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flow of a third grade fluid in a circular cylindrical tube is undertaken when the no-slip condition at the tube wall is no longer valid.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.

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.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

THE EFFECTS OF ENDOSCOPE AND HEAT TRANSFER ON THE PERISTALTIC FLOW OF A SECOND GRADE FLUID IN AN INCLINED TUBE

2016 ◽  
Vol 16 (04) ◽  
pp. 1650057 ◽  
Author(s):  
K. RAMESH ◽  
M. DEVAKAR
Keyword(s):  
Heat Transfer ◽  
Vertical Tube ◽  
Peristaltic Flow ◽  
Temperature Fields ◽  
Second Grade ◽  
Physical Parameters ◽  
Second Grade Fluid ◽  
Pumping Rate ◽  
Inclined Tube ◽  
Grade Fluid

In the present paper, we have studied the effects of endoscope and heat transfer on the peristaltic flow of second grade fluid through an inclined tube. The endoscope is a solid circular cylinder which is inserted in a peristaltic tube, and the flow takes place through the gap between endoscope and the peristaltic tube. The endoscope is maintained at a temperature [Formula: see text], while the outer tube has a sinusoidal wave traveling down its wall and is exposed to temperature [Formula: see text]. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The equations governing the flow of second grade fluid are modeled in cylindrical coordinates. Using perturbation method, the solutions are obtained for the stream function, pressure gradient and temperature fields. The pressure difference and frictional force at both the walls are calculated using numerical integration. The graphical results are presented to interpret the effect of various physical parameters of interest. It is found that, velocity increases with an increase in inclination angle and the best pumping rate appear in the vertical tube as compared to the horizontal tube. It is also found that, the heat generation parameter has an increasing effect on the velocity of the fluid.

Numerical study for nonlinear radiative peristaltic flow in a rotating frame

2018 ◽  
Vol 96 (6) ◽  
pp. 569-575 ◽  
Author(s):  
H. Zahir ◽  
T. Hayat ◽  
A. Alsaedi ◽  
B. Ahmad
Keyword(s):  
Transfer Rate ◽  
Numerical Study ◽  
Peristaltic Flow ◽  
Rotating Frame ◽  
Asymmetric Channel ◽  
Third Grade Fluid ◽  
Inertial Frames ◽  
Nonlinear Version ◽  
Grade Fluid ◽  
Parameters Of Interest

Peristaltic flow of third-grade fluid in a tapered asymmetric channel is discussed. The whole system is considered in a rotating frame. Unlike the traditional situation, the nonlinear version of thermal radiation is invoked. The resulting problems are solved numerically. Comparative study between rotating and inertial frames is presented. The results of velocity, temperature, and heat transfer rate are analyzed for different parameters of interest.

Numerical Results of a Flow in a Third Grade Fluid between Two Porous Walls

2009 ◽  
Vol 64 (1-2) ◽  
pp. 59-64 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Tasawar Hayat ◽  
Rahmat Ellahi ◽  
Saleem Asghar
Keyword(s):  
Numerical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Material Parameter ◽  
Third Grade ◽  
Analysis Method ◽  
Third Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Porous Walls

Series solution for a steady flow of a third grade fluid between two porous walls is given by the homotopy analysis method (HAM). Comparison with the existing numerical solution is shown. It is found that, unlike the numerical solution, the present series solution holds for all values of the material parameter of a third grade fluid.

scholarly journals Peristaltic Flow of a Third-Grade Fluid in a Planar Channel

1999 ◽  
Vol 4 (2) ◽  
pp. 113-120
Author(s):  
F. Akyıldız ◽  
H. Demir ◽  
V. Ertürk
Keyword(s):  
Peristaltic Flow ◽  
Third Grade ◽  
Planar Channel ◽  
Third Grade Fluid ◽  
Grade Fluid

The Study of Peristaltic Motion of Third Grade Fluid under the Effects of Hall Current and Heat Transfer

2015 ◽  
Vol 70 (4) ◽  
pp. 281-293 ◽  
Author(s):  
Kambiz Vafai ◽  
Ambreen Afsar Khan ◽  
Saba Sajjad ◽  
Rahmat Ellahi
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Amplitude Ratio ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Closed Form Solutions ◽  
Peristaltic Pumping ◽  
Grade Fluid ◽  
Energy Equations

AbstractThis article is concerned with the peristaltic pumping of an incompressible, electrically conducting third grade fluid in a uniform channel. The Hall effect under the influence of wall properties and heat transfer is taken into account. Mathematical modelling is based upon continuity, momentum, and energy equations. Closed form solutions for velocity, temperature, concentration, and heat transfer coefficient are obtained. Effects of pertinent parameters, such as third grade parameter Γ, Hall parameter M, amplitude ratio ε, Brickman number Br, Soret number Sc, wall tension E1 and elasticity parameters E2 and E3 on the velocity u, temperature θ, concentration φ, and heat transfer coefficient Z, are discussed through graphs.

scholarly journals Numerical Study of MHD Third-Grade Fluid Flow through an Inclined Channel with Ohmic Heating under Fuzzy Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Muhammad Nadeem ◽  
Imran Siddique ◽  
Fahd Jarad ◽  
Raja Noshad Jamil
Keyword(s):  
Boundary Conditions ◽  
Poiseuille Flow ◽  
Operating Conditions ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Governing Equations ◽  
Inclined Channel ◽  
Magnetic Parameters ◽  
Fuzzy Environment ◽  
Grade Fluid

The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.

EFFECT OF AN INDUCED MAGNETIC FIELD ON PERISTALTIC FLOW OF NON-NEWTONIAN FLUID IN A CURVED CHANNEL

2012 ◽  
Vol 12 (03) ◽  
pp. 1250058 ◽  
Author(s):  
T. HAYAT ◽  
S. NOREEN ◽  
A. ALSAEDI
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Magnetic Force ◽  
Problem Formulation ◽  
Peristaltic Flow ◽  
Frame Of Reference ◽  
Third Grade Fluid ◽  
Induced Magnetic Field ◽  
Curved Channel ◽  
Grade Fluid

The purpose of this study is to discuss the influence of induced magnetic field on the peristaltic flow of an incompressible third-grade fluid in a curved channel. The problem formulation is presented in a wave frame of reference. The continuity, linear momentum, and induction equations lead to the mathematical development. The relations of stream function, pressure gradient, magnetic force function, induced magnetic field, and current density are developed. The effects of embedded parameters are explained by plots.

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