Analysis of pressure and heat distribution in a dilating or contracting filter chamber with two outlets using multivariate spectral quasilinearization method

Abstract

The development of efficient filters is an essential part of industrial machinery design, specifically to increase the lifespan of a machine. In the filter chamber design considered in this study, the magnetic material is placed along the horizontal surface of the filter chamber. The inside of the filter chamber is layered with a porous material to restrict the outflow of unwanted particles. This study aims to investigate the flow, pressure, and heat distribution in a dilating or contracting filter chamber with two outlets driven by injection through a permeable surface. The proposed model of the fluid dynamics within the filter chamber follows the conservation equations in the form of partial differential equations. The model equations are further reduced to a steady case through Lie's symmetry group of transformation. They are then solved using a multivariate spectral-based quasilinearization method on the Chebyshev-Gauss-Lobatto nodes. Insights and analyses of the thermophysical parameters that drive optimal outflow during the filtration process are provided through the graphs of the numerical solutions of the differential equations. We find, among other results, that expansion of the filter chamber leads to an overall decrease in internal pressure and an increase in heat distribution inside the

Exact solutions of flow and pressure variation inside a horizontalfilter chamber using Lie symmetry analysis

“…In their works, they have shown how the Lie symmetry technique could be used to reduce the mathematical model and transform the governing equations to those that can be solved easily, particularly in fluid dynamics. The works of Lekoko et al [20,21] used Lie group method along with the spectral method to study the filtration process.…”

“…The investigation of heat and mass transfer dynamics has prompted logical investigations that have assisted engineers with creating successful optimal channels for various industrial use. Motivated by the literature above, the current study aims to advance the filtration process by further investigating the unsteady state regime of the filtration process studied by [20,21].…”

A Novel Multivariate Spectral Local Quasilinearization Method (MV-SLQLM) for Modelling Flow, Moisture, Heat, and Solute Transport in Soil

“…Dlamini and Magagula [72] proposed a multivariate SQLM (MV-SQLM) to solve 2D Burger's equations. Lekoko et al [73] and Goqo et al [74] applied the MV-SQLM to analyze pressure and heat distribution in a filter chamber and to study heat and mass transfer in a porous media saturated with nanofluid, respectively. Related to the MV-SQLM is the trivariate spectral collocation method (TV-SCM) proposed by Samuel and Motsa [75].…”