SCATTERING OF A THIN LAYER OVER A NONLINEAR RADIALLY EXTENDING SURFACE WITH MAGNETO HYDRODYNAMIC AND THERMAL DISSIPATION

2019 ◽  
Vol 26 (01) ◽  
pp. 1850123 ◽  
Author(s):  
TAZA GUL
Keyword(s):  
Temperature Field ◽  
Thin Layer ◽  
Nonlinear Differential Equations ◽  
Thermal Dissipation ◽  
Flow Equations ◽  
Dissipation Term ◽  
Homotopy Analysis ◽  
Number Formula ◽  
Optimal Approach ◽  
The Impact

The recent research is allied with the analysis of a thin layer, spreading over the nonlinear surface of a radially extended sheet. The temperature field has been taken with the accumulation of dissipation term. The similarity variables have been used to transform the basic flow equations into a set of nonlinear differential equations. The thickness of the spreading phenomenon has been taken as a variable. The approximate outcomes of the problem have been achieved using the optimal approach of the homotopy analysis method (HAM). The convergence of the HAM has been computed with numerical method. The impact of the variable thickness parameter [Formula: see text], generalized magnetic parameter [Formula: see text], Eckert number [Formula: see text] and [Formula: see text] on the spreading pattern and temperature field has been calculated and discussed. The attention has been paid to the important physical quantities of interest like the skin friction and Nusselt number under the effect of various embedded parameters.

scholarly journals The flow of ferromagnetic nanofluid over an extending surface under the effect of operative Prandtl model: A numerical study

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989612 ◽  
Author(s):  
Abbas Khan ◽  
Taza Gul ◽  
Zafar Zaheer ◽  
Iraj S Amiri
Keyword(s):  
Differential Equations ◽  
Magnetic Dipole ◽  
Volume Fraction ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
Governing Equations ◽  
Heat Transfer Fluids ◽  
Dissipation Term ◽  
Prandtl Model ◽  
The Impact

The purpose of this research is to investigate the impact of magnetic dipole on the flow of nanofluids over the extending surface. This study is based on steady and non-porous medium with no-slip conditions. Two types of nanofluids are examined under the effect of operative Prandtl model and thermal convection. The experimental results comprising the spreading of [Formula: see text] and [Formula: see text] have been used from the existing literature with and without the magnetic dipole. The basic governing equations are transformed using the transformation into a set of nonlinear differential equations for both categories of nanofluids. The fourth-order Runge Kutta numerical scheme has been executed to solve the nonlinear ordinary differential equations. The impacts of the embedded parameters such as nanofluid volume fraction, Prandtl number, and dissipation term have been examined and discussed. The important features of the study such as Curie temperature, skin friction, and local Nusselt number are also analyzed physically and numerically. (1) It is perceived that ethylene glycol–based nanofluids are more effective due to their strong thermophysical properties compared to water-based nanofluids. By increasing the volume fraction [Formula: see text], the temperature of the nanofluids [Formula: see text] and [Formula: see text] is increased, and this is due to the fact that nanofluids exhibit high thermal conductivity compared to ordinary heat transfer fluids. (2) It is observed from the obtained results that the magnetic dipole is usually used to control the turbulence behavior of the fluid flow.

Influence of Dynamics Viscosity on the Water Base Graphene Oxide–Ethylene Glycol/Graphene Oxide–Water Nanofluid Flow Over a Stretching Cylinder

2019 ◽  
Vol 8 (8) ◽  
pp. 1661-1667
Author(s):  
Ali Rehman ◽  
Zabidin Salleh ◽  
Taza Gul
Keyword(s):  
Differential Equation ◽  
Graphene Oxide ◽  
Ethylene Glycol ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Homotopy Analysis ◽  
Water Base ◽  
The Impact

This research paper presents the impact of dynamics viscosity of water base GO–EG (graphene oxide–ethylene glycol)/GO–W (graphene oxide–water) nanofluid over a stretching cylinder with non-porous medium. The impact of different parameter for both velocity and temperature profile are displayed and discussed graphically. The similarity transformation are used to convert the partial differential equation to nonlinear ordinary differential equation. The solution of the problem is obtained using the optimal homotopy analysis method (OHAM). (Liao, S. J., 2010. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15, pp.2003–2016) used this method for the solution of nonlinear problem and show that this method is quickly convergent to the approximate solution. This method gives us series solution in the form of function, and all the physical parameters of the problem involved in this method. The stability of the problems is also obtained up to the 30th order approximation using the BVPh 2.0 package. The outputs are displayed graphically and discussed. The effects of various parameters on the skin friction coefficient and Nusselt number coefficient of base GO–EG/GO–Ware displayed and discussed.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

Nonlinear mixed convective Williamson nanofluid flow with the suspension of gyrotactic microorganisms

