IJPAM: Volume 78, No. 5 (2012)

A FOURIER SERIES-BASED ANALYTICAL SOLUTION
FOR THE OSCILLATING AIRFLOW IN
A HUMAN RESPIRATORY TRACT

S. Kongnuan$^1$, J. Pholuang$^2$
$^{1,2}$Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University
Rangsit Center, Khlong Luang, Pathum Thani, 12121, THAILAND
$^{1,2}$Centre of Excellence in Mathematics, CHE
Si Ayutthaya Rd., Bangkok, 10400, THAILAND


Abstract. Understanding of the airflow behavior in a human respiratory tract is very important to the drug delivery treatment. In this work, we propose a mathematical modelling of the airflow in a human upper respiratory tract. The governing equations are composed of the Navier-Stokes equations and the continuity equation. The oscillating flow is described by setting one side of boundaries be a periodic pressure function. Due to the complexity and requirement of high performance computing resources of numerical methods, we therefore, present an efficient alternative method that is the method of analytical expression. The obtained solution is in a Fourier series-based form. The simulation of an airflow field is done on a two-dimensional geometry of a human upper respiratory tract model. The obtained results show a good agreement to the fact of the airflow in a human respiratory tract and other related publications.

Received: April 24, 2012

AMS Subject Classification: 92B05, 97M60

Key Words and Phrases: airflow in a human respiratory tract, Navier-Stokes equations, analytical solution, Fourier series, mathematical modelling, oscillating flow

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 5