Stagnation point flow of MHD chemically reacting nanofluid over a stretching convective surface with slip and radiative heat

2016 ◽  
Vol 231 (4) ◽  
pp. 695-703 ◽  
Author(s):  
OD Makinde ◽  
WA Khan ◽  
ZH Khan
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Local Skin ◽  
Local Skin Friction ◽  
Homogeneous Chemical ◽  
Chemically Reacting

This paper investigates the combined effects of buoyancy forces, homogeneous chemical reaction, thermal radiation, partial slip, heat source, Thermophoresis and Brownian motion on hydromagnetic stagnation point flow of nanofluid with heat and mass transfer over a stretching convective surface. The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. Using similarity transformation, the governing nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations which are solved numerically by employing by shooting method coupled with Runge–Kutta Fehlberg integration technique. Graphical results showing the effects of various thermophysical parameters on the velocity, temperature, nanoparticle concentration, local skin friction, local Nusselt number and local Sherwood number are presented and discussed quantitatively.

scholarly journals Buoyancy-Induced MHD Stagnation Point Flow of Williamson Fluid with Thermal Radiation

2020 ◽  
pp. 9-18 ◽  
Author(s):  
J. O. Ouru ◽  
W. N. Mutuku ◽  
A. S. Oke
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Polymer Processing ◽  
Stagnation Point Flow ◽  
Radiation Parameter ◽  
Williamson Fluid

Flow of fluids subjected to thermal radiation has enormous application in polymer processing, glass blowing, cooling of nuclear reactant and harvesting solar energy. This paper considers the MHD stagnation point flow of non-Newtonian pseudoplastic Williamson fluid induced by buoyancy in the presence of thermal radiation. A system of nonlinear partial differential equations suitable to describe the MHD stagnation point flow of Williamson fluid over a stretching sheet is formulated and then transformed using similarity variables to boundary value ordinary differential equations. The graphs depicting the effect of thermal radiation parameter, buoyancy and electromagnetic force on the fluid velocity and temperature of the stagnation point flow are given and the results revealed that increase in buoyancy leads to an increase in the overall velocity of the flow but a decrease in the temperature of the flow.

Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface

2016 ◽  
Vol 71 (3) ◽  
pp. 273-280 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

AbstractThe stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.

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.

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.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

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 Numerical Solution of Stagnation Point Flow and Heat Transfer over a Nonlinear Stretching/Shrinking Sheet in Hybrid Nanofluid: Stability Analysis

2020 ◽  
Vol 76 (2) ◽  
pp. 85-98
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Pure Water ◽  
Nonlinear Parameter ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Local Skin

The steady, laminar, stagnation point flow of hybrid nanofluid past a nonlinearly stretching and shrinking sheet is studied. Hybrid nanofluid is regarded by disseminated two distinct nano-sized particles, silver (Ag) and copper oxide (CuO) in pure water. Similarity technique was used for the transformation of partial differential equations (PDEs) into an ordinary differential equations (ODEs). Obtained ODEs were solved using Matlab’s built in function (bvp4c). The results of important governing parameters which are nonlinear parameter, stretching/shrinking parameter and nanoparticle volume fraction are evaluated and discussed in graphical and tabular form for the velocity and temperature profiles, along with local skin friction, local Nusselt number. Nonunique solutions (first and second branch) are visible for some limit of shrinking parameter. It is noticed that nonlinear parameter hastens flow separations. Hence, a stability analysis is executed to identify which solutions are stable and physically feasible.

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 The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Assad Ayub ◽  
Juan L. G. Guirao ◽  
Saira Bhatti ◽  
Syed Zahir Hussain Shah
Keyword(s):  
Activation Energy ◽  
Brownian Motion ◽  
Differential Equations ◽  
Concentration Profile ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Local Skin ◽  
Arrhenius Function ◽  
Local Skin Friction

The present study is related to the effects of activation energy and thermophoretic diffusion on steady micropolar fluid along with Brownian motion. The activation energy and thermal conductivity of steady micropolar fluid are also discussed. The equation of motion, angular momentum, temperature, concentration, and their boundary conditions are presented for the micropolar fluid. The detail of geometry reveals the effects of several parameters on the parts of the system. The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. The comparison of the obtained results by the shooting technique and the numerical bvp4c technique is presented. The behavior of local skin friction numbers and couple stress number is tabulated for different parameters, and some figures are plotted to present the different parameters. For uplifting the values of AE for parameter λA, the concentration profile is increased because of the Arrhenius function, and AE increases with the reduction of this function. The increasing values of the parameter of rotation G show the decrement in velocity because of the rotation of the particle of the fluid, so the linear motion decreases. Thermophoresis is responsible for shifting the molecules within the fluid, and due to this, an increment in boundary layer thickness is found, so by a greater value of Nt, the concentration profile decreases and temperature profile goes down.

scholarly journals Diffussion-thermo and chemical reaction effects on an unsteady MHD free convection flow in a micropolar fluid

2016 ◽  
Vol 43 (1) ◽  
pp. 117-131 ◽  
Author(s):  
Siva Sheri ◽  
M.D. Shamshuddin
Keyword(s):  
Boundary Layer ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Layer Analysis ◽  
Local Skin Friction ◽  
Homogeneous Chemical ◽  
Chemically Reacting

This paper considers a boundary layer analysis on the effects of diffusion-thermo, heat absorption and homogeneous chemical reaction on mag- netohydrodynamic flow of an incompressible, laminar chemically reacting mi- cropolar fluid past a semi-infinite vertical porous plate is made numerically. The governing partial differential equations are solved numerically using the finite element method. The numerical results are compared and found to be in good agreement with previous results as special case of the present inves- tigation. The effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed and explained graphically. Also the effects of the pertinent parameters on the local Skin friction coefficient, wall Couple stress and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are presented numerically in tabular form.

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