2021 ◽  
pp. 2150145
Author(s):  
Shuang-Shuang Zhou ◽  
M. Ijaz Khan ◽  
Sumaira Qayyum ◽  
B. C. Prasannakumara ◽  
R. Naveen Kumar ◽  
...  
Keyword(s):  
Heat Source ◽  
Lewis Number ◽  
Solution Procedure ◽  
Energy Concentration ◽  
Gyrotactic Microorganisms ◽  
Dimensionless Parameters ◽  
Flow Equations ◽  
Fluid Parameter ◽  
Source Sink ◽  
The Impact

This investigation aims to present the thermally developed bioconvection flow of Williamson nanoliquid over an inclined stretching cylinder in presence of linear mixed convection and nonuniform heat source/sink. The activation energy and suspension of gyrotactic microorganisms are accounted with applications of bioconvection phenomenon. Appropriate nondimensional variables are opted to attain the dimensionless form of flow equations. The resulting momentum, energy, concentration and motile density equations are abridged to highly coupled and nonlinear in nature. The numerical treatment is followed for the solution procedure by employing the shooting method. The influence of some relevant dimensionless parameters is discoursed graphically along with physical justifications. Moreover, the impact of several dimensionless parameters on skin friction and Nusselt number is obtained and listed in tables. It is observed that the velocity of fluid shows a decreasing variation for Williamson fluid parameter. The change in unsteadiness parameter and heat source parameter enhanced the nanofluid temperature. The motile microorganisms profile declines with bioconvection constant and bio-convection Lewis number.

Suppressing Cracking in Resistance Welding AA5754 by Mechanical Means

2000 ◽  
Author(s):  
Hongyan Zhang ◽  
Jacek Senkara ◽  
Xin Wu
Keyword(s):  
Temperature Field ◽  
Crack Initiation ◽  
Spot Welding ◽  
Mechanical Analysis ◽  
Crack Initiation And Propagation ◽  
State Of Stress ◽  
Initiation And Propagation ◽  
Thermal Mechanical Analysis ◽  
The Impact ◽  
Analytical Approaches

Abstract In this paper mechanical aspects of cracking during single- and multi-spot welding of AA5754 was investigated by both experimental and analytical approaches. The impact of mechanical loading on crack initiation and propagation was studied with the consideration of various process parameters including the loading imposed by electrodes, the formation of liquid nugget, and constraining factors during and after welding. Tensile properties of AA5754 and their dependence on the temperature were tested at room and up to solidus temperatures, in order to provide a reference of cracking stress. Thermal-mechanical analysis was conducted based on the temperature field around the nugget and the state of stress encountered during welding. This analysis revealed that tensile stress might build up in the vicinity of the nugget during cooling, thus explained the experimental observation. General guidelines for suppressing cracking were proposed, i.e. to provide sufficient constraint around the weld spot during and after welding.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

The Evolution Model of Emergency Response System for Sudden Accidents of Construction Projects

2012 ◽  
Vol 226-228 ◽  
pp. 2253-2257
Author(s):  
Ren Hui Liu ◽  
Bo Yu
Keyword(s):  
Emergency Response ◽  
Construction Projects ◽  
Nonlinear Differential Equations ◽  
Continuous Process ◽  
Construction Project ◽  
Equation Model ◽  
Emergency Response System ◽  
Response System ◽  
The Impact ◽  
Emergency System

It is a nonlinear complex system for project emergency response system, that is a continuous process for the evolution of emergency construction project development process. The nonlinear differential equations that can describe the sudden emergency construction project the evolution of mathematical models. Emergency system by Logistic model was modified, taking into account the development of emergency systems will certainly be outside the system during the impact, combined with the project incidents of law principles of the role of Heinrich proposed TS-based emergency response system evolution equation Model, demonstrated the system at different stages of the emergency rules and features. For the emergency system in which the different stages of development, the corresponding measures to improve emergency response capabilities.

scholarly journals Homotopy Analysis of Carreau Fluid Flow Over a Stretching Cylinder

2021 ◽  
Vol 88 (2) ◽  
pp. 80-92
Author(s):  
Lim Yeou Jiann ◽  
Sharidan Shafie ◽  
Ahmad Qushairi Mohamad ◽  
Noraihan Afiqah Rawi
Keyword(s):  
Nonlinear Differential Equations ◽  
Velocity Profiles ◽  
Weissenberg Number ◽  
Stretching Cylinder ◽  
Series Solutions ◽  
Carreau Fluid ◽  
Keller Box Method ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Curvature Parameter

Carreau fluid flows past a stretching cylinder is elucidated in the present study. The transformed self-similarity and dimensionless boundary layer equations are solved by using the Homotopy analysis method. A convergence study of the method is illustrated explicitly. Series solutions of the highly nonlinear differential equations are computed and it is very efficient in demonstrating the characteristic of the Carreau fluid. Validation of the series solutions is achieved via comparing with earlier published results. Those results are obtained by using the Keller-Box method. The effects of the Weissenberg number and curvature parameter on the velocity profiles are discussed by graphs and tabular. The velocity curves have shown different behavior in and for an increase of the Weissenberg number. Further, the curvature parameter K does increase the velocity profiles.

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