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.

Application of Rabinowitsch Fluid Model for the Mathematical Analysis of Peristaltic Flow in a Curved Channel

2015 ◽  
Vol 70 (7) ◽  
pp. 513-520 ◽  
Author(s):  
Ehnber Naheed Maraj ◽  
Sohail Nadeem
Keyword(s):  
Current Problem ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Shear Stresses ◽  
Curved Channel ◽  
Long Wavelength ◽  
Long Wavelength Approximation ◽  
Dimensional Parameters ◽  
Wavelength Approximation

AbstractThe present work is the mathematical investigation of peristaltic flow of Rabinowitsch fluid in a curved channel. The current problem is modeled and solutions for non-dimensional differential equation are obtained under low Reynolds number and long wavelength approximation. The effects of long lasting non-dimensional parameters on exact solution for velocity profile, pressure rise and shear stresses are studied graphically in the last section. Tables are also incorporated for shear stresses at the walls of the curved channel.

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.

scholarly journals Williamson Fluid Model for the Peristaltic Flow of Chyme in Small Intestine

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Sohail Nadeem ◽  
Sadaf Ashiq ◽  
Mohamed Ali
Keyword(s):  
Small Intestine ◽  
Fluid Model ◽  
Flow Characteristics ◽  
Pressure Rise ◽  
Intestinal Wall ◽  
Peristaltic Flow ◽  
Weissenberg Number ◽  
Regular Perturbation ◽  
Williamson Fluid ◽  
Axial Pressure Gradient

Mathematical model for the peristaltic flow of chyme in small intestine along with inserted endoscope is considered. Here, chyme is treated as Williamson fluid, and the flow is considered between the annular region formed by two concentric tubes (i.e., outer tube as small intestine and inner tube as endoscope). Flow is induced by two sinusoidal peristaltic waves of different wave lengths, traveling down the intestinal wall with the same speed. The governing equations of Williamson fluid in cylindrical coordinates have been modeled. The resulting nonlinear momentum equations are simplified using long wavelength and low Reynolds number approximations. The resulting problem is solved using regular perturbation method in terms of a variant of Weissenberg numberWe. The numerical solution of the problem is also computed by using shooting method, and comparison of results of both solutions for velocity field is presented. The expressions for axial velocity, frictional force, pressure rise, stream function, and axial pressure gradient are obtained, and the effects of various emerging parameters on the flow characteristics are illustrated graphically. Furthermore, the streamlines pattern is plotted, and it is observed that trapping occurs, and the size of the trapped bolus varies with varying embedded flow parameters.

scholarly journals Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
R. Ellahi ◽  
Arshad Riaz ◽  
S. Nadeem ◽  
M. Ali
Keyword(s):  
Porous Medium ◽  
Equations Of Motion ◽  
Rectangular Channel ◽  
Nonlinear Partial Differential Equations ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Carreau Fluid ◽  
Highly Nonlinear ◽  
Stream Functions ◽  
Physical Features

We have examined the peristaltic flow of Carreau fluid in a rectangular channel through a porous medium. The governing equations of motion are simplified by applying the long wavelength and low Reynolds number approximations. The reduced highly nonlinear partial differential equations are solved jointly by homotopy perturbation and Eigen function expansion methods. The expression for pressure rise is computed numerically by evaluating the numerical integration. The physical features of pertinent parameters have been discussed by plotting graphs of velocity, pressure rise, pressure gradient, and stream functions.

scholarly journals Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Weimin Zhang
Keyword(s):  
Water Wave ◽  
Inverse Method ◽  
Variational Principles ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Variational Formula ◽  
Generalized Variational Principle ◽  
Partial Differential ◽  
Water Wave Problem ◽  
Mathematics And Physics

Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.

scholarly journals Theoretical Study of Heat Transfer on Peristaltic Transport of Non-Newtonian Fluid Flowing in a Channel: Rabinowitsch Fluid Model

2018 ◽  
Vol 3 (4) ◽  
pp. 450-471 ◽  
Author(s):  
U. P. Singh ◽  
Amit Medhavi ◽  
R. S. Gupta ◽  
Siddharth Shankar Bhatt
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Friction Force ◽  
Newtonian Fluid ◽  
Theoretical Study ◽  
Fluid Model ◽  
Pressure Rise ◽  
Peristaltic Flow ◽  
Long Wavelength ◽  
Velocity Pressure

The present investigation is concerned with the problem of heat transfer and peristaltic flow of non-Newtonian fluid using Rabinowitsch fluid model through a channel under long wavelength and low Reynolds number approximation. Expressions for velocity, pressure gradient, pressure rise, friction force and temperature have been obtained. The effect of different parameters on velocity, pressure gradient, pressure rise, streamlines, friction force and temperature have been discussed through graphs.

