scholarly journals Computational analysis of hydromagnetic boundary layer stagnation point flow of nano liquid by a stretched heated surface with convective conditions and radiation effect

2021 ◽  
Vol 13 (10) ◽  
pp. 168781402110531
Author(s):  
Haroon Ur Rasheed ◽  
Saeed Islam ◽  
Zeeshan Khan ◽  
Jahangir Khan ◽  
Wali Khan Mashwani ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Heated Surface ◽  
Stagnation Point Flow ◽  
Stability And Convergence ◽  
Convective Heating ◽  
Flow Equations ◽  
Nonlinear Stretching ◽  
Mathematica Software

In this study, the boundary layer phenomena for stagnation point flow of water-based nanofluids is being observed with the upshot of MHD and convective heating on a nonlinear stretching surface. To develop a fundamental flow model, a boundary layer approximation is done, which signifies time-dependent momentum, energy, and concentration expressions. Through a proper transformation framework, the modeled boundary layer partial differential equations (PDEs) have been diminished to a dimensionless system of nonlinear ordinary differential equations (ODEs). With the assistance of a built-in algorithm in Mathematica software, the fundamental flow equations are analyzed numerically by imposing a shooting technique explicitly. A stability and convergence analysis were also unveiled, and the ongoing investigation was found to have converged. The effect of mathematical abstractions on velocity, energy, and concentration is plotted and discussed. The influence of skin-friction and Nusselt number on the sheet are debated for the various values of important parameters.

scholarly journals Analysis of Electromagnetohydrodynamic Stagnation Point Flow of Nanofluid Over a Nonlinear Stretching Sheet with Variable Thickness

2019 ◽  
Vol 35 (5) ◽  
pp. 719-733 ◽  
Author(s):  
G. S. Seth ◽  
P. K. Mandal
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Variable Thickness ◽  
Stretching Sheet ◽  
Power Index ◽  
Stagnation Point Flow ◽  
Convective Heating ◽  
Fluid Temperature ◽  
Nanoparticle Concentration ◽  
Nonlinear Stretching

ABSTRACTPresent study explores stagnation point flow of nanofluid towards a nonlinear stretching sheet of variable thickness in the presence of electromagnetic field and convective heating. The effect of viscous dissipation and Joule heating are also taken into consideration. Novel concept of non-linear radiative heat flux is also considered. The nanofluid is inspired by Lorentz force which is instigated from the interaction of magnetic and electric fields. Using similarity transformation, the governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and then solved numerically by fourth order Runge-Kutta method along with shooting technique. The velocity, temperature and nanoparticle concentration profiles are plotted and analysed corresponding to various pertinent flow parameters. Also, the skin friction and rate of heat and mass transfers at the surface are computed and explained in detail. It is observed that higher wall thickness parameter results in the reduction of velocity, temperature and nanoparticle concentration when velocity power index is less than unity and opposite effect is observed when velocity power index is greater than unity. Due to intensification of electric field, nanofluid velocity is getting retarded and thereby resulting in enhancement of fluid temperature and nanoparticle concentration.

scholarly journals Nonviscous Oblique Stagnation Point Flow towards Riga Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sobia Akbar ◽  
Azad Hussain
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stagnation Point ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Riga Plate ◽  
Mathematical Techniques

Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

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.

Stagnation Point Flow of Burgers' Fluid and Mass Transfer with Chemical Reaction and Porosity

2013 ◽  
Vol 29 (3) ◽  
pp. 453-460 ◽  
Author(s):  
A. Alsaedi ◽  
F. E. Alsaadi ◽  
S. Ali ◽  
T. Hayat
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Nonlinear Ordinary Differential Equation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Surface Mass ◽  
Flow Equations ◽  
Burgers Fluid

AbstractThis paper studies the influence of mass transfer in the magnetohydrodynamic (MHD) boundary layer stagnation point flow of Burgers' fluid over a shrinking sheet. Analysis has been carried out in the presence of first order chemical reaction. The two-dimensional flow equations are modeled and then simplified using boundary layer approach. Similarity variables are used to transform the partial differential equations into nonlinear ordinary differential equation. The resulting system is computed using homotopy analysis method (HAM). It is noted that retardation time in Burgers' fluid enhances the magnitude of the flow. The gradient of mass transfer and surface mass transfer for various interesting parameters are also tabulated and analyzed.

