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.

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 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.

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.

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.

Novel epoxy/anhydride alternatives for biological electron microscopy: Physical and performance characteristis of embed 812 and LX 112 in combination with NSA/NMA/DMAE

1989 ◽  
Vol 47 ◽  
pp. 1000-1001
Author(s):  
Joe A. Mascorro ◽  
Gerald S. Kirby
Keyword(s):  
Electron Microscopy ◽  
Flow Rate ◽  
Succinic Anhydride ◽  
Volume Flow Rate ◽  
Mass Density ◽  
Uranyl Acetate ◽  
Volume Flow ◽  
Base Resin ◽  
And Performance ◽  
Acid Anhydrides

Embedding media based upon an epoxy resin of choice and the acid anhydrides dodecenyl succinic anhydride (DDSA), nadic methyl anhydride (NMA), and catalyzed by the tertiary amine 2,4,6-Tri(dimethylaminomethyl) phenol (DMP-30) are widely used in biological electron microscopy. These media possess a viscosity character that can impair tissue infiltration, particularly if original Epon 812 is utilized as the base resin. Other resins that are considerably less viscous than Epon 812 now are available as replacements. Likewise, nonenyl succinic anhydride (NSA) and dimethylaminoethanol (DMAE) are more fluid than their counterparts DDSA and DMP- 30 commonly used in earlier formulations. This work utilizes novel epoxy and anhydride combinations in order to produce embedding media with desirable flow rate and viscosity parameters that, in turn, would allow the medium to optimally infiltrate tissues. Specifically, embeding media based on EmBed 812 or LX 112 with NSA (in place of DDSA) and DMAE (replacing DMP-30), with NMA remaining constant, are formulated and offered as alternatives for routine biological work.Individual epoxy resins (Table I) or complete embedding media (Tables II-III) were tested for flow rate and viscosity. The novel media were further examined for their ability to infilftrate tissues, polymerize, sectioning and staining character, as well as strength and stability to the electron beam and column vacuum. For physical comparisons, a volume (9 ml) of either resin or media was aspirated into a capillary viscocimeter oriented vertically. The material was then allowed to flow out freely under the influence of gravity and the flow time necessary for the volume to exit was recored (Col B,C; Tables). In addition, the volume flow rate (ml flowing/second; Col D, Tables) was measured. Viscosity (n) could then be determined by using the Hagen-Poiseville relation for laminar flow, n = c.p/Q, where c = a geometric constant from an instrument calibration with water, p = mass density, and Q = volume flow rate. Mass weight and density of the materials were determined as well (Col F,G; Tables). Infiltration schedules utilized were short (1/2 hr 1:1, 3 hrs full resin), intermediate (1/2 hr 1:1, 6 hrs full resin) , or long (1/2 hr 1:1, 6 hrs full resin) in total time. Polymerization schedules ranging from 15 hrs (overnight) through 24, 36, or 48 hrs were tested. Sections demonstrating gold interference colors were collected on unsupported 200- 300 mesh grids and stained sequentially with uranyl acetate and lead citrate.

Multi-objective optimization of squirrel cage fan for range hood based on Kriging model

2021 ◽  
pp. 095440622199586
Author(s):  
Qianhao Xiao ◽  
Jun Wang ◽  
Boyan Jiang ◽  
Weigang Yang ◽  
Xiaopei Yang
Keyword(s):  
Flow Rate ◽  
Optimization Design ◽  
Volume Flow Rate ◽  
Kriging Model ◽  
Volume Flow ◽  
Design Parameters ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Squirrel Cage

In view of the multi-objective optimization design of the squirrel cage fan for the range hood, a blade parameterization method based on the quadratic non-uniform B-spline (NUBS) determined by four control points was proposed to control the outlet angle, chord length and maximum camber of the blade. Morris-Mitchell criteria were used to obtain the optimal Latin hypercube sample based on the evolutionary operation, and different subsets of sample numbers were created to study the influence of sample numbers on the multi-objective optimization results. The Kriging model, which can accurately reflect the response relationship between design variables and optimization objectives, was established. The second-generation Non-dominated Sorting Genetic algorithm (NSGA-II) was used to optimize the volume flow rate at the best efficiency point (BEP) and the maximum volume flow rate point (MVP). The results show that the design parameters corresponding to the optimization results under different sample numbers are not the same, and the fluctuation range of the optimal design parameters is related to the influence of the design parameters on the optimization objectives. Compared with the prototype, the optimized impeller increases the radial velocity of the impeller outlet, reduces the flow loss in the volute, and increases the diffusion capacity, which improves the volume flow rate, and efficiency of the range hood system under multiple working conditions.

scholarly journals Influence of Magnetic Field on the Peristaltic Flow of a Viscous Fluid through a Finite-Length Cylindrical Tube

2010 ◽  
Vol 7 (3) ◽  
pp. 169-176 ◽  
Author(s):  
S. K. Pandey ◽  
Dharmendra Tripathi
Keyword(s):  
Magnetic Field ◽  
Viscous Fluid ◽  
Transverse Magnetic Field ◽  
Finite Length ◽  
Flow Rate ◽  
Hartmann Number ◽  
Volume Flow Rate ◽  
Critical Value ◽  
Transverse Magnetic ◽  
Volume Flow

The paper presents an analytical investigation of the peristaltic transport of a viscous fluid under the influence of a magnetic field through a tube of finite length in a dimensionless form. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress have been obtained. The effects of the transverse magnetic field and electrical conductivity (i.e. the Hartmann number) on the mechanical efficiency of a peristaltic pump have also been studied. The reflux phenomenon is also investigated. It is concluded, on the basis of the pressure distribution along the tubular length and pumping efficiency, that if the transverse magnetic field and the electric conductivity increase, the pumping machinery exerts more pressure for pushing the fluid forward. There is a linear relation between the averaged flow rate and the pressure applied across one wavelength that can restrain the flow due to peristalsis. It is found that there is a particular value of the averaged flow rate corresponding to a particular pressure that does not depend on the Hartmann number. Naming these values ‘critical values’, it is concluded that the pressure required for checking the flow increases with the Hartmann number above the critical value and decreases with it below the critical value. It is also inferred that magneto-hydrodynamic parameters make the fluid more prone to flow reversal. The conclusion applied to oesophageal swallowing reveals that normal water is easier to swallow than saline water. The latter is more prone to flow reversal. A significant difference between the propagation of the integral and non-integral number of waves along the tube is that pressure peaks are identical in the former and different in the latter cases.

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.

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