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.

Numerical solution of peristaltic transport of an Oldroyd 8-constant fluid in a circular cylindrical tube

2009 ◽  
Vol 87 (9) ◽  
pp. 1047-1058 ◽  
Author(s):  
N. Ali ◽  
Y. Wang ◽  
T. Hayat ◽  
M. Oberlack
Keyword(s):  
Fluid Model ◽  
Flow Characteristics ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Problem Definition ◽  
Shear Thinning Fluids ◽  
Strong Shear ◽  
Circular Cylindrical Tube

The present paper is concerned with the peristaltic flow of a non-Newtonian fluid in circular cylindrical tube. Long wavelength and low Reynolds number approximations are adopted in the problem definition. The non-Newtonian behaviour of the fluid is characterized by the constitutive equation of an Oldroyd 8-constant fluid. The governing nonlinear equation and boundary conditions are solved numerically by a suitable finite-difference method with an iterative scheme. It is seen that shear-thinning and shear-thickening phenomena can be explained through the chosen fluid model. The interaction of shear-thinning and shear-thickening effects with peristaltic motion is studied in detail with particular focus on the basic features of peristalsis such as flow characteristics, pumping characteristics, and trapping. It is found that pressure rise per wavelength against which peristalsis has to work as a positive displacement pump decreases in going from shear-thickening to shear-thinning fluids. Moreover, for strong shear-thinning fluids trapping does not appear. However, a trapped bolus occurs for a weak shear-thinning fluid and its size increases as the fluid is changing from shear thinning towards weak shear thickening. For strong shear-thickening fluids such increase in the size and circulation of bolus stops.

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.

scholarly journals Exact Solution for Peristaltic Flow of Jeffrey Fluid Model in a Three Dimensional Rectangular Duct having Slip at the Walls

2014 ◽  
Vol 11 (1-2) ◽  
pp. 81-90 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi ◽  
A. Zeeshan
Keyword(s):  
Exact Solution ◽  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Jeffrey Fluid ◽  
Long Wavelength ◽  
Peristaltic Pumping ◽  
Stream Functions

In the present article, we tried to develop the exact solutions for the peristaltic flow of Jeffrey fluid model in a cross section of three dimensional rectangular channel having slip at the peristaltic boundaries. Equation of motion and boundary conditions are made dimensionless by introducing some suitable nondimensional parameters. The flow is considered under the approximations of low Reynolds number and long wavelength. Exact solution of the obtained linear boundary value problem is evaluated. However, the expression for pressure rise is calculated numerically with the help of numerical integration. All pertinent parameters are discussed through graphs of pressure rise, pressure gradient, velocity and stream functions. It is found that presence of slip at the walls reduces the flow velocity but increases the peristaltic pumping characteristics.

Slip Effects on the Peristaltic Flow of a Third Grade Fluid in a Circular Cylindrical Tube

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
N. Ali ◽  
Y. Wang ◽  
T. Hayat ◽  
M. Oberlack
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Cylindrical Tube ◽  
Peristaltic Flow ◽  
Slip Parameter ◽  
Third Grade Fluid ◽  
Pumping Rate ◽  
Peristaltic Pumping ◽  
Grade Fluid ◽  
Circular Cylindrical Tube

Peristaltic flow of a third grade fluid in a circular cylindrical tube is undertaken when the no-slip condition at the tube wall is no longer valid. The governing nonlinear equation together with nonlinear boundary conditions is solved analytically by means of the perturbation method for small values of the non-Newtonian parameter, the Debroah number. A numerical solution is also obtained for which no restriction is imposed on the non-Newtonian parameter involved in the governing equation and the boundary conditions. A comparison of the series solution and the numerical solution is presented. Furthermore, the effects of slip and non-Newtonian parameters on the axial velocity and stream function are discussed in detail. The salient features of pumping and trapping are discussed with particular focus on the effects of slip and non-Newtonian parameters. It is observed that an increase in the slip parameter decreases the peristaltic pumping rate for a given pressure rise. On the contrary, the peristaltic pumping rate increases with an increase in the slip parameter for a given pressure drop (copumping). The size of the trapped bolus decreases and finally vanishes for large values of the slip parameter.

Application of Rabinowitsch Fluid Model in Peristalsis

2014 ◽  
Vol 69 (8-9) ◽  
pp. 473-480 ◽  
Author(s):  
Noreen Sher Akbar ◽  
Sohail Nadeemb
Keyword(s):  
Pressure Gradient ◽  
Wave Motion ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Process Time ◽  
Peristaltic Pumping ◽  
Uniform Tube ◽  
Velocity Pressure

In the present article, we have studied the Rabinowitsch fluid model for the peristaltic flow. The non-Newtonian nature of the fluid is analyzed mathematically by considering the Rabinowitsch fluid. The Rabinowitsch fluid model for the peristaltic flow is not discussed so far. This is the first article describing the features of Rabinowitsch fluid in peristaltic literature. The fluid is flowing in a uniform tube with the wave motion. Exact solutions have been calculated for velocity and pressure gradient. The physical behavior of different parameters for velocity, pressure rise, streamlines, and pressure gradient have been examined graphically. It is observed that when Weissenberg number is large then the relaxation time of the fluid is greater than a specific process time in which the pressure rise increases rapidly in the peristaltic pumping regions. Trapping phenomena have been discussed at the end of the article

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.