Three dimensional MHD stagnation point flow of Al-Cu alloy suspended water based nanofluid with second order slip and convective heating

2017 ◽  
Vol 27 (12) ◽  
pp. 2879-2901
Author(s):  
N. Nithyadevi ◽  
P. Gayathri ◽  
A. Chamkha
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Convective Heating ◽  
Slip Effect ◽  
Content Type ◽  
Water Based

Purpose The paper aims to examine the boundary layers of a three-dimensional stagnation point flow of Al-Cu nanoparticle-suspended water-based nanofluid in an electrically conducting medium. The effect of magnetic field on second-order slip effect and convective heating is also taken into account. Design/methodology/approach The thermophysical properties of alloy nanoparticles such as density, specific heat capacity and thermal conductivity are computed using appropriate formula. The non-linear parabolic partial differential equations are transformed to ordinary differential equations and solved by shooting technique. Findings The influence of compositional variation of alloy nanoparticle, nanoparticle concentration, magnetic effect, slip parameters and Biot number are presented for various flow characteristics. Interesting results on skin friction and Nusselt number are obtained for different composition of aluminium and copper. Originality/value A novel result of the analysis reveals that impact of magnetic field near the boundary is suppressed by the slip effect.

scholarly journals Impact of nonlinear thermal radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy

2017 ◽  
Vol 232 (6) ◽  
pp. 962-972 ◽  
Author(s):  
A Zaib ◽  
MM Rashidi ◽  
AJ Chamkha ◽  
NF Mohammad
Keyword(s):  
Activation Energy ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Velocity Ratio ◽  
Stagnation Point Flow ◽  
Nonlinear Thermal Radiation ◽  
Nonlinear Stretching

This research peruses the characteristics of nanoparticles on stagnation point flow of a generalized Newtonian Carreau fluid past a nonlinear stretching sheet with nonlinear thermal radiation. The process of mass transfer is modeled using activation energy and binary chemical reaction along with the Brownian motion and thermophoresis. For energy activation a modified Arrhenius function is invoked. With regard to the solution of the governing differential equations, suitable transformation variables are used to obtain the system of nonlinear ordinary differential equations before being numerically solved using the shooting method. Graphical results are shown in order to scrutinize the behavior of pertinent parameters on velocity, temperature profiles, and concentration of nanoparticle. Also, the behavior of fluid flow is investigated through the coefficient of the skin friction, Nusselt number, Sherwood number, and streamlines. Results showed that the velocity ratio parameter serves to increase the velocity of fluid and reduces the temperature distribution and nanoparticle concentration. The results were compared with the available studies and were found to be in excellent agreement.

scholarly journals Cu-Al2O3/Water Hybrid Nanofluid Stagnation Point Flow Past MHD Stretching/Shrinking Sheet in Presence of Homogeneous-Heterogeneous and Convective Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1237
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Heterogeneous Reactions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Convective Boundary

The intent of this research was to present numerical solutions to homogeneous–heterogeneous reactions of the magnetohydrodynamic (MHD) stagnation point flow of a Cu-Al2O3/water hybrid nanofluid induced by a stretching or shrinking sheet with a convective boundary condition. A proper similarity variable was applied to the system of partial differential equations (PDEs) and converted into a system of ordinary (similarity) differential equations (ODEs). These equations were solved using Matlab’s in-built function (bvp4c) for various values of the governing parameters numerically. The present investigation considered the effects of homogeneous–heterogeneous reactions and magnetic field in the hybrid nanofluid flow. It was observed that dual solutions were visible for the shrinking sheet, and an analysis of stability was done to determine the physically realizable in the practice of these solutions. It was also concluded that hybrid nanofluid acts as a cooler for some increasing parameters. The magnetohydrodynamic parameter delayed the boundary layer separation; meanwhile, the nanoparticle volume fraction quickened the separation of the boundary layer that occurred. In addition, the first solution of hybrid nanofluid was found to be stable; meanwhile, the second solution was not stable. This study is therefore valuable for engineers and scientists to get acquainted with the properties of hybrid nanofluid flow, its behavior and the way to predict it.

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.

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