Analytical Solution for a 3D Model of the Airflow in a Human Upper Respiratory Tract

Chatvarin Tasawang, Supachara Kongnuan

Abstract


Understanding the airflow characteristics in the human respiratory tract is an important factor for treating a variety of respiratory diseases. This paper aims to demonstrate the behaviour of airflow in a human upper respiratory tract. The behaviour of airflow is described by a three-dimensional mathematical model under the assumptions that the airflow is axially symmetric flow and driven by the oscillating pressure gradient within the pulmonary. The proposed model composes of Navier-Stokes equations and the continuity equation. In this paper, we propose a method of analytical solution based on the Fourier-Bessel series form for the airflow field in the proposed model. The obtained solution of the airflow field is simulated on a three-dimensional geometry of a human respiratory tract. The results, both magnitude, and direction of the airflow characteristics show a good agreement to the fact of the airflow behaviour in the human airway and the previous research works.


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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|