Dharmendra Tripathi

Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects.

This investigation deals with the peristaltic flow of generalised Oldroyd-B fluids (with the fractional model) through a cylindrical tube under the influence of wall slip conditions. The analysis is carried out under the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions are obtained by using the highly versatile and rigorous semi-numerical procedure known as the homotopy analysis method. It is assumed that the cross section of the tube varies sinusoidally along the length of the tube. The effects of the dominant hydromechanical parameters, i.e. fractional parameters, material constants, slip parameter, time and amplitude on the pressure difference across one wavelength, are studied. Graphical plots reveal that the influence of both fractional parameters on pressure is opposite to each other. Interesting responses to a variation in the constants are obtained. Pressure is shown to be reduced by increasing the slip parameter. Furthermore, the pressure in the case of fractional models (fractional Oldroyd-B model and fractional Maxwell model) of viscoelastic fluids is considerably more substantial than that in the corresponding classical viscoelastic models (Oldroyd-B and Maxwell models). Applications of the study arise in biophysical food processing, embryology and gastro-fluid dynamics.

Mathematica simulation of peristaltic pumping with double-diffusive convection in nanofluids: a bio-nano-engineering model:

A theoretical study is presented to examine the peristaltic pumping with double-diffusive (thermal and concentration diffusive) convection in nanofluids through a deformable channel. The model is motivated by the need to explore nanofluid dynamic effects on peristaltic transport in biological vessels as typified by transport of oxygen and carbon dioxide, food molecules, ions, wastes, hormones and heat in blood flow. Analytical approximate solutions are obtained under the restrictions of large wavelength ( a ≪ λ → ∞ ) and low Reynolds number ( Re → 0 ), for nanoparticle fraction field, concentration field, temperature field, axial velocity, volume flow rate, pressure gradient and stream function in terms of axial and transverse coordinates, transverse vibration of the wall, amplitude of the wave and averaged flow rate. The influence of the dominant hydrodynamic parameters (Brownian motion, thermophoresis, Dufour and Soret) and Grashof numbers (thermal, concentration, nanoparticle) on peristaltic flow patterns with double-diffusive convection are discussed with the help of computational results obtained with the Mathematica software. The classical Newtonian viscous model constitutes a special case ( G r T = 0 , G r C = 0 , G r F = 0 ) of the present model. Applications of the study include novel pharmaco-dynamic pumps and engineered gastro-intestinal motility enhancement.

A Numerical Study of Oscillating Peristaltic Flow of Generalized Maxwell Viscoelastic Fluids Through a Porous Medium

This article presents a numerical study on oscillating peristaltic flow of generalized Maxwell fluids through a porous medium. A sinusoidal model is employed for the oscillating flow regime. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a homogenous, isotropic porous medium. The governing equations are simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, and permeability parameter on the flow characteristics are depicted graphically. The size of the trapped bolus is slightly enhanced by increasing the magnitude of permeability parameter whereas it is decreased with increasing amplitude ratio. Furthermore, it is shown that in the entire pumping region and the free pumping region, both volumetric flow rate and pressure decrease with increasing relaxation time, whereas in the co-pumping region, the volumetric flow rate is elevated with rising magnitude of relaxation time.

UNSTEADY MODEL OF TRANSPORTATION OF JEFFREY-FLUID BY PERISTALSIS

The investigation is to explore the transportation of a viscoelastic fluid by peristalsis in a channel as well as in a circular cylindrical tube by considering Jeffrey-model. In order to apply the model to the swallowing of food-bolus through the oesophagus, the wave equation assumed to propagate along the walls is such that the walls contract in the transverse/radial direction and relax but do not expand further. Solutions have been presented in the closed form by using small Reynolds number and long wavelength approximations. The expressions of pressure gradient, volume flow rate and average volume flow rate have been derived. It is revealed on the basis of computational investigation that for a fixed flow rate, pressure decreases when the ratio of relaxation time to retardation time is increased. In both the channel and tubular flows, the pressure decreases on increasing the ratio of relaxation time to retardation time if the averaged flow rate is less than the maximum flow rate. It is also revealed that the maximum tubular flow rate is higher than that of the channel-flow. It is further found through the theoretical analysis that mechanical efficiency, reflux and local wall shear stress remain unaffected by viscoelastic property of the fluid modelled as Jeffrey-fluid.

Peristaltic Hemodynamic Flow of Couple-Stress Fluids Through a Porous Medium with Slip Effect

The present investigation deals with a theoretical study of the peristaltic hemodynamic flow of couple-stress fluids through a porous medium under the influence of wall slip condition. This study is motivated towards the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for axial velocity, pressure gradient, frictional force, stream function and mechanical efficiency are obtained. Effects of different physical parameters reflecting couple-stress parameter, permeability parameter, slip parameter, as well as amplitude ratio on pumping characteristics and frictional force, streamlines pattern and trapping of peristaltic flow pattern are studied with particular emphasis. The computational results are presented in graphical form. This study puts forward an important observation that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the amplitude ratio.