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 Peristaltic-Ciliary Flow of A Casson Fluid through An Inclined Tube

2021 ◽  
Vol 4 (1) ◽  
pp. 23-38
Author(s):  
Saravana Ramachandran ◽  
Kuppalapalle Vajravelu ◽  
K.V. Prasad ◽  
S. Sreenadh
Keyword(s):  
Axial Velocity ◽  
Flow Characteristics ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Flow Region ◽  
Casson Fluid ◽  
Viscoplastic Fluid ◽  
Moving Frame ◽  
Physical Parameters ◽  
Axial Pressure Gradient

The paper is concerned with the peristaltic-ciliary transport of a viscoplastic fluid (Casson fluid) through an inclined cylindrical tube. The peristalsis-cilia induced motion is analysed in the moving frame of reference under the lubrication approximations. Solutions to the flow characteristics petering to yielded and unyielded regions are obtained. The effects of various physical parameters on the axial velocity, the pumping characteristics, the pressure rise, and the frictional force over one wavelength, along with the trapping phenomenon are presented through graphs. Further, the peristaltic flow and peristaltic-ciliary flow results are compared. It is noticed that the axial velocity and the size of trapping bolus in the unplug flow region decrease with an increase in the yield stress. In addition, the axial velocity and the axial pressure gradient in the peristaltic-ciliary pumping are higher than those in the peristaltic pumping.

MHD Peristaltic Pumping of a Jeffrey Fluid Between Two Deformable Coaxial Tubes with Different Wavelengths

2016 ◽  
Vol 08 (04) ◽  
pp. 1650056 ◽  
Author(s):  
H. Rachid ◽  
M. T. Ouazzani
Keyword(s):  
Axial Velocity ◽  
Hartmann Number ◽  
Equations Of Motion ◽  
Pressure Rise ◽  
Mechanical Efficiency ◽  
Outer Tube ◽  
Jeffrey Fluid ◽  
Peristaltic Pumping ◽  
Efficiency Increase ◽  
Opposite Behavior

The study of MHD peristaltic transport of a Jeffrey fluid through the gap between two deformable tubes has been investigated in this paper. The outer and the inner tubes have both sinusoidal waves travelling down their walls when the amplitudes and the wavelengths are different. The equations of motion are simplified under the assumption of long wavelengths and low Reynolds number approximations. Analytical solutions for the pressure rise and axial velocity has been obtained in the closed form. Effects of pertinent parameters on pressure gradient, pressure rise, axial velocity and mechanical efficiency have been discussed through graphs. The results show that we have two cases, the first one is [Formula: see text], i.e., the wavelength of the inner tube is smaller than that of the outer tube and the second case is the opposite one [Formula: see text]. It is found that an increase of [Formula: see text] causes a decrease of the pumping and the mechanical efficiency when [Formula: see text] while an opposite behavior for [Formula: see text] is observed. In addition and for the two cases, the pumping and the mechanical efficiency increase with increasing the amplitude ration of the outer tube or the radius ratio while they decrease with the increase in the Hartmann number, amplitude ration of the inner tube or in the ratio of relaxation to retardation times.

scholarly journals Impact of partial slip and lateral walls on peristaltic transport of a couple stress fluid in a rectangular duct

2021 ◽  
Vol 104 (2) ◽  
pp. 003685042110136
Author(s):  
Safia Akram ◽  
Najma Saleem ◽  
Mir Yasir Umair ◽  
Sufian Munawar
Keyword(s):  
Couple Stress ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Partial Slip ◽  
Couple Stress Fluid ◽  
Rectangular Duct ◽  
Peristaltic Pumping ◽  
Current Article ◽  
The Impact ◽  
Lateral Walls

The impact of lateral walls and partial slip with different waveforms on peristaltic pumping of couple stress fluid in a rectangular duct with different waveforms has been discussed in the current article. By means of a wave frame of reference the flow is explored travelling away from a fixed frame with velocity c. Peristaltic waves generated on horizontal surface walls of rectangular duct are considered using lubrication technique. Mathematical modelling of couple fluid for three-dimensional flow are first discussed in detail. Lubrication approaches are used to simplify the proposed problem. Exact solutions of pressure gradient, pressure rise, velocity and stream function have been calculated. Numerical and graphical descriptions are displayed to look at the behaviour of diverse emerging parameters.

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