J.C. Misra

A non-newtonian fluid model for blood flow through arteries under stenotic conditions

This paper presents an analytical study on the behaviour of blood flow through an arterial segment having a mild stenosis. The artery has been treated as a thin-walled initially stressed orthotropic non-linear viscoelastic cylindrical tube filled with a non-Newtonian fluid representing blood. The analysis is restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is large compared to the radius of the arterial segment. For the equations of motion of the arterial wall consideration is made of a pair of appropriate equations derived by using suitable constitutive relations and the principle of superimposition of a small additional deformation on a state of known finite deformation. It has been shown through numerical computations of the resulting analytical expressions that the resistance to flow and the wall shear increase as the size of the stenosis increases. A quantitative analysis is also made for the frequency variation of the flow rate at different locations of the artery, as well as of the phase velocities and transmission per wavelength.

A mathematical model for oesophageal swallowing of a food-bolus

The flow of a food-bolus through the oesophagus is investigated by considering a model that involves the study of the axisymmetric peristaltic transport of a power-law fluid through a circular tube of finite length where a single wave is supposed to propagate along the wall. The wall equation of the tube has been taken to fit the natural oesophageal wall contraction that does not involve the expansion beyond the stationary boundary. The spatial, as well as temporal, dependence of pressure has been studied for a fixedtime-averaged flow-rate in the laboratory frame of reference. Comparisons are made between the effects of a single wave transport and a train wave transport with an integral number of waves in the train. The effect of the nature of the wave and the power-law index on the pressure distribution along the length of the oesophagus is examined. Computational results for the shear stress distribution along the length of the oesophagus are used to investigate the impact of the single wave propagation vis-a-vis the train wave propagation.

Peristaltic transport of blood in small vessels: study of a mathematical model

Abstract The peristaltic flow of blood in small vessels is investigated in the paper by developing a mathematical model in which blood has been treated as a two-layer fluid where the core region is described by Casson model and the peripheral region is taken to be Newtonian viscous. Wave frame steady solutions for channel flow as well as axisymmetric flow are presented. Due care has been taken to consider the conservation of mass separately in the two layers. It is found that the higher the viscosity of the peripheral layer, the greater is the flow rate. Moreover, a thinner peripheral layer enhances the flow rate, whereas the flow rate reduces when the yield stress increases. It is further observed that the flow-rate in the case of a single layer is more than the two layer flow-rate when the peripheral layer is more viscous than the core layer. Besides, the flow-rate in the case of axisymmetric flow is always found to be much greater than that of channel flow under identical conditions.

Peristaltic transport of a non-Newtonian fluid with a peripheral layer

Abstract This paper is devoted to the analytical study of the two-dimensional flow of a power-law fluid with a peripheral layer. The analysis is carried out by using wavelength approximations. The solution has been obtained in the form of a stream function from which the shape of the interface has been determined. The relation between the flow-rate and the pressure difference for one wavelength has been derived. This is used to determine the maximum pressure and the maximum flow-rate. The expressions for the efficiency of pumping, the trapping limit and the reflux limit have also been determined. The computational results indicate that the flow is increased when the value of the flow behaviour index is raised or the viscosity of the outer layer is increased. The study reveals that in the case of physiological flows where the viscosity of the peripheral layer is usually less than that of the core layer, a thinner peripheral layer is responsible for a greater flow-rate.

MAGNETOTHERMOELASTIC INTERACTION IN AN INFINITE ELASTIC CONTINUUM WITH A CYLINDRICAL HOLE SUBJECTED TO RAMP-TYPE HEATING

Abstract A solution is given for the induced temperature and stress fields in an infinite transversely isotropic solid continuum with a cylindrical hole. The solid medium is considered to be exposed to a magnetic field and the cavity surface is assumed to be subjected to a ramp-type heating. Green and Lindsay model has been used to account for finite velocity of heat conduction. Magnetic field induced within the cavity is also determined. The problem is solved analytically by using integral transform technique.

