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Peristaltic flow of blood under effect of a magnetic field in non-uniform channels. (English) Zbl 1041.92006

Summary: The effect of a magnetic field on peristaltic transport of blood in a non-uniform two-dimensional channel has been investigated under zero Reynolds number with long wavelength approximation. Blood is represented by a viscous, incompressible and electrically conducting couple-stress fluid (a fluid where particle sizes are taken into account, a special case of a non-Newtonian fluid). It is found that the pressure rise decreases as the couple-stress fluid parameter \(\gamma\) increases (i.e., small size fluid particles) and increases as the Hartmann number \(M\) increases. So the pressure rise for a couple-stress fluid (as a blood model) is greater than that for a Newtonian fluid and is smaller for a magnetohydrodynamic fluid than for a fluid without an effect of a magnetic field. Finally, the maximum pressure rise \((\overline Q=0)\) increases as \(M\) increases and \(\gamma\) decreases, and the effect of the Hartmann number \(M\) is more obvious (for the same \((\Delta \overline p_L)_{\max}\) as the couple-stress parameter \(\gamma\) increases (Newtonian fluid).

MSC:

92C35 Physiological flow
76Z05 Physiological flows
78A70 Biological applications of optics and electromagnetic theory
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