A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping

Magnetohydrodynamic peristaltic flows arise in controlled magnetic drug targeting, hybrid haemodynamic pumps and biomagnetic phenomena interacting with the human digestive system. Motivated by the objective of improving an understanding of the complex fluid dynamics in such flows, we consider in the present article the transient magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for temperature field, axial velocity, transverse velocity, pressure gradient, local wall shear stress, volume flowrate and averaged volume flowrate are obtained. The effects of the transverse magnetic field, Grashof number and thermal conductivity on the flow patterns induced by peristaltic waves (sinusoidal propagation along the length of channel) are studied using graphical plots. The present study identifies that greater pressure is required to propel the magneto-fluid by peristaltic pumping in comparison to a non-conducting Newtonian fluid, whereas, a lower pressure is required if heat transfer is effective. The analytical solutions further provide an important benchmark for future numerical simulations.

A Mathematical Study on Three Layered Oscillatory Blood Flow Through Stenosed Arteries

A mathematical model is constructed to examine the characteristics of three layered blood flow through the oscillatory cylindrical tube (stenosed arteries). The proposed model basically consists three layers of blood (viscous fluids with different viscosities) named as core layer (red blood cells), intermediate layer (platelets/white blood cells) and peripheral layer (plasma). The analysis was restricted to propagation of small-amplitude harmonic waves, generated due to blood flow whose wave length is larger compared to the radius of the arterial segment. The impacts of viscosity of fluid in peripheral layer and intermediate layer on the interfaces, average flow rate, mechanical efficiency, trapping and reflux are discussed with the help of numerical and computational results. This model is the generalized form of the preceding models. On the basis of present discussion, it is found that the size of intermediate and peripheral layers reduces in expanded region and enhances in contracted region with the increasing viscosity of fluid in peripheral layer, whereas, opposite effect is observed for viscosity of fluid in intermediate layer. Final conclusion is that the average flow rate and mechanical efficiency increase with the increasing viscosity of fluid in both layers, however, the effects of the viscosity of fluid in both layers on trapping and reflux are opposite to each other.

PERISTALTIC TRANSPORT OF A CASSON FLUID IN A FINITE CHANNEL: APPLICATION TO FLOWS OF CONCENTRATED FLUIDS IN OESOPHAGUS

This model is targeted to study the swallowing of peristaltically driven food stuff such as jelly, tomato puree, soup, concentrated fruit juices and honey in the aboral direction confined to an oesophagus by modeling it as finite channel. Considering such highly concentrated fluids as Casson fluid in the fully stretched activated state, the dependence of pressure on space and time has been investigated for time averaged flow rate. Pressure distribution has been studied along the oesophageal length for an integral and also a non-integral number of waves at different time instants. Local wall shear stress and the role of yield stress have also been the areas of investigation. Mechanical efficiency of oesophageal pump during the Casson food transportation has been obtained. Reflux limit of perstaltically driven flow of Casson food bolus has also been discussed. The effect of Casson food bolus vis-a-vis Newtonian food bolus has been compared analytically, numerically and computationally from investigation point of view. It is observed that the pressure distribution is even and uneven respectively for the case of integral and non-integral number of waves. It is also concluded that it is not as easy to swallow Casson fluids (such as concentrated jelly, honey, soup, juice, etc.) as Newtonian fluids (such as water). As plug flow region widens, the pressure difference increases, indicating thereby that the averaged flow rate will be less for a Casson fluid. Physically, the oesophagus works more to swallow fluids with high concentration. It is also inferred that such fluids are more prone to reflux.

Effects of Non-Integral Number of PeristalticWaves Transporting Couple Stress Fluids in Finite Length Channels

Peristaltic flow of couple stress fluids is studied here in a finite length channel. The analysis is carried out under the assumption of long wavelength and low Reynolds number approximations. When the couple stress parameter increases, it is found that pressure diminishes, maximum averaged flow rate increases, mechanical efficiency decreases, area experiencing reflux reduces, and trapped bolus-size increases. A comparative study of integral and non-integral number of waves propagating along the channel is also done.

Unsteady Peristaltic Flow of Micro-Polar Fluid in a Finite Channel

This is an attempt to model an unsteady peristaltic flow of micro-polar fluid in a channel of finite length. The channel is subjected to progressive sinusoidal waves that help the walls contract and relax but not expand beyond the natural boundary. It is found that the coupling number increases pressure along the entire length of the channel, while the micro-polar parameter decreases it. The coupling number increases the efficiency; while the micro-polar parameter decreases it. The reflux region is found to increase with the coupling number. One significant difference between integral and non-integral number of waves in the train propagating along the channel walls is that the peaks of pressure are identical in the integral case while the peaks are different in the non-integral case.