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Mathematical analysis of non-Newtonian blood flow in stenosis narrow arteries.

Sriyab S - Comput Math Methods Med (2014)

Bottom Line: When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood.The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand.

ABSTRACT
The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonian fluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of either stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonian fluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

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Variation of skin friction  with axial distance for the different values of plasma viscosity.
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fig11: Variation of skin friction with axial distance for the different values of plasma viscosity.

Mentions: Many researchers studied the Newtonian blood flow. Since the blood behaves as non-Newtonian fluid at the low shear rate, we would like to know how the non-Newtonian blood behavior affects the skin friction of artery. The variation of skin friction along the z-axis for different values of L0/L is plotted in Figure 10. It is indicated that skin friction increases significantly when the stenosis length increases. By our simulation, the yield stress does not affect the skin friction in non-Newtonian behavior that is consistent with the Casson model [16]. Figure 11 shows the plot of skin friction along the z-axis for the different values of plasma viscosity coefficient. It is noticed that skin friction decreases marginally with increase of plasma viscosity coefficient. The plot skin friction at midpoint of stenosis with stenosis height (a) for the different values of plasma viscosity coefficient is shown in Figure 12. It informs that the skin friction decreases linearly with increase of plasma viscosity coefficient.


Mathematical analysis of non-Newtonian blood flow in stenosis narrow arteries.

Sriyab S - Comput Math Methods Med (2014)

Variation of skin friction  with axial distance for the different values of plasma viscosity.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4281458&req=5

fig11: Variation of skin friction with axial distance for the different values of plasma viscosity.
Mentions: Many researchers studied the Newtonian blood flow. Since the blood behaves as non-Newtonian fluid at the low shear rate, we would like to know how the non-Newtonian blood behavior affects the skin friction of artery. The variation of skin friction along the z-axis for different values of L0/L is plotted in Figure 10. It is indicated that skin friction increases significantly when the stenosis length increases. By our simulation, the yield stress does not affect the skin friction in non-Newtonian behavior that is consistent with the Casson model [16]. Figure 11 shows the plot of skin friction along the z-axis for the different values of plasma viscosity coefficient. It is noticed that skin friction decreases marginally with increase of plasma viscosity coefficient. The plot skin friction at midpoint of stenosis with stenosis height (a) for the different values of plasma viscosity coefficient is shown in Figure 12. It informs that the skin friction decreases linearly with increase of plasma viscosity coefficient.

Bottom Line: When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood.The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Chiang Mai University, Chiang Mai 50200, Thailand.

ABSTRACT
The flow of blood in narrow arteries with bell-shaped mild stenosis is investigated that treats blood as non-Newtonian fluid by using the K-L model. When skin friction and resistance of blood flow are normalized with respect to non-Newtonian blood in normal artery, the results present the effect of stenosis length. When skin friction and resistance of blood flow are normalized with respect to Newtonian blood in stenosis artery, the results present the effect of non-Newtonian blood. The effect of stenosis length and effect of non-Newtonian fluid on skin friction are consistent with the Casson model in which the skin friction increases with the increase of either stenosis length or the yield stress but the skin friction decreases with the increase of plasma viscosity coefficient. The effect of stenosis length and effect of non-Newtonian fluid on resistance of blood flow are contradictory. The resistance of blood flow (when normalized by non-Newtonian blood in normal artery) increases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length. The resistance of blood flow (when normalized by Newtonian blood in stenosis artery) decreases when either the plasma viscosity coefficient or the yield stress increases, but it decreases with the increase of stenosis length.

Show MeSH
Related in: MedlinePlus