Indian Society for Heat and Mass Transfer

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Proceedings of the 25th National and 3rd International ISHMT-ASTFE Heat and Mass Transfer Conference (IHMTC-2019)

ISSN: 2688-7231 (Online)


Bharat Soni
Department of Mathematics, IIT Roorkee

Ameeya Kumar Nayak
Department of Mathematics, IIT Roorkee, Roorkee, Uttarakhand, 247667, India

DOI: 10.1615/IHMTC-2019.1410
pages 841-846


The tree shaped self similar branching network and bifurcation flows are the crucial factors for the functioning of human respiratory system. In this article, bronchial tree network is explored for the transport of air during breathing using fractal geometry and computational fluid dynamics methods. Firstly, a local mathematical model is solved for laminar, Newtonian and fully developed flow in a cylindrical tube to obtain relation among flow rate, pressure and impedance. Then it is applied for a single generation tree network consisting a parent and two daughter tubes. The outcomes of this process are the optimized homothetic ratios of parent - daughter tube diameters and lengths as well as branching angles which obey modified Murray's law. This analysis is executed with help of electrical circuits to determine the equivalent flow impedance which can help in diagnosing the possible blockage to flow in case of disease. It is shown that there are 6 circuits possible: 1 for steady and 5 for unsteady case and using optimization technique for global network, the best circuit is found which give minimum resistance for all breathing frequency. It is also concluded that the resistive and reactive components depend on the flow and fluid parameters and the choice of circuit play significant role to pick the optimized homothetic ratio.

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