Mathematical Analysis of Single and Two-Phase Flow of Blood in Narrow Arteries with Multiple Contrictions


1 Engineering Mathematics Unit, Faculty of Engineering, Institut Teknologi Brunei, Jalan Tungku Link, Gadong BE1410, Brunei Darussalam

2 Department of Mathematics and Computer Science, Centre for Applicable Mathematics and Systems Science, Liverpool Hope University, Hope Park, Liverpool L16 9JD, UK

3 Department of Mathematics, National Institute of Technology, Yupia- 791112, Arunachal Pradesh, India


The pulsatile flow of blood in narrow arteries with multiple-stenoses under body acceleration is analyzed mathematically, treating blood as (i) single-phase Herschel-Bulkley fluid model and (ii) two-phase Herschel- Bulkley fluid model. The expressions for various flow quantities obtained by Sankar and Ismail (2010) for single-phase Herschel-Bulkley fluid model and Sankar (2010c) for two-phase Herschel-Bulkley fluid model are used to compute the data for comparing these fluid models in a new flow geometry. It is noted that the plug core radius, wall shear stress and longitudinal impedance to flow are marginally lower for two-phase HB fluid model than those of the single-phase H-B fluid model. It is found that the velocity decreases significantly with the increase yield stress of the fluid and the reverse behavior is noticed for longitudinal impedance to flow. It is also noticed that the velocity distribution and flow rate are higher for two-phase Herschel-Bulkley fluid model than those of the single-phase Herschel-Bulkley fluid model. It is also recorded that the estimates of the mean velocity increase with the increase of the body acceleration and this behavior is reversed when the stenosis depth increases.