scholarly journals A Mathematical Model for Peristaltic Transport of Micro-Polar Fluids

2011 ◽  
Vol 8 (3-4) ◽  
pp. 279-293 ◽  
Author(s):  
S. K. Pandey ◽  
Dharmendra Tripathi
Keyword(s):  
Mathematical Model ◽  
Cylindrical Tube ◽  
Mechanical Efficiency ◽  
Peristaltic Transport ◽  
Tube Length ◽  
Polar Fluid ◽  
Significant Difference ◽  
Wave Trains ◽  
Circular Cylindrical Tube ◽  
Coupling Number

A mathematical model has been constructed for peristaltic transport of micro-polar fluid in a circular cylindrical tube of finite length by letting sinusoidal waves propagate along the wall that induce contraction and relaxation but not expansion beyond the natural boundary. Axial and radial velocities and micro-rotation components are formulated for micro-polar fluid transportations by applying the method of long wavelength and low Reynolds number approximations in the analysis. Pressure distribution along the tube length is studied to investigate temporal effects. An in-depth study has been done to learn the effects of coupling number and micro-polar parameter. The effects of coupling number and micro-polar parameter are investigated also on mechanical efficiency, reflux and trapping. A significant difference observed is that unlike integral wave-trains propagating along the tube walls that have identical peaks of pressure, non-integral wave-trains have peaks of different sizes.

scholarly journals Effects of Rheological Parameters of a Viscoplastic Fluid on Peristaltic Pumping in a Cylindrical Tube

2019 ◽  
Vol 286 ◽  
pp. 09003
Author(s):  
H. Rachid ◽  
M. Ouazzani Touhami
Keyword(s):  
Fluid Model ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Mechanical Efficiency ◽  
Viscoplastic Fluid ◽  
Rheological Parameters ◽  
Rheological Characterization ◽  
Peristaltic Pumping ◽  
Fluid Foods ◽  
Circular Cylindrical Tube

In this paper, we study theoretically the peristaltic transport of a generalized four-parameter plastic fluid in a circular cylindrical tube. The present fluid model is presented for the rheological characterization of inelastic fluid foods. Long wavelength and low Reynolds number approximations are taken into account to get solution. The effects of embedded parameters on pressure rise, frictional force and especially on the mechanical efficiency have been numerically displayed and physically discussed.

UNSTEADY MODEL OF TRANSPORTATION OF JEFFREY-FLUID BY PERISTALSIS

2010 ◽  
Vol 03 (04) ◽  
pp. 473-491 ◽  
Author(s):  
S. K. PANDEY ◽  
DHARMENDRA TRIPATHI
Keyword(s):  
Relaxation Time ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Cylindrical Tube ◽  
Maximum Flow ◽  
Mechanical Efficiency ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Retardation Time ◽  
Circular Cylindrical Tube

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 TRANSPORT OF A THIRD-ORDER FLUID IN A CIRCULAR CYLINDRICAL TUBE

2002 ◽  
Vol 12 (12) ◽  
pp. 1691-1706 ◽  
Author(s):  
T. HAYAT ◽  
Y. WANG ◽  
A. M. SIDDIQUI ◽  
K. HUTTER ◽  
S. ASGHAR
Keyword(s):  
Numerical Solutions ◽  
Cylindrical Tube ◽  
Deborah Number ◽  
Peristaltic Transport ◽  
Average Radius ◽  
Third Order ◽  
Living Body ◽  
Analytic Perturbation ◽  
Circular Cylindrical Tube ◽  
Problem Comparison

The effect of a third-order fluid on the peristaltic transport is analysed in a circular cylindrical tube, such as some organs in the living body. The third-order flow of an incompressible fluid in a circular cylindrical tube, on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The wavelength of the peristaltic waves is assumed to be large compared to the tube average radius, whereas the amplitude of the wave need not be small compared to the average radius. Both analytic (perturbation) and numerical solutions are given. For the perturbation solution, a systematic approach based on an asymptotic expansion of the solution in terms of a small Deborah number is used and solutions up to the first order are presented in closed forms. The numerical solution, valid for any Deborah number, represents a new approach to peristaltic flows, and its features illuminate the physical behaviour much more than the analytical research on this problem. Comparison is made between the analytic (perturbation) and numerical results. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.

