scholarly journals On Behavioral Response of 3D Squeezing Flow of Nanofluids in a Rotating Channel

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Mubashir Qayyum ◽  
Omar Khan ◽  
Thabet Abdeljawad ◽  
Naveed Imran ◽  
Muhammad Sohail ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Porous Wall ◽  
Coupled System ◽  
Characteristic Parameter ◽  
Squeezing Flow ◽  
Suction Parameter ◽  
Nonlinear Coupled System ◽  
Highly Nonlinear ◽  
Rotating Channel

In this article, a behavioral study of three-dimensional (3D) squeezing flow of nanofluids with magnetic effect in a rotating channel has been performed. Using Navier–Stokes equations along with suitable similarity transformations, a nonlinear coupled ordinary differential system has been derived which models the 3D squeezing flow of nanofluids with lower permeable stretching porous wall where the channel is also rotating. The base fluid in the channel is considered to be water that contains different nanoparticles including silicon, copper, silver, gold, and platinum. The homotopy perturbation method (HPM) is employed for the solution of highly nonlinear coupled system. For validation purpose, system of equations is also solved through the Runge–Kutta–Fehlberg (RK45) scheme and results are compared with homotopy solutions, and excellent agreement has been found between analytical and numerical results. Also, validation has been performed by finding average residual error of the coupled system. Furthermore, the effects of various parameters such as nanoparticle volume fraction, suction parameter, characteristic parameter of the flow, magnetic parameter, rotation parameter, and different types of nanoparticles are studied graphically.

scholarly journals Analytical Modelling of Three-Dimensional Squeezing Nanofluid Flow in a Rotating Channel on a Lower Stretching Porous Wall

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Navid Freidoonimehr ◽  
Behnam Rostami ◽  
Mohammad Mehdi Rashidi ◽  
Ebrahim Momoniat
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Porous Wall ◽  
Coupled System ◽  
Physical Parameters ◽  
Nonlinear Ordinary Differential Equations ◽  
Suction Parameter ◽  
Rotating Channel

A coupled system of nonlinear ordinary differential equations that models the three-dimensional flow of a nanofluid in a rotating channel on a lower permeable stretching porous wall is derived. The mathematical equations are derived from the Navier-Stokes equations where the governing equations are normalized by suitable similarity transformations. The fluid in the rotating channel is water that contains different nanoparticles: silver, copper, copper oxide, titanium oxide, and aluminum oxide. The differential transform method (DTM) is employed to solve the coupled system of nonlinear ordinary differential equations. The effects of the following physical parameters on the flow are investigated: characteristic parameter of the flow, rotation parameter, the magnetic parameter, nanoparticle volume fraction, the suction parameter, and different types of nanoparticles. Results are illustrated graphically and discussed in detail.

scholarly journals On Mixed Convection Squeezing Flow of Nanofluids

Energies ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 3138 ◽  
Author(s):  
Sheikh Irfan Ullah Khan ◽  
Ebraheem Alzahrani ◽  
Umar Khan ◽  
Noreena Zeb ◽  
Anwar Zeb
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Mixed Convection ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Squeezing Flow ◽  
Physical Parameters ◽  
Gamma Alumina ◽  
Highly Nonlinear ◽  
The Impact

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force C f and the rate of heat transfer N u are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter ( β ), mixed convection parameter λ , and volume fraction ( φ ) are also incorporated graphically for γ — alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids.

scholarly journals Role of the hydrological cycle in regulating the planetary climate system of a simple nonlinear dynamical model

2005 ◽  
Vol 12 (5) ◽  
pp. 741-753 ◽  
Author(s):  
K. M. Nordstrom ◽  
V. K. Gupta ◽  
T. N. Chase
Keyword(s):  
Hydrological Cycle ◽  
Water Cycle ◽  
Coupled Model ◽  
Coupled System ◽  
Relative Distribution ◽  
Species Trees ◽  
Nonlinear Coupled System ◽  
Highly Nonlinear ◽  
Negative Feedbacks ◽  
Fully Coupled

Abstract. We present the construction of a dynamic area fraction model (DAFM), representing a new class of models for an earth-like planet. The model presented here has no spatial dimensions, but contains coupled parameterizations for all the major components of the hydrological cycle involving liquid, solid and vapor phases. We investigate the nature of feedback processes with this model in regulating Earth's climate as a highly nonlinear coupled system. The model includes solar radiation, evapotranspiration from dynamically competing trees and grasses, an ocean, an ice cap, precipitation, dynamic clouds, and a static carbon greenhouse effect. This model therefore shares some of the characteristics of an Earth System Model of Intermediate complexity. We perform two experiments with this model to determine the potential effects of positive and negative feedbacks due to a dynamic hydrological cycle, and due to the relative distribution of trees and grasses, in regulating global mean temperature. In the first experiment, we vary the intensity of insolation on the model's surface both with and without an active (fully coupled) water cycle. In the second, we test the strength of feedbacks with biota in a fully coupled model by varying the optimal growing temperature for our two plant species (trees and grasses). We find that the negative feedbacks associated with the water cycle are far more powerful than those associated with the biota, but that the biota still play a significant role in shaping the model climate. third experiment, we vary the heat and moisture transport coefficient in an attempt to represent changing atmospheric circulations.

