Investigation of flow and heat transfer inside horizontal filter chamber using Lie symmetry method

Abstract

In pursuit of evidence-based findings, this dissertation investigates mathematical models that predict the dynamics of filters to have a filter design that produces the best possible balance between factors that limit the movement of the particles and permit the desired outflow and heat transmission. The primary goal of this project is to theoretically examine two filter designs which model flow and pressure variation, and flow, heat and pressure variation in horizontal filter chambers. Depending on the type of particles, the calibre of the filter media, and the filter design, these parameters form different filtering techniques, which are more or less effective at reducing or removing particles deposited inside a fluid based on how effective the filter design is. This theoretical analysis seeks to give engineers and scientists better insight into how flow, pressure and heat transfer dynamics affect filtration process, thus helping design and build effective filters. Hence, this project aims to understand how mass, pressure, heat, and momentum transfer change during filtration. Physical laws reflecting forces that affect the process according to each filter design willbe used along with continuity, momentum and energy conservation laws to formulate the models representing the two filter designs under consideration. The flow and heat transfer model(s) under consideration are solved using analytical and semi-analytical techniques. Each model's solutionsare then utilised to analyse flow, heat and pressure to comprehend the dynamics of each model and identify the best model between the two designs. To arrive at a conclusion supported by scientific facts that highlight a way to have a filter that produces more permeates, the study also investigated the impacts of numerous parameters that arise from each filter design in depth using graphical analysis