Abstract
<p>The exact solution of the two-dimensional momentum and continuity equations governing the unsteady airflow in an inclined trachea was carried out. The oscillating airflow was described by setting one side of the boundaries be a periodic pressure function. The solution was obtained using Bromwich integral. The present results show that the inclination angle θ and gravitational force g reduces the pressure drop and has a greater effect on the velocity profile of airflow from the trachea to the lungs. Therefore, sleeping in a horizontal position may lead to negative effects for many patients. However, the inclined position is better, and it is dependent on the slope angle position taking, the benefits of gravitational force and utilizing it to improve the breathing of the body. These results are of help in breathing problems, mild sleep apnea, snoring, asthma and chronic obstructive pulmonary disease.</p>
Highlights
Nowadays, predicting and understanding in depth of the mathematical modelling phenomena development in life science and physiology has increased dramatically
The objective of the present study is to investigate the effect of the inclination angle and the gravitational force of the airflow in the trachea using Bromwich integral
The effect of the inclination angle on the velocity profile is displayed in Figure 4, which shows that the increasing of θ (0o, 15o, 30o, 45o, and 60o) leads to increasing the velocity of airflow
Summary
Nowadays, predicting and understanding in depth of the mathematical modelling phenomena development in life science and physiology has increased dramatically. Many researchers applied mathematical models to solve problems in different branches of science (Orakbayev et al, 2015; Shangytbayeva et al, 2015; Stroiteleva & Vukovich, 2015; Efimov et al, 2015). In recent years, inclined bed therapy (IBT) has been the subject of ongoing research. It is a new therapy introduced by Andrew Fletcher (1990), (Billen & Ting, 2013; Inclined Bed Therapy, 2013; Life & Gravity, 2013). The key to this therapy is to maximize the ability of the body to perform on its own without introducing harmful chemicals or other substances. The advantage of the technique is clear for many of the diseases like breathing problems, mild sleep apnea, snoring, asthma and chronic obstructive pulmonary disease (Rowley et al, 2009; Van Vliet, Ellis, & Hila, 2005; Ragavan, Evrensel, & Krumpe, 2010)
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