scholarly journals Boussinesq's Equations for (2+1)-Dimensional Surface Gravity Waves in an Ideal Fluid Model

2021 ◽  
Author(s):  
Anna Karczewska ◽  
Piotr Rozmej
Keyword(s):  
Ideal Fluid ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equation ◽  
Boussinesq Equations ◽  
Auxiliary Function ◽  
Surface Elevation ◽  
Long Wavelength ◽  
Highly Nonlinear ◽  
Variation Parameter ◽  
Fifth Order

Abstract We study the problem of gravity surface wa\-ves for the ideal fluid model in (2+1)-dimensional case. We apply a systematic procedure for deriving the Boussinesq equations for a prescribed relationship between the orders of four expansion parameters, the amplitude parameter $\alpha$, the long-wavelength parameter $\beta$, the transverse wavelength parameter $\gamma$, and the bottom variation parameter $\delta$. We also take into account surface tension effects when relevant. For all considered cases, the (2+1)-dimensional Boussinesq equations can not be reduced to a single nonlinear wave equation for surface elevation function. On the other hand, they can be reduced to a single, highly nonlinear partial differential equation for an auxiliary function $f(x,y,t)$ which determines the velocity potential but is not directly observed quantity. The solution $f$ of this equation, if known, determines the surface elevation function. We also show that limiting the obtained the Boussinesq equations to (1+1)-dimensions one recovers well-known cases of the KdV, extended KdV, fifth-order KdV, and Gardner equations.PACS 02.30.Jr · 05.45.-a · 47.35.Bb · 47.35.Fg

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.

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 Crossbreed impact of double-diffusivity convection on peristaltic pumping of magneto Sisko nanofluids in non-uniform inclined channel: A bio-nanoengineering model

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110336
Author(s):  
Safia Akram ◽  
Maria Athar ◽  
Khalid Saeed ◽  
Alia Razia
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Long Wavelength ◽  
Inclined Channel ◽  
Graphical Data ◽  
Peristaltic Pumping ◽  
Highly Nonlinear ◽  
Linear Pdes

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase.

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.

Effects of heat and mass transfer on the peristaltic motion of Sutterby fluid in an inclined channel

2020 ◽  
Vol 16 (6) ◽  
pp. 1357-1372 ◽  
Author(s):  
Faseeha Atlas ◽  
Maryiam Javed ◽  
Naveed Imran
Keyword(s):  
Heat Transfer ◽  
Magnetic Force ◽  
Fluid Model ◽  
The Body ◽  
Content Type ◽  
Long Wavelength ◽  
Symmetric Channel ◽  
Diseased Part ◽  
Fluid Parameter ◽  
Mass And Heat Transfer

PurposeThe purpose of this paper is to study the peristaltic mechanism of Sutterby fluid in a symmetric channel with mass and heat transfer.Design/methodology/approachMass and heat transfer are investigated in the assumption of Reynolds number and the long wavelength. The velocity, temperature and concentration terms for small values of Sutterby fluid parameter are achieved.FindingsGraphical results have been introduced for various important parameters. The effects of emerging key parameters are also highlighted.Originality/valueSutterby fluid model is one that represents the high polymer aqueous solutions. It is now strongly believed that any diseased part of the body would be cured better when exposed to magnetic force when compared with a drug. Peristalsis with mass and heat transfer occurs in treatment to destroy the unwanted tissues, hemodialysis and oxygenation process, etc.

Flow of a fourth grade fluid between rotating disks

2020 ◽  
Vol 34 (10) ◽  
pp. 2050091
Author(s):  
A. M. Siddiqui ◽  
Ayesha Sohail ◽  
Khush Bakhat Akram ◽  
Qurat-ul-Ain Azim
Keyword(s):  
Nonlinear Models ◽  
Fluid Model ◽  
Three Dimensional ◽  
Fourth Grade ◽  
Perturbation Approach ◽  
Rotating Disks ◽  
Highly Nonlinear ◽  
Rotating Surface ◽  
Grade Fluid ◽  
Fourth Grade Fluid

Flow of fluids between rotating surface is encountered in many industrial, manufacturing, mixing and biological processes. These fluids are complex, exhibit various rheological characteristics, and thus follow highly nonlinear models. In this paper, we have used fourth grade fluid model to represent fluids involved in such processes. The steady flow between two coaxial rotating disks is modeled. The resulting highly nonlinear equations are solved using perturbation approach. The velocity field in three-dimensional cylindrical coordinate system is reported. The results are then simulated to present a visual understanding of the flow.

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.

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