Mathematical modelling of air flow in the human respiratory system

A. Issakhov, A. M. Yessenkozha


Nasal inspiration is important for maintaining the internal milieu of the lung, since ambient air is conditioned to nearly alveolar conditions (body temperature and fully saturated with water vapor) on reaching the nasopharynx. In this work conducted a two-dimensional computational study of transport phenomena in model transverse cross sections of the nasal cavity of normal human noses based on the two dimensional Navier-Stokes equation. For discretization Navier-Stokes equation used finite volume method.Projection method applied for solution of the Navier-Stokes equations. The results suggest that during breathing via the normal human nose there is ample time for heat and water exchange to enable equilibration to near intraalveolar conditions. A normal nose can maintain this equilibrium under extreme
conditions. The turbinates increase the rate of local heat and moisture transport by narrowing the passageways for air and by induction of laminar swirls downstream of the turbinate wall.

Ключевые слова

Respiratory air conditioning, alveolar condition, 2D modeling, heat transfer, Navier-Stokes equations, finite volume method

Полный текст:



Naftali S., Schroter R. C., Shiner R. J., Elad D. Transport Phenomena in the Human Nasal Cavity: A Computational Model // Annals of biomedical engineering. – 1998. – P. 831-839.

Cole P. Some aspects of temperature, moisture and heat relationships in the upper respiratory tract // J. Laryngol. Otol. 67. – 1953. – P. 669–681.

Ingelstedt S. Studies on conditioning of air in the respiratory tract // Acta Oto-Laryngol. Suppl. 131. – 1956. – P. 1–80.

Webb P. Air temperatures in respiratory tracts of resting subjects // J. Appl. Physiol. 4. – 1951. – P. 378–382.

Farley R. D., and Patel K. R. Comparison of air warming in human airway with thermodynamic model // Med. Biol. Eng. Comput. 26. – 1988. – P. 628–632.

Hanna L. M., and Scherer P. W. Measurement of local mass transfer coefficients in a cast model of the human upper respiratory tract // J. Biomech. Eng. 108. – 1986. – P. 12–18.

McFadden E. R. Respiratory heat and water exchange: Physiological and clinical implications // J. Appl. Physiol. 54. – 1983. – P. 331–336.

Maran A. G. D., and Lund V. J. Clinical Rhinology – New York: Thieme Medical. – 1990.

Anderson D., Tannehil Dzh., Pletcher R. Vyichislitelnaya gidromehanika i teploobmen. – M..: Mir, 1990. – 337 p.

Anderson D., Tannehill Dzh., Pletcher R. Vyichislitelnaya gidromehanika i teploobmen. –M.:Mir, 1990. – 384 p.

Fletcher K. Vyichislitelnyie metodyi v dinamike zhidkostey. – Moskva: Mir, 1991. – 552 p.

Rouch P. Vyichislitelnaya gidrodinamika. – M.:Mir, 1972. – 612 p.

Chung T.J. Computational fluid dynamics. – 2002. – 1034 p.

Issakhov A., Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant // International Journal of Nonlinear Science and Numerical Simulation. – 2015. Vol. 16, No 5. – P. 229–238.

Issakhov A., Mathematical modeling of the discharged heat water effect on the aquatic environment from thermal power plant under various operational capacities // Applied Mathematical Modelling. –2016. – Vol. 40, No 2. – P. 1082–1096

Issakhov A. Large eddy simulation of turbulent mixing by using 3D decomposition method // J. Phys.: Conf. Ser. – 2011. – Vol. 318, No 4. – P. 1282-1288.

Chorin A.J. Numerical solution of the Navier-Stokes equations // Math. Comp. – 1968. – Vol. 22. – P. 745-762.