Wave-Deck-Load Analysis for a Jack-Up Platform

2009 ◽  
Author(s):  
Thomas E. Schellin ◽  
Milovan Peric´ ◽  
Ould el Moctar
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Wave Theory ◽  
Breaking Waves ◽  
Design Parameters ◽  
Wave Direction ◽  
Wave Load ◽  
Two Phase ◽  
Highly Nonlinear ◽  
Jack Up

The paper analyzes freak wave-in-deck load effects on a typical three-leg jack-up platform stationed in the North Sea. Considered were cases where the air gap is small and the hull is subject to impact-related wave-in-deck loads. Wave load predictions were based on the use of a validated CFD code that solves the Reynolds-averaged Navier-Stokes equations. The code relies on the interface-capturing technique of the volume-of-fluid type to account for highly nonlinear wave effects. It computes the two-phase flow of water and air to describe the physics associated with complex free-surface shapes with breaking waves and air trapping, hydrodynamic phenomena that had to be considered to yield reliable predictions. Stokes 5th order wave theory was used to initialize volume fraction of water and velocity distribution in the solution domain, as well as to prescribe time-dependent boundary conditions at inlet and outlet boundaries. It was demonstrated that CFD methods can be used to predict the load phenomena under extreme wave conditions and thus serve as a valuable tool for both initial design and subsequent assessment of safety aspects. In particular, we demonstrated that effects of different operating and design parameters on wave-in-deck loads, such as wave direction, wave height, wave period, and wind speed, can be evaluated with an affordable computing effort using personal computers.

scholarly journals Quasi-stability and continuity of attractors for nonlinear system of wave equations

2021 ◽  
Vol 8 (1) ◽  
pp. 27-45
Author(s):  
M. M. Freitas ◽  
M. J. Dos Santos ◽  
A. J. A. Ramos ◽  
M. S. Vinhote ◽  
M. L. Santos
Keyword(s):  
Wave Equations ◽  
Coupled System ◽  
Global Attractors ◽  
Time Behavior ◽  
Exponential Attractors ◽  
Small Perturbations ◽  
Recent Approach ◽  
Nonlinear Coupled System ◽  
Long Time ◽  
External Forces

Abstract In this paper, we study the long-time behavior of a nonlinear coupled system of wave equations with damping terms and subjected to small perturbations of autonomous external forces. Using the recent approach by Chueshov and Lasiecka in [21], we prove that this dynamical system is quasi-stable by establishing a quasistability estimate, as consequence, the existence of global and exponential attractors is proved. Finally, we investigate the upper and lower semicontinuity of global attractors under autonomous perturbations.

scholarly journals A COMPARISON OF THE ADOMIAN AND HOMOTOPY PERTURBATION METHODS IN SOLVING THE PROBLEM OF SQUEEZING FLOW BETWEEN TWO CIRCULAR PLATES

2010 ◽  
Vol 15 (4) ◽  
pp. 491-504 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Tahira Haroon ◽  
Saira Bhatti ◽  
Ali R. Ansari
Keyword(s):  
Stokes Equations ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Computational Effort ◽  
Navier Stokes ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Navier Stokes Equations ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The objective of this paper is to compare two methods employed for solving nonlinear problems, namely the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM). To this effect we solve the Navier‐Stokes equations for the unsteady flow between two circular plates approaching each other symmetrically. The comparison between HPM and ADM is bench‐marked against a numerical solution. The results show that the ADM is more reliable and efficient than HPM from a computational viewpoint. The ADM requires slightly more computational effort than the HPM, but it yields more accurate results than the HPM.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Numerical simulation for magnetized transport of hybrid nanofluids with exponential space-based heat source

2021 ◽  
Author(s):  
M. S. Alqarni ◽  
Hassan Waqas ◽  
Sumeira Yasmin ◽  
Taseer Muhammad
Keyword(s):  
Heat Source ◽  
Propylene Glycol ◽  
Volume Fraction ◽  
Numerical Data ◽  
Temperature Dependent Viscosity ◽  
Nonlinear Odes ◽  
Highly Nonlinear ◽  
Nanoparticles Volume Fraction ◽  
Dependent Viscosity ◽  
Exponential Space

The prime aim of this investigation is to discuss the two-dimensional steady analysis of hybrid nanoliquids in the existence of magnetohydrodynamics (MHD), thermally radiation and viscous dissipation effects over a linear stretchable sheet. Carbon nanotubes (SWCNT and MWCNT) with copper (Cu) are comprised in the propylene glycol-based fluid. The significance of propylene glycol-based fluid is affected under the exponential space-based heat source phenomenon. The remarkable role of propylene glycol on thermal transport of hybrid nanoliquids is influenced in the presence of temperature-dependent viscosity. The highly nonlinear governing partial differential structures are reduced to nonlinear ODEs by using suitable transformations. The transformed nonlinear ODEs of flow problem have been solved numerically by employing bvp4c (shooting) scheme with Lobatto-IIIA formula in MATLAB. The physical outcomes of involved parameters are obtained by utilizing the graphical and tabular data. The heat transport rate and the skin friction under the numerical data are also presented. From the results, we concluded that the velocity of fluid is declined for higher nanoparticles volume fraction. Velocity of fluid is declined with growing magnetic parameter. Furthermore, the temperature is upgraded with the growing thermal Biot number.

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