THREE-DIMENSIONAL PERISTALTIC FLOW OF A WILLIAMSON FLUID IN A RECTANGULAR CHANNEL HAVING COMPLIANT WALLS

2014 ◽  
Vol 14 (01) ◽  
pp. 1450002 ◽  
Author(s):  
R. ELLAHI ◽  
ARSHAD RIAZ ◽  
S. NADEEM
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Williamson Fluid ◽  
Eigenfunction Expansion Method ◽  
Compliant Walls

In this study, the mathematical observations for the peristaltic flow of a Williamson fluid model (e.g., chyme) in a cross-section of a rectangular duct having compliant walls were considered. The flow was assumed incompressible and unsteady. The constitutive equations were reduced under the assumptions of low Reynolds number and long wavelength approximations. The resulting dimensionless governing equations were solved using the homotopy perturbation method (HPM) and eigenfunction expansion method. The results obtained were explained graphically. The velocity distribution was plotted for physical parameters both in two and three dimensions. The streamline graphs are presented in the end, which explain the trapping bolus phenomenon. All theoretical and graphical results are then discussed simultaneously.

scholarly journals Peristaltic flow of a Jeffrey fluid in a rectangular duct having compliant walls

2013 ◽  
Vol 19 (3) ◽  
pp. 399-409 ◽  
Author(s):  
S. Nadeem ◽  
Arshad Riaz ◽  
R. Ellahi
Keyword(s):  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Jeffrey Fluid ◽  
Rectangular Duct ◽  
Mathematical Study ◽  
Three Dimensional Flow ◽  
Long Wavelength ◽  
Compliant Walls ◽  
Parameters Of Interest

In this article, the theoretical and mathematical study of peristaltic transport of a Jeffrey fluid in a rectangular duct with compliant walls is discussed. The constitutive equations are simplified under the implementation of low Reynolds number and long wavelength approximations. The analytical solution of the resulting equations is evaluated by Eigen function expansion method. The graphical aspects of all the parameters of interest are also analyzed. The graphs of velocity for two and three dimensional flow are plotted. The trapping bolus phenomenon is also discussed though streamlines.

Effects of the wall properties on unsteady peristaltic flow of an Eyring–Powell fluid in a three-dimensional rectangular duct

2015 ◽  
Vol 08 (06) ◽  
pp. 1550081 ◽  
Author(s):  
Arshad Riaz ◽  
S. Nadeem ◽  
R. Ellahi
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Peristaltic Flow ◽  
Solution Technique ◽  
Rectangular Duct ◽  
Governing Equations ◽  
Long Wavelength ◽  
Stream Functions

In the present investigation, peristaltic flow of non-Newtonian fluid model (Eyring–Powell) has been taken into consideration in a cross-section of three-dimensional rectangular channel. The flow is taken to be unsteady and incompressible. The observations are made under the limitations of low Reynolds number and long wavelength which helps in reducing the governing equations. The walls of the channel are supposed to be compliant. The obtained equations are nonlinear partial differential equation of second order and have been solved analytically by using series solution technique. The achieved results are then portrayed graphically to see the variation of various emerging parameters on the profile of velocity. The stream functions have also been sketched in order to discuss the trapping behavior of the circular bolus.

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.

ANALYTICAL AND NUMERICAL SOLUTIONS OF PERISTALTIC FLOW OF WILLIAMSON FLUID MODEL IN AN ENDOSCOPE

2011 ◽  
Vol 11 (04) ◽  
pp. 941-957 ◽  
Author(s):  
NOREEN SHER AKBAR ◽  
S. NADEEM
Keyword(s):  
Numerical Solutions ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Physical Parameters ◽  
Peristaltic Motion ◽  
Governing Equations ◽  
Williamson Fluid ◽  
Long Wavelength ◽  
Good Agreement

The present studies deal with the peristaltic motion of an incompressible Williamson fluid model in an endoscope. The governing equations of Williamson fluid model are first simplify using the assumptions of long wavelength and low Reynolds number. The four types of solutions have been presented for velocity profile named (i) exact solution, (ii) perturbation solution, (iii) HAM solution, and (iv) numerical solutions. The comparisons of four solutions have been found a very good agreement between all the solutions. In addition, the expressions for pressure rise and velocity against various physical parameters are discussed through graphs.

Mathematical study for peristaltic flow of Williamson fluid in a curved channel

2015 ◽  
Vol 08 (01) ◽  
pp. 1550005 ◽  
Author(s):  
E. N. Maraj ◽  
Noreen Sher Akbar ◽  
S. Nadeem
Keyword(s):  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Curved Channel ◽  
Partial Differential ◽  
Williamson Fluid ◽  
Highly Nonlinear ◽  
Frame Transformation

In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

scholarly journals Mathematical Modeling of Partial-Porous Circular Cylinders with Water Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Min-Su Park ◽  
Weoncheol Koo
Keyword(s):  
Water Waves ◽  
Body Wave ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Expansion Method ◽  
The Body ◽  
Circular Cylinders ◽  
Exterior Region ◽  
Eigenfunction Expansion Method ◽  
Body Regions

The interaction of water waves with partially porous-surfaced circular cylinders was investigated. A three-dimensional numerical modeling was developed based on the complete mathematical formulation of the eigenfunction expansion method in the potential flow. Darcy’s law was applied to describe the porous boundary. The partial-porous cylinder is composed of a porous-surfaced body near the free surface, and an impermeable-surfaced body with an end-capped rigid bottom below the porous region. The optimal ratio of the porous portion to the impermeable portion can be adopted to design an effective ocean structure with minimal hydrodynamic impact. To scrutinize the hydrodynamic interactions inNpartial-porous circular cylinders, the computational fluid domain is divided into three regions: an exterior region,Ninner porous body regions, andNregions beneath the body. Wave excitation forces and wave run-up on multibodied partial-porous cylinders are calculated and compared for various porous-portion ratios and wave conditions, all of which significantly influence the hydrodynamic property.

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

2014 ◽  
Vol 92 (10) ◽  
pp. 1249-1257 ◽  
Author(s):  
M.F. El-Sayed ◽  
N.T. Eldabe ◽  
M.H. Haroun ◽  
D.M. Mostafa
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Potential Flow ◽  
Flow Instability ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Two Dimensional ◽  
Dielectric Fluids ◽  
Fluid Velocities

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.

scholarly journals Dynamic triaxial constitutive model for rock subjected to initial stress

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 149-163
Author(s):  
Junzhe Li ◽  
Guang Zhang ◽  
Mingze Liu ◽  
Shaohua Hu ◽  
Xinlong Zhou
Keyword(s):  
Constitutive Model ◽  
Impact Load ◽  
Three Dimensional ◽  
Estimation Method ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Initial Pressure ◽  
Expansion Method ◽  
Three Dimensions ◽  
Model Parameters

AbstractBuilding on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

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