New modeling and analytical solution of fourth grade (non-Newtonian) fluid by a stretchable magnetized Riga device

2021 ◽  
Author(s):  
Yun-Jie Xu ◽  
Faisal Shah ◽  
M. Ijaz Khan ◽  
R. Naveen Kumar ◽  
R. J. Punith Gowda ◽  
...  
Keyword(s):  
Thermal Relaxation ◽  
Fourth Grade ◽  
Analytic Solutions ◽  
Fluid Temperature ◽  
Viscoelastic Parameter ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Riga Plate ◽  
Layer Flow ◽  
Source Sink

The aim of this paper is to examine the influence of heat source/sink on boundary layer flow of a fourth-grade liquid over a stretchable Riga plate on taking account of induced magnetic field and mixed convection. Analysis of mass and heat transport is studied through modified Fourier heat flux model. The governing flow issue is demonstrated with the help of momentum, energy, temperature and concentration equation. The modeled equations are reduced into nondimensional ODEs by opting suitable similarity transformations. The analytic solutions are discussed by means of the optimal technique of homotopy analysis. The influence of several nondimensional parameters on velocity, thermal and concentration gradients are deliberated by using suitable graphs. Also, the skin friction is discussed with the help of graphs. The result outcomes reveal that, velocity of fluid diminishes for advanced values of viscoelastic parameter and fourth-grade liquid parameter but contrary movement is seen for third grade fluid parameters. Fluid temperature boosts up for thermal relaxation parameter and concentration is abridged for rising values of solutal concentration parameter and Schmidt number.

Implication of fluid rheology on the Cattaneo–Christov heat flux theory for fourth grade nanofluid over a riga device with thermal radiation

2021 ◽  
pp. 2150189
Author(s):  
M. Ijaz Khan ◽  
F. Alzahrani
Keyword(s):  
Thermal Radiation ◽  
Thermal Relaxation ◽  
Fourth Grade ◽  
Variable Thermal Conductivity ◽  
Fluid Temperature ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Fluid Rheology ◽  
Fourth Grade Fluid

This paper analyzes the influence of mixed convective fourth grade nanofluid flow by a stretchable Riga device in the presence variable thermal conductivity and mass diffusivity. Heat and mass transportation are considered with Cattaneo–Christov (CC) model. Thermal radiation and dissipation are also taken in the energy expression. Suitable transformation is employed to reduce partial differential system into nonlinear ordinary system. The governing nonlinear expression is solved via optimal homotopy analysis method. Impact of different physical variables is discussed via graphs. Velocity profile is enhanced for higher values of cross viscous parameter and fourth grade fluid variable. Fluid temperature enhances for higher estimation of thermal relaxation parameter but reverse behavior is seen for solutal concentration variable on nanoparticle concentration.

Stagnation Flow of a Jeffrey Fluid over a Shrinking Sheet

2010 ◽  
Vol 65 (6-7) ◽  
pp. 540-548 ◽  
Author(s):  
Sohail Nadeem ◽  
Anwar Hussain ◽  
Majid K
Keyword(s):  
Jeffrey Fluid ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Governing Equations ◽  
Stagnation Flow ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Equations Of Motions

January 22, 2009 The present paper describes the analytical solutions for the steady boundary layer flow of a Jeffrey fluid over a shrinking sheet. The governing equations of motions are reduced into a set of nonlinear ordinary differential equations by using similarity transformations. Two types of problems, namely, (1) two-dimensional stagnation flow towards a shrinking sheet and (2) axisymmetric stagnation flow towards an axisymmetric shrinking sheet, have been discussed. The series solutions of the problems are obtained by using the homotopy analysis method (HAM). The convergence of the obtained series solutions are analyzed and discussed in detail through graphs for various parameters of interest.

scholarly journals Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

2009 ◽  
Vol 64 (9-10) ◽  
pp. 575-582 ◽  
Author(s):  
Sohail Nadeem ◽  
Saeid Abbasbandy ◽  
Majid Hussain
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