Peristaltic transport in a tapered tube

The axisymmetric peristaltic flow of a viscous incompressible Newtonian fluid through a circular tube of varying cross section has been studied when the wave propagating along the wall of the tube is sinusoidal and the initial flow is Hagen-Poiseuille. A perturbation technique has been employed to analyze the problem where an attempt has been made to account for the nonlinear convective acceleration terms. Two particular cases have been studied in a greater detail. These are 1.(i) when the Reynolds number (wavespeed x radius/coefficientofkinematicviscosity) is small and 2.(ii) when the wave number ([emailxa0protected] x radius/wavelength) is small. The analysis is based upon second order approximations. The derived analytical expressions have been computed in order to have an in-depth study of an important physiological problem, viz. spermatic flow through the vas deferens, in which peristaltic motion is quite dominant.

Magneto-thermoelastic interaction in an aeolotropic solid cylinder subjected to a ramp-type heating

Abstract The present theoretical study is concerned with the generation of stress and magnetic fields in a solid cylindrical continuum subjected to a ramp-type heating on its surface when the cylinder and its adjoining vacuum is subjected to a uniform axial magnetic field. The perturbed magnetic field induced in the free space surrounding the cylinder is also analysed. The material of the cylinder is supposed to be anisotropic both mechanically and thermally. Numerical values of the stress and temperature at various points of the cylindrical medium at different instants of time as well as those of the magnetic field in the surrounding free space are computed for an appropriate material for the purpose of illustration.

Peristaltic flow of a multilayered power-law fluid through a cylindrical tube

Abstract This paper is an analytical study of the flow of a power-law fluid through a cylindrical tube in the presence of a peripheral layer of another power-law fluid with different viscosity. It serves as a model for the study of flow of chyme through small intestines. The interface which is a streamline in the flow pattern has been determined as a solution of an algebraic equation obtained from the function by imposing the condition for the mass conservation within the core fluid. The relation between the flow-rate and the pressure difference for one wavelength has been determined. Moreover, the trapping and the reflux limits as well as the efficiency of pumping have also been determined. It is found that unlike Newtonian flows in cylindrical vessels, the power-law fluid flow does not experience reflux throughout the domain. The computational results indicate that the flow-rate decreases with the decrease in the value of the flow behaviour index or in the viscosity of the outer layer. In physiological flows, it is found that the viscosity of the peripheral layer is often less than that of the core layer. In that case, a thinner peripheral layer is responsible for a greater flow-rate. The cylindrical flow-rate is higher than that in the two-dimensional case under identical conditions.

Peristaltic transport of a particle-fluid suspension in a cylindrical tube

Abstract Peristaltic pumping induced by a sinusoidal travelling wave of moderate amplitude is analysed in the axisymmetrical case for a viscous incompressible and Newtonian fluid mixed with rigid spherical particles which are of identical size. A perturbation method has been employed to find the solution of the problem, choosing the amplitude ratio (i.e., wave amplitude/tube radius) as a parameter. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms, and the nonslip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth order terms yield the Poiseuille flow and the first order terms give the Orr-Sommerfeld equation. In the absence of the pressure gradient and the wall motion, the mean flows (for the fluid and the solid particles) and the mean pressure gradient (averaged over time) are all found to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating complicated groups of the products of Bessel functions by polynomials. It is observed that a reversal of flow occurs when the pressure gradient exceeds the critical value; this is favoured by the presence of the solid particles. The reversal of flow may take place near the boundaries also.

Flow through blood vessels under the action of a periodic acceleration field: A mathematical analysis

Abstract The paper is devoted to an analytical study of flow through blood vessels subjected to a periodic acceleration field. The analysis consists of two parts. In the first case, the wall is treated as a non-linear orthotropic elastic cylindrical membrane and the blood as a Newtonian viscous fluid, while in the second case the experimentally observed material damping properties of the wall tissues and the viscoelasticity of blood have been incorporated in the analysis. In each of these two cases, analytical expressions for the displacement and shear stresses developed in the wall as well as the velocity distribution, fluid acceleration and volume flow rate of blood are derived. The influence of material damping of the wall tissues as well as the viscoelastic properties of blood on the flow and deformation characteristic of a blood vessel has been estimated by using the values of the different material constants (involved in the analysis) determined experimentally for the human abdominal aorta. Numerical results presented in the paper correspond to observed parameters of the circulatory system of living animals.