Peristaltic transport of a conducting Jeffrey fluid in an inclined asymmetric channel

2014 ◽  
Vol 07 (06) ◽  
pp. 1450064 ◽  
Author(s):  
K. Vajravelu ◽  
S. Sreenadh ◽  
G. Sucharitha ◽  
P. Lakshminarayana
Keyword(s):  
Flow Rate ◽  
Magnetic Parameter ◽  
Volume Flow Rate ◽  
Wave Train ◽  
Pressure Rise ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Inclined Asymmetric Channel

Peristaltic flow of a conducting Jeffrey fluid in an inclined asymmetric channel is investigated. The channel asymmetry is produced by considering a peristaltic wave train on the flexible walls of the channel with different amplitudes and phases. The nonlinear governing equations are solved analytically by a perturbation technique. The expressions for the stream function, axial velocity and the pressure rise per wavelength are determined in terms of the Jeffrey number λ1, the Froude number Fr, the perturbation parameter δ, the angle of inclination θ and the phase difference ϕ. Effects of the physical parameters on the velocity field and the pumping characteristics are discussed. It is observed that the size of the trapping bolus increase with an increase in the magnetic parameter and the volume flow rate. That is, the magnetic parameter and the volume flow rate have strong influence on the trapping bolus phenomenon.

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.

Influence of Heat Transfer and Magnetic Field on a Peristaltic Transport of a Jeffrey Fluid in an Asymmetric Channel with Partial Slip

2010 ◽  
Vol 65 (6-7) ◽  
pp. 483-494 ◽  
Author(s):  
Sohail Nadeem ◽  
Safia Akram
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Wave Length ◽  
Pressure Rise ◽  
Peristaltic Transport ◽  
Partial Slip ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Asymmetric Channel ◽  
Wave Forms

In the present paper, we have studied the influence of heat transfer and magnetic field on a peristaltic transport of a Jeffrey fluid in an asymmetric channel with partial slip. The complicated Jeffrey fluid equations are simplified using the long wave length and low Reynolds number assumptions. In the wave frame of reference, an exact and closed form of Adomian solution is presented. The expressions for pressure drop, pressure rise, stream function, and temperature field have been calculated. The behaviour of different physical parameters has been discussed graphically. The pumping and trapping phenomena of various wave forms (sinusoidal, multisinusoidal, square, triangular, and trapezoidal) are also studied.

scholarly journals A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. Siddiqui ◽  
A. A. Farooq ◽  
M. A. Rana
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Casson Fluid ◽  
Volume Flow ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
Axial Pressure Gradient

A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow regionHpas well as the cilia length parameterε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.

Effects of heat transfer and the endoscope on Jeffrey fluid peristaltic flow in tubes

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
A.M. Abd-Alla ◽  
S.M. Abo-Dahab ◽  
M.A. Abdelhafez ◽  
Esraa N. Thabet
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Volume Flow Rate ◽  
Peristaltic Flow ◽  
Volume Flow ◽  
Jeffrey Fluid ◽  
Temperature Profiles ◽  
Content Type

PurposeThis article aims to describe the effect of an endoscope and heat transfer on the peristaltic flow of a Jeffrey fluid through the gap between concentric uniform tubes.Design/methodology/approachThe mathematical model of the present problem is carried out under long wavelength and low Reynolds number approximations. Analytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained.FindingsThe results indicate that the effect of the wave amplitude, radius ratio, Grashof number, the ratio of relaxation to retardation times and the radius are very pronounced in the phenomena. Also, a comparison of obtaining an analytical solution against previous literatures shows satisfactory agreement.Originality/valueAnalytical solutions for the velocity, temperature profiles, pressure gradient and volume flow rate are obtained. Numerical integration is performed to analyze the pressure rise and frictional forces on the inner and outer tubes.

scholarly journals Slip Effects on Peristaltic Transport in an Inclined Channel with Mass Transfer and Chemical Reaction

2013 ◽  
Vol 10 (1) ◽  
pp. 41-58 ◽  
Author(s):  
T. Hayat ◽  
Humaira Yasmin ◽  
S. Asghar ◽  
Awatif A. Hendi
Keyword(s):  
Mass Transfer ◽  
Chemical Reaction ◽  
Wave Train ◽  
Longitudinal Velocity ◽  
Pressure Rise ◽  
Asymmetric Channel ◽  
Long Wavelength ◽  
Slip Effects ◽  
Inclined Asymmetric Channel ◽  
Pumping And Trapping

An analysis is carried out for the peristaltic flow in an inclined asymmetric channel when no-slip condition does not hold. The whole analysis has been carried out in the presence of mass transfer and chemical reaction. The channel asymmetry is generated because of peristaltic wave train on the walls through different amplitudes and phases. Long wavelength and low Reynolds number assumption is adopted in the whole mathematical analysis. Expressions for the stream function and longitudinal pressure gradient have been developed. Numerical integration is performed for the analysis of pressure rise per wavelength. Longitudinal velocity, pumping and trapping phenomena are analyzed in detail via plots.

