Solutions of Flow over Periciliary Layer Using Finite Difference and n-Dimensional Newton-Raphson Methods
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Abstract
Nowadays, air is contaminated with pollution. When we take this polluted air into the lungs, organs involved in breathing system produce mucus to catch the particles and remove them from the human body by the movement of tiny hair lining on the epithelium cell in the respiratory system. The layer containing the tiny hair called is cilia. The cilia are arranged on the epithelium called the Periciliary Layer (PCL). The fluid around that layer or PCL fluid will affect the movement of cilia and the mucus from the body. In this research, we find the velocity of the fluid in the PCL by using the nonlinear Brinkman equation, where the fluid flows by the movement of cilia, not just the pressure gradient. The second-order finite difference method and the Newton-Raphson approach are employed to calculate the numerical solutions. The results are compared with the exact solution for the linear terms of the equation without nonlinear term, with a good agreement. We present the solutions of the nonlinear Brinkman equation when the cilia make angles 70∘, 80∘ and 90∘ with the horizontal plane. Applications are fluid flow through rice field and other similarly porous media.
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References
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