Abstract
A three-dimensional (3D) thermo-fluid model is developed to study regional distributions of temperature and water vapor in three multi-detector row computed-tomography-based human airways with minute ventilations of 6, 15 and 30 L/min. A one-dimensional (1D) model is also solved to provide necessary initial and boundary conditions for the 3D model. Both 3D and 1D predicted temperature distributions agree well with available in vivo measurement data. On inspiration, the 3D cold high-speed air stream is split at the bifurcation to form secondary flows, with its cold regions biased toward the inner wall. The cold air flowing along the wall is warmed up more rapidly than the air in the lumen center. The repeated splitting pattern of air streams caused by bifurcations acts as an effective mechanism for rapid heat and mass transfer in 3D. This provides a key difference from the 1D model, where heating relies largely on diffusion in the radial direction, thus significantly affecting gradient-dependent variables, such as energy flux and water loss rate. We then propose the correlations for respective heat and mass transfer in the airways of up to 6 generations: \(Nu = 3.504\left( {Re\frac{{D_{\text{a}} }}{{D_{\text{t}} }}} \right)^{0.277} , \quad R = 0.841\) and \(Sh = 3.652\left( {Re\frac{{D_{\text{a}} }}{{D_{\text{t}} }}} \right)^{0.268} , \quad R = 0.825\), where Nu is the Nusselt number, Sh is the Sherwood number, Re is the branch Reynolds number, D a is the airway equivalent diameter, and \(D_{\text{t}}\) is the tracheal equivalent diameter.
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Acknowledgments
This work was supported in part by NIH Grants R01-HL094315, U01-HL114494, and S10-RR022421, and MBIE Grant 20959-NMTS-UOA. We also thank SDSC, TACC, and XSEDE for the computer time.
Conflicts of interest
E. A. Hoffman is a shareholder in VIDA diagnostics, which is commercializing lung image analysis software derived from the University of Iowa lung imaging group.
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Associate Editor John H. Linehan oversaw the review of this article.
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Wu, D., Tawhai, M.H., Hoffman, E.A. et al. A Numerical Study of Heat and Water Vapor Transfer in MDCT-Based Human Airway Models. Ann Biomed Eng 42, 2117–2131 (2014). https://doi.org/10.1007/s10439-014-1074-9
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DOI: https://doi.org/10.1007/s10439-014-1074-9