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 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.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

Influence of nonlinear thermal radiation and viscous dissipation on three-dimensional flow of Jeffrey nano fluid over a stretching sheet in the presence of Joule heating

2017 ◽  
Vol 6 (3) ◽  
Author(s):  
K. Ganesh Kumar ◽  
N.G. Rudraswamy ◽  
B.J. Gireesha ◽  
M.R. Krishnamurthy
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Nonlinear Thermal Radiation ◽  
Nonlinear Ordinary Differential Equations ◽  
Three Dimensional Flow

AbstractPresent exploration discusses the combined effect of viscous dissipation and Joule heating on three dimensional flow and heat transfer of a Jeffrey nanofluid in the presence of nonlinear thermal radiation. Here the flow is generated over bidirectional stretching sheet in the presence of applied magnetic field by accounting thermophoresis and Brownian motion of nanoparticles. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are solved numerically by using the Runge–Kutta–Fehlberg fourth–fifth order method with shooting technique. Graphically results are presented and discussed for various parameters. Validation of the current method is proved by comparing our results with the existing results under limiting situations. It can be concluded that combined effect of Joule and viscous heating increases the temperature profile and thermal boundary layer thickness.

scholarly journals The Shape Effect of Gold Nanoparticles on Squeezing Nanofluid Flow and Heat Transfer between Parallel Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Umair Rashid ◽  
Thabet Abdeljawad ◽  
Haiyi Liang ◽  
Azhar Iqbal ◽  
Muhammad Abbas ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Graphical Form ◽  
Shape Effect ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Suction Parameter ◽  
Flow And Heat Transfer

The focus of the present paper is to analyze the shape effect of gold (Au) nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates. The different shapes of nanoparticles, namely, column, sphere, hexahedron, tetrahedron, and lamina, have been examined using water as base fluid. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable transformations. As a result, nonlinear boundary value ordinary differential equations are tackled analytically using the homotopy analysis method (HAM) and convergence of the series solution is ensured. The effects of various parameters such as solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, suction parameter, and shape factor on velocity and temperature profiles are plotted in graphical form. For various values of involved parameters, Nusselt number is analyzed in graphical form. The obtained results demonstrate that the rate of heat transfer is maximum for lamina shape nanoparticles and the sphere shape of nanoparticles has performed a considerable role in temperature distribution as compared to other shapes of nanoparticles.

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 Adomian Decomposition Method for a Class of Nonlinear Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
J. A. Sánchez Cano
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Coupled System ◽  
Nonlinear Ordinary Differential Equations ◽  
Adomian Decomposition

The Adomian decomposition method together with some properties of nested integrals is used to provide a solution to a class of nonlinear ordinary differential equations and a coupled system.

scholarly journals On the complete integrability and linearization of nonlinear ordinary differential equations. III. Coupled first-order equations

2008 ◽  
Vol 465 (2102) ◽  
pp. 585-608 ◽  
Author(s):  
V.K Chandrasekar ◽  
M Senthilvelan ◽  
M Lakshmanan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Complete Integrability ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
First Order ◽  
Open Questions ◽  
Motion Time

Continuing our study on the complete integrability of nonlinear ordinary differential equations (ODEs), in this paper we consider the integrability of a system of coupled first-order nonlinear ODEs of both autonomous and non-autonomous types. For this purpose, we modify the original Prelle–Singer (PS) procedure so as to apply it to both autonomous and non-autonomous systems of coupled first-order ODEs. We briefly explain the method of finding integrals of motion (time-independent as well as time-dependent integrals) for two and three coupled first-order ODEs by extending the PS method. From this we try to answer some of the open questions in the original PS method. We also identify integrable cases for the two-dimensional Lotka–Volterra system and three-dimensional Rössler system as well as other examples including non-autonomous systems in a straightforward way using this procedure. Finally, we develop a linearization procedure for coupled first-order ODEs.

scholarly journals Impact of double-diffusive convection and motile gyrotactic microorganisms on magnetohydrodynamics bioconvection tangent hyperbolic nanofluid

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 74-88 ◽  
Author(s):  
Tanveer Sajid ◽  
Muhammad Sagheer ◽  
Shafqat Hussain ◽  
Faisal Shahzad
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Physical Nature ◽  
Working Fluid ◽  
Nonlinear Ordinary Differential Equations ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms ◽  
Double Diffusive

AbstractThe double-diffusive tangent hyperbolic nanofluid containing motile gyrotactic microorganisms and magnetohydrodynamics past a stretching sheet is examined. By adopting the scaling group of transformation, the governing equations of motion are transformed into a system of nonlinear ordinary differential equations. The Keller box scheme, a finite difference method, has been employed for the solution of the nonlinear ordinary differential equations. The behaviour of the working fluid against various parameters of physical nature has been analyzed through graphs and tables. The behaviour of different physical quantities of interest such as heat transfer rate, density of the motile gyrotactic microorganisms and mass transfer rate is also discussed in the form of tables and graphs. It is found that the modified Dufour parameter has an increasing effect on the temperature profile. The solute profile is observed to decay as a result of an augmentation in the nanofluid Lewis number.

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