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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

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An analysis has been carried out for the flow and heat transfer of an incompressible laminar and viscous fluid in a rectangular domain bounded by two moving porous walls which enable the fluid to enter or exit during successive expansions or contractions. The basic equations governing the flow are reduced to the ordinary differential equations using Lie-group analysis. Effects of the permeation Reynolds number , porosity , and the dimensionless wall dilation rate on the self-axial velocity are studied both analytically and numerically. The solutions are represented graphically. The analytical procedure is based on double perturbation in the permeation Reynolds number and the wall expansion ratio , whereas the numerical solution is obtained using Runge-Kutta method with shooting technique. Results are correlated and compared for some values of the physical parameters. Lastly, we look at the temperature distribution.