Analytical Solution of Brinkman Type Fluid in Vertical Channel with Suction and Injection Effects: Water Filtration Application

Water filtration through media filters, screen filters, disk filters, slow sand filter beds, rapid sand filters, and cloth filters is one method used to remove contaminants. Several elements involved in this process include suction and injection. Many experimental-based research have been conducted to examine the best filtration methods, but analytically, they are rare. In analytical methods, water passing through the filtration area can mimic Brinkman type fluid. Through literature review, analytical studies of Brinkman type fluid through cross-sectional cylinder (vertical channel) with suction and injection effects have not yet been explored. Therefore, this research aims to derive the theoretical solution for the mathematical models of Brinkman type fluid through vertical channel, incorporating suction and injection effects. Through the utilization of appropriate dimensionless variables, the governing equation is transformed into dimensionless forms, considering the associated initial and boundary conditions. The Laplace transform method is employed to obtain analytical solution. Dimensionless parameters, including suction, injection, Brinkman type fluid parameter, and time are determined through dimensionless processes. The velocity profile are graphically depicted to explore the impact of dimensionless variables on the profiles. The results reveal that fluid velocity decrease with growing suction and Brinkman type fluid while increasing with increasing time. To validate the findings, comparisons with published results in limiting cases demonstrate a mutual agreement.