Explorations and Expectations of Equidistribution Adaptations for Nonlinear Quenching Problems

2013 ◽  
Vol 5 (04) ◽  
pp. 407-422 ◽  
Author(s):  
Matthew A. Beauregard ◽  
Qin Sheng
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Nonlinear Partial Differential Equation ◽  
Partial Differential ◽  
Spatial Adaptation ◽  
Monitor Function ◽  
Monitoring Strategies ◽  
Highly Nonlinear ◽  
Equidistribution Principle

AbstractFinite difference computations that involve spatial adaptation commonly employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This straightforward concept has proven to be extremely effective and practical. However, selections of core monitoring functions are often challenging and crucial to the computational success. This paper concerns six different designs of the monitoring function that targets a highly nonlinear partial differential equation that exhibits both quenching-type and degeneracy singularities. While the first four monitoring strategies are within the so-calledprimitiveregime, the rest belong to a later category of themodifiedtype, which requires the priori knowledge of certain important quenching solution characteristics. Simulated examples are given to illustrate our study and conclusions.

scholarly journals Nonlinear elliptic problems with the method of finite volumes

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Sanjay Kumar Khattri
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Elliptic Problems ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Nonlinear Elliptic Problems ◽  
Partial Differential ◽  
Nonlinear Elliptic ◽  
Finite Volume Discretization ◽  
Nonlinear Algebraic Equations

We present a finite volume discretization of the nonlinear elliptic problems. The discretization results in a nonlinear algebraic system of equations. A Newton-Krylov algorithm is also presented for solving the system of nonlinear algebraic equations. Numerically solving nonlinear partial differential equations consists of discretizing the nonlinear partial differential equation and then solving the formed nonlinear system of equations. We demonstrate the convergence of the discretization scheme and also the convergence of the Newton solver through a variety of practical numerical examples.

scholarly journals A Numerical Well-Balanced Scheme for One-Dimensional Heat Transfer in Longitudinal Triangular Fins

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
I. Rusagara ◽  
C. Harley
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Transfer Coefficients ◽  
Partial Differential ◽  
One Dimensional ◽  
Heat Transfer Coefficients ◽  
Highly Nonlinear ◽  
Triangular Fin

The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution in a one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile.

scholarly journals Modeling Nonlinear Partial Differential Equations and Construction of Solitary Wave Solutions in an Inductive Electrical Line

2019 ◽  
pp. 1-10 ◽  
Author(s):  
Tiague Takongmo Guy ◽  
Jean Roger Bogning
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Magnetic Flux ◽  
Differential Equations ◽  
Solitary Waves ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Hyperbolic Function ◽  
Flux Linkage ◽  
Partial Differential

A soliton is considered nowadays as a future wave reason being the fact that it is a stable, robust and non-dissipative solitary wave. If one uses a soliton as a transmission signal in electrical lines, this will have a great impacts in the domain of economic, technology and education. Given the fact that the propagation of the soliton is due to the interaction between dispersion and nonlinearity, it necessitates that the transmission medium should be dispersive and nonlinear. The physical system we have chosen for our survey is an inductive electrical line reason being the fact that it is the cheapest and very easy to manufacture than any other transmission lines; furthermore we find out the analytical variation that the magnetic flux linkage of inductors in the electrical line must undergo so that its transmission medium admits the propagation of solitary waves of required type. The aim of this work is to model nonlinear partial differential equations which govern the dynamics of those solitary waves in the line, to define the analytical expression of the magnetic flux linkage of inductors in the line and to find out some exact solutions of solitary waves types of those equations. To meet our objectives, we apply Kirchhoff laws to the circuit of a nonlinear inductive electrical line to model the nonlinear partial differential equation which describe the dynamics of those solitons. Further we apply the effective and direct Bogning-Djeumen Tchaho-Kofane method based on the identification of basic hyperbolic function coefficients to construct some exact soliton solutions of modeled equations. Numerical simulations have enabled to draw and observe the real profile of those solitary waves which are Kink soliton and Pulse soliton. The obtained results are supposed to permits: The facilitation of the choice of the type of line relative to the type of signal one wishes to send across, to increase the mathematical field knowledge, the reduction of amplification stations of those lines, The manufacturing of new inductors and new electrical lines susceptible of propagating those solitary waves.

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