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.

scholarly journals Darcy-Forchheimer hybrid nanofluid flow over a stretching curved surface with heat and mass transfer

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0249434
Author(s):  
Anwar Saeed ◽  
Wajdi Alghamdi ◽  
Safyan Mukhtar ◽  
Syed Imad Ali Shah ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Curved Surface ◽  
Hybrid Nanofluid ◽  
Porous Space ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Curvature Parameter ◽  
Swcnts And Mwcnts

The present article provides a detailed analysis of the Darcy Forchheimer flow of hybrid nanoliquid past an exponentially extending curved surface. In the porous space, the viscous fluid is expressed by Darcy-Forchheimer. The cylindrical shaped carbon nanotubes (SWCNTs and MWCNTs) and Fe3O4 (iron oxide) are used to synthesize hybrid nanofluid. At first, the appropriate similarity transformation is used to convert the modeled nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations. Then the resulting highly nonlinear coupled ordinary differential equations are analytically solved by the utilization of the “Homotopy analysis method” (HAM) method. The influence of sundry flow factors on velocity, temperature, and concentration profile are sketched and briefly discussed. The enhancement in both volume fraction parameter and curvature parameter k results in raises of the velocity profile. The uses of both Fe3O4 and CNTs nanoparticles are expressively improving the thermophysical properties of the base fluid. Apart from this, the numerical values of some physical quantities such as skin friction coefficients, local Nusselt number, and Sherwood number for the variation of the values of pertinent parameters are displayed in tabular forms. The obtained results show that the hybrid nanofluid enhances the heat transfer rate 2.21%, 2.1%, and 2.3% using the MWCNTs, SWCNTs, and Fe3O4 nanomaterials.

MHD Flow of a Carreau Fluid Past a Stretching Cylinder with Cattaneo-Christov Heat Flux Using Spectral Relaxation Method

2018 ◽  
Vol 387 ◽  
pp. 91-105 ◽  
Author(s):  
K. Gangadhar ◽  
K.V. Ramana ◽  
Oluwole Daniel Makinde ◽  
B. Rushi Kumar
Keyword(s):  
Heat Flux ◽  
Temperature Jump ◽  
Thermal Relaxation ◽  
Mhd Flow ◽  
Relaxation Method ◽  
Stretching Cylinder ◽  
Carreau Fluid ◽  
Highly Nonlinear ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

A theoretical investigation of a hydromagnetic boundary layer flow of Carreau fluid over a stretching cylinder with surface slippage and temperature jump is presented in this paper. It is assumed that heat transfer characteristics of the flow follows Cattaneo-Christov heat flux model base on conventional Fourier’s law with thermal relaxation time. The spectral relaxation method (SRM) is being utilized to provide the solution of highly nonlinear system of coupled partial differential equations converted into dimensionless governing equations. The behaviour of flow parameters on velocity, temperature distributions are sketched as well as analyzed physically. The result indicates that the temperature distribution decay for higher temperature jump and thermal relaxation parameters respectively.

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.

scholarly journals Engineering Applications of Peristaltic Fluid Flow with Hall Current, Thermal Deposition and Convective Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1710
Author(s):  
Humaira Yasmin ◽  
Naveed Iqbal ◽  
Anum Tanveer
Keyword(s):  
Hall Current ◽  
Weissenberg Number ◽  
Series Solutions ◽  
Convective Conditions ◽  
Carreau Fluid ◽  
Thermal Deposition ◽  
Compliant Wall ◽  
Channel Analysis ◽  
Deposition Effect ◽  
Physical Quantities

This article addresses the peristaltic flow in a compliant wall channel. Analysis has been carried out in the presence of a Hall current and chemical reaction. Convective conditions in terms of both heat and mass transfer are employed. Mathematical modeling is developed for an incompressible Carreau fluid. Thermal deposition effect and convection at the channel walls are considered. Series solutions are obtained for small Weissenberg number We. Solution expressions of velocity, temperature, concentration and stream function are obtained. These physical quantities are displayed and analyzed. Heat transfer coefficient and trapping are explored in detail.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

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. 

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.

scholarly journals Modelling Study on Internal Energy Loss Due to Entropy Generation for Non-Darcy Poiseuille Flow of Silver-Water Nanofluid: An Application of Purification

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 851 ◽  
Author(s):  
Nasir Shehzad ◽  
Ahmed Zeeshan ◽  
Rahmat Ellahi ◽  
Saman Rashidi
Keyword(s):  
Porous Media ◽  
Internal Energy ◽  
Entropy Generation ◽  
Poiseuille Flow ◽  
Volume Fraction ◽  
Low Cost ◽  
Theoretical Estimate ◽  
Industrial Process ◽  
Highly Nonlinear ◽  
Homotopy Analysis

In this paper, an analytical study of internal energy losses for the non-Darcy Poiseuille flow of silver-water nanofluid due to entropy generation in porous media is investigated. Spherical-shaped silver (Ag) nanosize particles with volume fraction 0.3%, 0.6%, and 0.9% are utilized. Four illustrative models are considered: (i) heat transfer irreversibility (HTI), (ii) fluid friction irreversibility (FFI), (iii) Joule dissipation irreversibility (JDI), and (iv) non-Darcy porous media irreversibility (NDI). The governing equations of continuity, momentum, energy, and entropy generation are simplified by taking long wavelength approximations on the channel walls. The results represent highly nonlinear coupled ordinary differential equations that are solved analytically with the help of the homotopy analysis method. It is shown that for minimum and maximum averaged entropy generation, 0.3% by vol and 0.9% by vol of nanoparticles, respectively, are observed. Also, a rise in entropy is evident due to an increase in pressure gradient. The current analysis provides an adequate theoretical estimate for low-cost purification of drinking water by silver nanoparticles in an industrial process.

Sign in / Sign up

Export Citation Format

Share Document