MHD Flow of an Oldroyd-B Fluid Through a Porous Channel

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Meraj Mustafa ◽  
Awatif Hendi
Keyword(s):  
Analytic Solution ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Porous Channel ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Number Comparison ◽  
Homotopy Analysis ◽  
Layer Flow

This paper discusses the hydromagnetic boundary layer flow of an Oldroyd-B fluid in a porous channel. Both suction and injection (blowing) cases are considered. Appropriate similarity transformations are invoked to convert the partial differential equations into ordinary ones. Homotopy analysis method (HAM) is used for the presentation of analytic solution of the nonlinear differential system. Graphical results provide the salient features of the embedded flow parameters which include the Reynolds number, the Deborah numbers, and the Hartman number. Comparison between the existing numerical solution in a Maxwell fluid and present deduced series solution in a limiting sense is excellent.

Computer-extended series solution for laminar flow between a fixed impermeable disk and a porous rotating disk

2018 ◽  
Vol 35 (4) ◽  
pp. 1655-1674 ◽  
Author(s):  
Vishwanath B. Awati ◽  
Oluwole Daniel Makinde ◽  
Manjunath Jyoti
Keyword(s):  
Series Solution ◽  
Rotating Disk ◽  
Polar Coordinates ◽  
Analysis Method ◽  
Content Type ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Cylindrical Polar Coordinates ◽  
Good Agreement

Purpose The purpose of this paper is to study the laminar boundary layer flow between a stationary nonporous disk and a porous rotating disk, both being immersed in large amount of fluid. Design/methodology/approach The governing nonlinear momentum equations in cylindrical polar coordinates together with relevant boundary conditions are reduced to a system of coupled nonlinear ordinary differential equations (NODEs) using similarity transformations. The resulting coupled NODEs are solved using computer-extended series solution and homotopy analysis method. Findings The analytical solutions are explicitly expressed in terms of recurrence relation for determining the universal coefficients. The nature and location of singularity which restricts the convergence of series is analyzed by using Domb–Sykes plot. Reversion of series is used for the improvement of series. The region of validity of series is extended for much larger values of Reynolds number (R), i.e. R = 6 to 15. Originality/value The resulting solutions are compared with earlier works in the literature and are found to be in good agreement.

MHD mixed convection flow of a viscoelastic fluid over an inclined surface with a nonuniform heat source/sink

2013 ◽  
Vol 91 (12) ◽  
pp. 1074-1080 ◽  
Author(s):  
G.K. Ramesh ◽  
Ali J. Chamkha ◽  
B.J. Gireesha
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Viscoelastic Fluid ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Different Types ◽  
Layer Flow ◽  
Source Sink ◽  
Inclined Surface

The steady mixed convection boundary layer flow over an inclined stretching surface immersed in an incompressible viscoelastic fluid is considered in this paper. Employing suitable similarity transformations, the governing partial differential equations are transformed into ordinary differential equations, and the transformed equations are solved numerically using Runge–Kutta–Fehlberg method. Herein, two different types of heating processes are considered, namely, (i) prescribed surface temperature and (ii) prescribed wall heat flux. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that velocity decreases and temperature increases with an increase in the value of angle of inclination.

scholarly journals Homotopy Analysis Method to determine Magneto Hydrodynamics flow of compressible fluid in a channel with porous walls

2016 ◽  
Vol 34 (1) ◽  
pp. 173-186
Author(s):  
Reza Mohammadyari ◽  
J. Rahimipetroudi ◽  
Iman Rahimipetroudi ◽  
Mazaher Rahimi Esboee
Keyword(s):  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Compressible Fluid ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Analysis Method ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Porous Walls ◽  
Layer Flow

In this article magnetohydrodynamics (MHD) boundary layer flow of compressible fluid in a channel with porous walls is researched. In this study it is shown that the nonlinear Navier-Stokes equations can be reduced to an ordinary differential equation, using the similarity transformations and boundary layer approximations. Analytical solution of the developed nonlinear equation is carried out by the Homotopy Analysis Method (HAM). In addition to applying HAM into the obtained equation, the result of the mentioned method is compared with a type of numerical analysis as Boundary Value Problem method (BVP) and a good agreement is seen. The effects of the Reynolds number and Hartman number are investigated.