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

2011 ◽  
Vol 66 (3-4) ◽  
pp. 181-192 ◽  
Author(s):  
Sanjay Kumar Pandey ◽  
Dharmendra Tripathi
Keyword(s):  
Finite Length ◽  
Peristaltic Flow ◽  
Entire Length ◽  
Natural Boundary ◽  
Polar Fluid ◽  
Integral Number ◽  
Significant Difference ◽  
Coupling Number

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.

INTERACTION OF PULSATILE FLOW WITH PERISTALTIC TRANSPORT OF A VISCOELASTIC FLUID: CASE OF A MAXWELL FLUID

2014 ◽  
Vol 06 (05) ◽  
pp. 1450061 ◽  
Author(s):  
H. RACHID ◽  
M. T. OUAZZANI
Keyword(s):  
Pulsatile Flow ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Maxwell Fluid ◽  
Mechanical Efficiency ◽  
Deborah Number ◽  
Peristaltic Transport ◽  
Long Wavelength ◽  
Viscoelastic Effects ◽  
The Impact

This article analytically investigates the interaction of pulsatile flow with peristaltic transport of a viscoelastic Maxwell fluid in a cylindrical tube. The flow is considered unsteady even in the wave frame analysis where we impose a periodic pressure gradient. This transport is studied under low Reynolds number and long wavelength approximations. The governing equations are developed up to the second-order in the Deborah number and the Womersley number. We first analyzed the impact of the pulsatile flow, of the occlusion and of the viscoelastic effects of fluid on the pressure rise and on the friction force. Physical behavior of different parameters of the problem has been graphically presented and the influence of these parameters on the mechanical efficiency has been analyzed.

scholarly journals Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1072
Author(s):  
Vladimir Shelukhin
Keyword(s):  
Mathematical Model ◽  
Rotational Diffusion ◽  
Particle Separation ◽  
Theory Approach ◽  
Steady Flows ◽  
Concentric Cylinder ◽  
Polar Fluid ◽  
Fluid Theory ◽  
Couette Cell ◽  
Granular Fluid

We develop a new mathematical model for rotational sedimentation of particles for steady flows of a viscoplastic granular fluid in a concentric-cylinder Couette geometry when rotation of the Couette cell inner cylinder is prescribed. We treat the suspension as a micro-polar fluid. The model is validated by comparison with known data of measurement. Within the proposed theory, we prove that sedimentation occurs due to particles’ rotation and rotational diffusion.

scholarly journals A Mathematical Model for Swallowing of Concentrated Fluids in Oesophagus

2011 ◽  
Vol 8 (3-4) ◽  
pp. 309-321 ◽  
Author(s):  
S. K. Pandey ◽  
Dharmendra Tripathi
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Plug Flow ◽  
Flow Region ◽  
Mechanical Efficiency ◽  
Casson Fluid ◽  
Local Pressure ◽  
Integral Number ◽  
Tomato Puree ◽  
The Impact

This model investigates particularly the impact of an integral and a non-integral number of waves on the swallowing of food stuff such as jelly, tomato puree, soup, concentrated fruits juices and honey transported peristaltically through the oesophagus. The fluid is considered as a Casson fluid. Emphasis is on the study of the dependence of local pressure distribution on space and time. Mechanical efficiency, reflux limit and trapping are also discussed. The effect of Casson fluid vis-à-vis Newtonian fluid is investigated analytically and numerically too. The result is physically interpreted as that the oesophagus makes more efforts to swallow fluids with higher concentration. It is observed that the pressure is uniformly distributed when an integral number of waves is there in the oesophagus; but it is non-uniform when a non-integral number of waves is present therein. It is further observed that as the plug flow region widens, the pressure difference increases, which indicates that the averaged flow rate will reduce for a Casson fluid. It is also concluded that Casson fluids are more prone to reflux.

scholarly journals Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Media Coverage ◽  
New Product ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Significant Difference ◽  
Form Theory ◽  
The Difference ◽  
The Stability

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

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