordinary differential equations (ODEs) using Lie point symmetry reduction without changing the dynamics under investigation. After that, the transformed equations are solved analytically using the perturbation approximation technique. The comparative analysis between the obtained semi-analytical and NDSolve numerical solutions was used to show the correlation of internal flow, temperature, and pressure profiles. The obtained solutions are used to find the best combination of dimensionless parameters that arise from flow and heat transfer dynamics that lead to optimum outflow. Graphical analysis of flow and heat transfer dynamics are used to indicate the combination of parameters that leads to maximum outflow based on scientific evidence. It is observed that, on average, the velocity increases significantly by 122.55% across all cases of Re ranging from 0 to 3.2 at the top permeable wall y=1. This significant increase is due to the motion of the moving wall and fluid injection happening at y=1. The results show that more chamber volume, small pores size, weak injection, weak magnetic force, and less Joule heating are crucial to increase internal temperature and permeate outflow velocity during filtration.