Abstract
The paper presents an analytical investigation of the peristaltic transport of a viscous fluid under the influence of a magnetic field through a tube of finite length in a dimensionless form. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress have been obtained. The effects of the transverse magnetic field and electrical conductivity (i.e. the Hartmann number) on the mechanical efficiency of a peristaltic pump have also been studied. The reflux phenomenon is also investigated. It is concluded, on the basis of the pressure distribution along the tubular length and pumping efficiency, that if the transverse magnetic field and the electric conductivity increase, the pumping machinery exerts more pressure for pushing the fluid forward. There is a linear relation between the averaged flow rate and the pressure applied across one wavelength that can restrain the flow due to peristalsis. It is found that there is a particular value of the averaged flow rate corresponding to a particular pressure that does not depend on the Hartmann number. Naming these values ‘critical values’, it is concluded that the pressure required for checking the flow increases with the Hartmann number above the critical value and decreases with it below the critical value. It is also inferred that magneto‐hydrodynamic parameters make the fluid more prone to flow reversal. The conclusion applied to oesophageal swallowing reveals that normal water is easier to swallow than saline water. The latter is more prone to flow reversal. A significant difference between the propagation of the integral and non‐integral number of waves along the tube is that pressure peaks are identical in the former and different in the latter cases.
Highlights
Physiological fluids are transported from one place to another by continuous muscle contractions and relaxations
The flow of blood through arteries and veins, the passage of urine through ureters, the flow of bile from the gall bladder into the duodenum, the movement of chyme in the entire gastro-intestinal tract, the transportation of food boluses through the alimentary canal and the movement of some worms are some important examples of peristaltic transport
The equations describing magneto-hydrodynamic (MHD) fluids are a combination of Navier–Stokes equations and Maxwell equations of electromagnetism
Summary
Physiological fluids are transported from one place to another by continuous muscle contractions and relaxations. None of the researchers has shown an interest in the reflux and mechanical efficiency in a tube Another important fact is that in physiological flows, the vessels contract and relax but do not expand so that the wall equations to model such flows will definitely differ from the ones fluctuating about the boundary line. Several physiological fluids, such as blood, behave like an MHD fluid. The model is applicable to swallowing of conducting fluids, such as saline water, through the oesophagus and blood flow through the aorta Both the vessels are small in length. This model will fit an artificial peristaltic pump carrying a saline solution for engineering applications
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