Analysis of MHD Fluid Flow and Heat Transfer Inside an Inclined Deformable Filter Chamber: Lie Group Method

Abstract

This paper investigates MHD fluid flow and distribution of heat inside a filter chamber during a process of filtering particles from the fluid. A flow model of MHD viscous incompressible fluid inside a filter is studied to seek semi-analytical solutions which are analysed to find flow and heat dynamics that lead to optimal outflow (maximum filtrates) during filtration. Lie group method is used to reduce a system of four partial differential equations describing fluid flow and temperature distribution inside the filter chamber to a system of two ordinary differential equations. The reduced system is then solved by perturbation process to obtain semi-analytical solutions for flow velocity and temperature variation inside the chamber. To understand the flow dynamics and heat distribution of the underlying case study better, the influence of different parameters during filtration resulting from the filter design, flow dynamics and heat effects are graphically presented and analysed in order to identify a combination of flow parameters that yields the best filtration process. The findings show that to maximise filtrates production, more fluid injection is required during filtration. Moreover, from the findings, it is evident that the temperature increase inside the chamber arising from the Joule heating effect is ideal since it increases internal work done and hence increases filtrates production.