Theoretical Interpretation of the CORDIER-Lines for Squirrel-Cage and Cross-Flow Fans

2012 ◽  
Author(s):  
Reinhard Willinger
Keyword(s):  
Flow Rate ◽  
Volume Flow Rate ◽  
Cross Flow ◽  
Pressure Rise ◽  
Low Noise ◽  
Volume Flow ◽  
Theoretical Interpretation ◽  
Outer Diameter ◽  
Flow Angle ◽  
Squirrel Cage

Squirrel-cage fans are centrifugal fans with forward-curved blades. A large number of short blades of thin circular arc sheet metal provide a low diameter drum-type rotor of high axial length. Cross-flow fans have a similar rotor design. However, the flow passes the rotor in radial direction two times. One consequence of the forward-curved blades is that there is more or less no pressure rise in the rotor and the casing has to convert the high absolute rotor exit velocity into a global pressure rise. Both types are used in applications requiring low size, relative high volume flow rates, low costs and low noise at the drawback of relative low efficiency. Volume flow rate, specific isentropic enthalpy difference, rotor outer diameter and rotational speed of a single stage fan can be transformed to speed number and diameter number. For axial, radial and mixed flow fans, a single relationship (CORDIER-diagram) exists and it is well accepted that this line represents “optimum” fan designs with high efficiency. The paper provides a theoretical interpretation of the CORDIER-lines for squirrel-cage and cross-flow fans, since they differ considerably from the classical relationship. Based on velocity triangles and energy transfer, CORDIER-line of squirrel-cage fans depends on absolute inlet flow angle, relative exit flow angle, rotor inlet to exit diameter ratio, relative axial rotor width and circumferential efficiency. Additionally, the CORDIER-line of cross-flow fans depends on the degree of admission. At a distinguished pressure coefficient, a maximum speed number is found, corresponding to maximum volume flow rate.

An investigation of non-Newtonian fluid flow due to metachronal beating of cilia in a tube

2015 ◽  
Vol 08 (02) ◽  
pp. 1550016 ◽  
Author(s):  
A. M. Siddiqui ◽  
A. A. Farooq ◽  
M. A. Rana
Keyword(s):  
Newtonian Fluid ◽  
Flow Rate ◽  
Fluid Model ◽  
Volume Flow Rate ◽  
Weissenberg Number ◽  
Volume Flow ◽  
Physical Parameters ◽  
Regular Perturbation ◽  
Ciliary Motion ◽  
Viscous Fluid Model

The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10-3 ml/h in the human ductus efferentes when We = 0.5 and ε is near by 0.25.

scholarly journals Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
A. Afsar Khan ◽  
R. Ellahi ◽  
K. Vafai
Keyword(s):  
Porous Medium ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Wave Train ◽  
Nonlinear Partial Differential Equations ◽  
Pressure Rise ◽  
Analytic Solutions ◽  
Jeffrey Fluid ◽  
Asymmetric Channel ◽  
Regular Perturbation

The peristaltic flow of a Jeffrey fluid with variable viscosity through a porous medium in an asymmetric channel is investigated. The channel asymmetric is produced by choosing the peristaltic wave train on the wall of different amplitude and phase. The governing nonlinear partial differential equations for the Jeffrey fluid model are derived in Cartesian coordinates system. Analytic solutions for stream function, velocity, pressure gradient, and pressure rise are first developed by regular perturbation method, and then the role of pertinent parameters is illustrated graphically.

scholarly journals Peristaltic Flow of a Jeffrey Fluid with Variable Viscosity in an Asymmetric Channel

2009 ◽  
Vol 64 (11) ◽  
pp. 713-722 ◽  
Author(s):  
Sohail Nadeem ◽  
Noreen Sher Akbar
Keyword(s):  
Variable Viscosity ◽  
Pressure Rise ◽  
Reynold Number ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Fluid Viscosity ◽  
Asymmetric Channel ◽  
Regular Perturbation ◽  
Viscosity Parameter ◽  
Energy Equations

In this article, we have considered incompressible Jeffrey fluids and studied the effects of variable viscosity in the form of a well-known Reynold’s model of viscosity in an asymmetric channel. The fluid viscosity is assumed to vary as an exponential function of temperature. The governing fundamental equations are approximated under the assumption of long wavelength and low Reynold number. The governing momentum and energy equations are solved using regular perturbation in terms of a small viscosity parameter β to obtain the expressions for stream functions pressure rise and temperature field. Numerical results are obtained for different values of viscosity parameter β , channel width d, wave amplitude b, and Jeffrey parameter λ1. It is observed that the behaviour of the physical parameters λ1, β , and d on pressure rise versus flow rate is as follows: when we increase these parameters pressure rise decreases while pressure rise increases with the increase in b. It is also observed that temperature profile increases when we increase Ec, Pr, and β . Trapping phenomena are also discussed at the end of the article to see the behaviour of different parameters on streamlines

Slip boundaries effects on double-diffusive convection of magneto-pseudoplastic nanofluid on peristaltic flux in an inclined asymmetric channel

2021 ◽  
pp. 095440892110630
Author(s):  
Safia Akram ◽  
Maria Athar ◽  
Khalid Saeed ◽  
Alia Razia ◽  
Taseer Muhammad ◽  
...  
Keyword(s):  
Numerical Technique ◽  
Pressure Rise ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Double Diffusive Convection ◽  
Asymmetric Channel ◽  
Diffusive Convection ◽  
Highly Nonlinear ◽  
Inclined Asymmetric Channel ◽  
Double Diffusive

The implications of double-diffusive convection and an inclined magnetic field on the peristaltic transport of a pseudoplastic nanofluid in an inclined asymmetric channel with slip boundaries were investigated in this research. The present problem is mathematically modeled using lubrication techniques, which results in highly nonlinear equations for the proposed problem that is solved using a numerical technique. The graphical findings show how temperature, pressure rise, concentration, pressure gradient, nanoparticle fraction, and stream functions affect key physical parameters of interest. It is revealed that the velocity value rises as the velocity slip parameter, temperature, and solutal Grashof number rise. Furthermore, increasing thermal slip, Dufour, Soret, Brownian motion, and thermophoresis factors increase the temperature profile. If [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] the viscous model of classical Newtonian fluid is a special case of the preceding model.

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