5. Lie Group Method Solution for Two-Dimensional Heat and Viscous Flow Driven by Injection Through a Deformable Rectangular Channel with Porous Walls

A two-dimensional laminar flow driven by fluid injection through porous surface which represents an incompressible fluid inside a filtration chamber during extraction of particles from the fluid is investigated. The study constructs a mathematical model that represents internal flow field during filtration process proficiently by using basic conservation laws of mass, momentum and energy. For better understanding of dynamics of the case study, solutions that lead to stable filtration process (balanced dynamical system) are obtained, hence provide an insight of the important dynamics that lead to an optimal filtration process. To solve a system of partial differential equations representing the internal flow field similarity transformation based on Lie group method is used to reduce the system to ordinary differential equations. Thereafter, double perturbation method is used to find semi-analytical solutions of the reduced system. Effects of various parameters that arise from the configuration (design) of the filter are presented graphically and analysed to show the connection between the case study and findings.