THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER AN UNSTEADY PERMEABLE SHRINKING SURFACE

2021 ◽  
Vol 10 (9) ◽  
pp. 3263-3272
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Viscous Flow ◽  
Stagnation Point ◽  
Multiple Solutions ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Shrinking Sheet ◽  
Governing System ◽  
Shrinking Surface

An analysis is carried out to theoretically investigate the unsteady three dimensional stagnation-point of a viscous flow over a permeable stretching/shrinking sheet. A similarity transformation is used to reduce the governing system of nonlinear partial differential equations to a set of nonlinear ordinary (similarity) differential equations, which are then solved numerically using the \texttt{bvp4c} function in MATLAB. Results show that multiple solutions exist for a certain range of unsteadiness and stretching/shrinking parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed.

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

2021 ◽  
Vol 10 (9) ◽  
pp. 3273-3282
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Flow Model ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

Unsteady separated stagnation-point flow and heat transfer past a stretching/shrinking sheet in a copper-water nanofluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2588-2605 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Similarity Transformation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das. Design/methodology/approach A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Findings It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case. Originality/value The authors believe that all numerical results are new and original, and have not been published elsewhere.

scholarly journals MHD stagnation-point flow and heat transfer past a stretching/shrinking sheet in a hybrid nanofluid with induced magnetic field

2019 ◽  
Vol 30 (3) ◽  
pp. 1345-1364 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Norihan Md Arifin ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type

Purpose The purpose of this paper is to investigate the steady magnetohydrodynamics (MHD) boundary layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking sheet with the effect of induced magnetic field. Design/methodology/approach The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations via the similarity transformations before they are solved numerically using the “bvp4c” function in MATLAB. Findings It is found that there exist non-unique solutions, namely, dual solutions for a certain range of the stretching/shrinking parameters. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable. Practical implications This problem is important in the heat transfer field such as electronic cooling, engine cooling, generator cooling, welding, nuclear system cooling, lubrication, thermal storage, solar heating, cooling and heating in buildings, biomedical, drug reduction, heat pipe, space aircrafts and ships with better efficiency than that of nanofluids applicability. The results obtained are very useful for researchers to determine which solution is physically stable, whereby, mathematically more than one solution exist. Originality/value The present results are new and original for the problem of MHD stagnation-point flow over a stretching/shrinking sheet in a hybrid nanofluid, with the effect of induced magnetic field.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

2016 ◽  
Vol 71 (9) ◽  
pp. 837-848 ◽  
Author(s):  
Ehtsham Azhar ◽  
Z. Iqbal ◽  
E.N. Maraj
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Computational Analysis ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Plate

AbstractThe present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

scholarly journals A New Numerical Solution of Maxwell Fluid over a Shrinking Sheet in the Region of a Stagnation Point

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Maxwell Fluid ◽  
Shrinking Sheet ◽  
Two Dimensional ◽  
Similarity Transformations ◽  
The Mathematical Model ◽  
Successive Linearisation Method ◽  
Fluid Parameters

The mathematical model for the incompressible two-dimensional stagnation flow of a Maxwell fluid towards a shrinking sheet is proposed. The developed equations are used to discuss the problem of being two dimensional in the region of stagnation point over a shrinking sheet. The nonlinear partial differential equations are transformed to ordinary differential equations by first-taking boundary-layer approximations into account and then using the similarity transformations. The obtained equations are then solved by using a successive linearisation method. The influence of the pertinent fluid parameters on the velocity is discussed through the help of graphs.

scholarly journals Dirichlet series and analytical solutions of MHD viscous flow with suction / blowing

2017 ◽  
Vol 2 (2) ◽  
pp. 341-350 ◽  
Author(s):  
Vishwanath B. Awati
Keyword(s):  
Differential Equations ◽  
Viscous Flow ◽  
Dirichlet Series ◽  
Analytical Solutions ◽  
Similarity Transformation ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Incompressible Viscous Flow ◽  
Approximate Analytical Solutions

AbstractThis paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.

scholarly journals Magnetohydrodynamics Stagnation-Point Flow of a Nanofluid Past a Stretching/Shrinking Sheet with Induced Magnetic Field: A Revised Model

