Analytical solution of a 3D model for the airflow in a human oral cavity

Understanding characteristic of the airflow in a human respiratory tract is very important factor to treatment in the respiratory disease. In this paper, we propose a three-dimensional mathematical modelling for the airflow in a human oral cavity. The airflow is assumed to be axially symmetric flow and driven by the oscillating pressure gradient. The governing equations for describing the behavior of airflow are composed the Navier-Stokes equations and the continuity equation in a cylindrical coordinates system. To solve the model, we presented method of analytical solution for the airflow velocity. We obtained a solution in a Fourier-Bessel series form. Then, we simulated the airflow field on a three-dimensional geometry of the oral cavity area. The obtained results show that the characteristic of magnitude and direction of the airflow correspond to the fact of the airflow in human airway and the previous research works.

Keywords: three-dimensional mathematical model, oral cavity, human upper respiratory tract, Navier-Stokes equations, analytical solution