Influence of non-uniform heat source/sink and variable viscosity on mixed convection flow of third grade nanofluid over an inclined stretched Riga plate

2019 ◽  
Vol 6 (4) ◽  
Author(s):  
M K Nayak ◽  
A K Abdul Hakeem ◽  
B Ganga
Keyword(s):  
Boundary Layer ◽  
Heat Source ◽  
Thermal Boundary Layer ◽  
Third Grade ◽  
Fluid Temperature ◽  
Temperature Dependent ◽  
Uniform Heat ◽  
Riga Plate ◽  
Source Sink ◽  
The Impact

The present study focuses on the impact of non-uniform heat source/sink and temperature dependent viscosity modeled by Reynolds on Cattaneo-Christov heat flow of third grade nanofluid subject to an inclined stretched Riga plate. Fourth order R-K and shooting methods have been implemented to obtain the numerical solution of the transformed boundary layer equations. The achievability of the present study is that the material constants associated with third grade fluid augment the fluid motion and boils down the fluid temperature leading to ascending velocity boundary layer and descending thermal boundary layer. And viscosity parameter enhances the heat transfer rate from the plate. Furthermore, augmented space and temperature dependent heat source upsurges the fluid temperature and the related thermal boundary layer thickness.

scholarly journals Influence of Inclined Magnetic Field on Carreau Nanoliquid Thin Film Flow and Heat Transfer with Graphene Nanoparticles

Energies ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1459 ◽  
Author(s):  
Noor Saeed Khan ◽  
Taza Gul ◽  
Poom Kumam ◽  
Zahir Shah ◽  
Saeed Islam ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Thin Film ◽  
Inclined Magnetic Field ◽  
Thin Film Flow ◽  
Analysis And Design ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Nice Agreement ◽  
Graphene Nanoparticles ◽  
Source Sink

The thermodynamics of a Carreau nanoliquid thin film embedded with graphene nanoparticles past a stretching sheet is studied in the presence of inclined magnetic field and non-uniform heat source/sink. Graphene is a new two-dimensional amphiphilic macromolecule which has great applications due to its electrical and mechanical properties. The basic constitutive equations of Carreau nanoliquid for velocity and temperature have been used. Similarity transformations are adopted to achieve the nonlinear coupled differential equations accompanying boundary conditions embedded with different parameters. HAM (Homotopy Analysis Method) is used to solve the transformed equations for expressions of velocity and temperature. Graphs are shown which illustrate the effects of various parameters of interest. There exists a nice agreement between the present and published results. The results are useful for the thermal conductivity and in the analysis and design of coating processes.

The HAM Solutions for Unsteady Boundary Layer Flow and Heat Transfer with Heat Source/Sink

2014 ◽  
Vol 887-888 ◽  
pp. 919-923 ◽  
Author(s):  
Jing Zhu ◽  
Zheng Liu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nonlinear Differential Equations ◽  
Physical Factors ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Analytical Approximations ◽  
Homotopy Analysis ◽  
Layer Flow ◽  
Source Sink

Considering the combined effects of the magnetic field and viscous dissipation, this paper investigates the problem of two-dimensional incompressible unsteady flow over a horizontal continuous stretching sheet. Due to the strongly nonlinear and various parameters of this problem, the governing boundary layer equations are transformed into a system of nonlinear differential equations through the similarity transformation, and then analytical approximations of solutions are derived by homotopy analysis method. In addition, the effects of physical factors on the flow and heat transfer characteristics are examed and discussed graphically.

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