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1078 ◽  
Author(s):  
Mohamad Mustaqim Junoh ◽  
Fadzilah Md Ali ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Governing Equations ◽  
Induced Magnetic Field ◽  
The Stability ◽  
Stretching Or Shrinking Sheet

The revised Buongiorno’s nanofluid model with the effect of induced magnetic field on steady magnetohydrodynamics (MHD) stagnation-point flow of nanofluid over a stretching or shrinking sheet is investigated. The effects of zero mass flux and suction are taken into account. A similarity transformation with symmetry variables are introduced in order to alter from the governing nonlinear partial differential equations into a nonlinear ordinary differential equations. These governing equations are numerically solved using the bvp4c function in Matlab solver, a very adequate finite difference method. The influences of considered parameters ( P r , M, χ , L e , N b , N t , S, and λ ) on velocity, induced magnetic, temperature, and concentration profiles together with the reduced skin friction and heat transfer rate are discussed. Results from these criterion exposed the existence of dual solutions when magnetic field and suction are applied for a specific range of λ . The stability of the solutions obtained is carried out by performing a stability analysis.

scholarly journals Mathematical Analysis of Magnetized Rotating Nanofluid Flow Over nonlinear shrinking surface: Duality and Stability

2021 ◽  
Vol 5 (2) ◽  
pp. 1-13
Author(s):  
Dr Sumera Dero ◽  
Ghulam Hyder Talpur ◽  
Abbas Ali Ghoto ◽  
Shokat Ali
Keyword(s):  
Differential Equations ◽  
Hartmann Number ◽  
Similarity Transformation ◽  
Flow Characteristics ◽  
Shrinking Sheet ◽  
Nanofluid Flow ◽  
Suction Parameter ◽  
Stable Branch ◽  
Shrinking Surface ◽  
Good Agreement

In this study, the MHD effect on boundary layer rotating flow of a nanofluid is investigated for the multiple branches case. The main focus of current research is to examine flow characteristics on a nonlinear permeable shrinking sheet. Moreover, the governing partial differential equations (PDEs) of the problem considered are reduced into coupled nonlinear ordinary differential equations (ODEs) with the appropriate similarity transformation.  Numerical results based on the plotted graphs are gotten by solving ODEs with help of the three-stage Labatto IIIA method in bvp4c solver in MATLAB. To confirm numerical outcomes, current results are compared with previously available outcomes and found in good agreement. Skin friction coefficients, Nusselt and Sherwood numbers, velocity profiles, temperature profiles, and concentration profiles are examined. The results show that dual (no) branches exist in certain ranges of the suction parameter i.e., SSc (SSc). Further, profiles of velocity decrease for rising values of Hartmann number in the upper branch, while reverse trend has been noticed in a lower branch. Profiles of temperature and concentration enhance for the increasing values of thermophoresis in both branches. stability analysis of the branches is also done and noticed that upper branch is a stable branch from both branches. Finally, it is noted that the stable branch has symmetrical behavior with regard to the parameter of rotation.

Stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet with a second-order slip velocity

2019 ◽  
Vol 29 (2) ◽  
pp. 738-762 ◽  
Author(s):  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Lewis Number ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet. Design/methodology/approach Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a1, a2) and second-order (b1) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1. Findings Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable. Originality/value The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.

A numerical study of the axisymmetric rotational stagnation point flow impinging radially a permeable stretching/shrinking surface in a nanofluid

2017 ◽  
Vol 27 (11) ◽  
pp. 2415-2432 ◽  
Author(s):  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Numerical Study ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
First Order ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose The purpose of this study is to analyze numerically the steady axisymmetric rotational stagnation point flow impinging on a radially permeable stretching/shrinking sheet in a nanofluid. Design/methodology/approach Similarity transformation is used to convert the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in MATLAB software. Findings Dual solutions exist when the surface is stretched, as well as when the surface is shrunk. For these solutions, a stability analysis is carried out revealing that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable and therefore not physically realizable. Originality/value The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Weidman (2016) to the case of nanofluids.

Sign in / Sign up

Export Citation Format

Share Document