scholarly journals Effect of induced magnetic field on non-Newtonian nanofluid Al2O3 motion through boundary layer with gyrotactic microorganisms

2021 ◽  
pp. 189-189
Author(s):  
Nabil Eldabe ◽  
Raafat Rizkalla ◽  
Mohamed Abou-Zeid ◽  
Vivian Ayad
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Velocity Ratio ◽  
Nonlinear Partial Differential Equations ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Gyrotactic Microorganisms ◽  
Field Temperature

The effect of the induced magnetic field on the motion of Eyring-Powell nanofluid Al2O3, containing gyrotactic microorganisms through the boundary layer is investigated. The viscoelastic dissipation is taken into consideration. The system is stressed by an external magnetic field. The continuity, momentum, induced magnetic field, temperature, concentration and microorganisms equations that describe our problem are written in the form of two-dimensional nonlinear differential equations. The system of nonlinear partial differential equations is transformed into ordinary differential equations using appropriate similarity transformations with suitable boundary conditions and solved numerically by applying the ND Solve command in the Mathematica program. The obtained numerical results for velocity, induced magnetic field, temperature, the nanoparticles concentration and microorganisms are discussed and presented graphically through some figures. The physical parameters of the problem play an important rule in the control of the obtained solutions. Moreover, it is obvious that as Grashof number Gr increases, both the velocity f' and the induced magnetic field h' increase, while, the reciprocal magnetic Prandtl number A works on decreasing both f' and h'. As Eckert number Ec increases the temperature increases, while it decreases as the velocity ratio B increases.

Magnetohydrodynamic Mixed Convective Flow Due to a Vertical Plate With Induced Magnetic Field

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
R. Nandkeolyar ◽  
M. Narayana ◽  
S. S. Motsa ◽  
P. Sibanda
Keyword(s):  
Magnetic Field ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Linearization Method ◽  
Fluid Temperature ◽  
Magnetic Field Effects ◽  
Induced Magnetic Field ◽  
Partial Differential

The steady hydromagnetic flow of a viscous, incompressible, perfectly conducting, and heat absorbing fluid past a vertical flat plate under the influence of an aligned magnetic field is studied. The flow is subject to mixed convective heat transfer. The fluid is assumed to have a reasonably high magnetic Prandtl number which causes significant-induced magnetic field effects. Such fluid flows find application in many magnetohydrodynamic devices including MHD power-generation. The effects of viscous dissipation and heat absorption by the fluid are investigated. The governing nonlinear partial differential equations are converted into a set of nonsimilar partial differential equations which are then solved using a spectral quasi-linearization method (SQLM). The effects of the important parameters on the fluid velocity, induced magnetic field, fluid temperature and as well as on the coefficient of skin-friction and the Nusselt number are discussed qualitatively.

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 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 Influences of Slip Velocity and Induced Magnetic Field on MHD Stagnation-Point Flow and Heat Transfer of Casson Fluid over a Stretching Sheet

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Ahmed A. Afify
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Casson Fluid ◽  
Integration Scheme ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Casson Fluid Model

The steady MHD boundary layer flow near the stagnation point over a stretching surface in the presence of the induced magnetic field, viscous dissipation, magnetic dissipation, slip velocity phenomenon, and heat generation/absorption effects has been investigated numerically. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. The governing partial differential equations using appropriate similarity transformations are reduced into a set of nonlinear ordinary differential equations, which are solved numerically using a shooting method with fourth-order Runge-Kutta integration scheme. Comparisons with the earlier results have been made and good agreements were found. Numerical results for the velocity, induced magnetic field, temperature profiles, skin friction coefficient, and Nusselt number are presented through graphs and tables for various values of physical parameters. Results predicted that the magnetic parameter with α<1 has the tendency to enhance the heat transfer rate, whereas the reverse trend is seen with α>1. It is also noticed that the rate of heat transfer is a decreasing function of the reciprocal of a magnetic Prandtl number, whereas the opposite phenomenon occurs with the magnitude of the friction factor.

scholarly journals Dual solution of boundary-layer flow driven by variable plate and streaming-free velocity

2020 ◽  
Vol 12 (7) ◽  
pp. 168781402093084
Author(s):  
M Ferdows ◽  
Faris Alzahrani ◽  
Shuyu Sun
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Differential Equations ◽  
Skin Friction ◽  
Numerical Study ◽  
Velocity Ratio ◽  
Dual Solutions ◽  
Physical Parameters ◽  
Branch Solution

This article presents a numerical study to investigate boundary-layer heat transfer fluid associated with a moving flat body in cooperation of variable plate and streaming-free velocity along the boundary surface in the laminar flow. The thermal conductivity is supposed to vary linearly with temperature. Similarity transformations are applied to render the governing partial differential equations for mass, momentum and energy into a system of ordinary differential equations to reveal the possible existence of dual solutions. MATLAB package has been used to solve the boundary value problem numerically. We present the effects of various parameters such as velocity ratio, thermal conductivity and variable viscosity on velocity and temperature distribution. The analysis of the results concerning Skin friction and Nusselt number near the wall is also presented. It is focused on the detection and description of the dual solutions. The study reveals that the undertaken problem admits dual solutions in particular range of values of different physical parameters. It can be seen that for the first branch solution, the fluid velocity decreases near the sheet, but it increases far away from the sheet for velocity ratio parameter, whereas the opposite effect is induced for second branch solution. Skin friction coefficient and rate of heat transfer increase due to increase in thermal conductivity parameter.

scholarly journals Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1929 ◽  
Author(s):  
Syed M. Hussain ◽  
Rohit Sharma ◽  
Manas R. Mishra ◽  
Sattam S. Alrashidy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Physical Parameters ◽  
Maxwell Nanofluid ◽  
Nusselt Numbers ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Relationship ◽  
The Magnetic Field

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

scholarly journals Magnetohydrodynamic flow due to noncoaxial rotations of a porous disk and a fourth-grade fluid at infinity

2003 ◽  
Vol 2003 (2) ◽  
pp. 47-64 ◽  
Author(s):  
Tasawar Hayat ◽  
Yongqi Wang
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Fourth Grade ◽  
Porous Disk ◽  
Grade Fluid ◽  
Fourth Grade Fluid ◽  
The Magnetic Field ◽  
Conditions At Infinity

The governing equations for the unsteady flow of a uniformly conducting incompressible fourth-grade fluid due to noncoaxial rotations of a porous disk and the fluid at infinity are constructed. The steady flow of the fourth-grade fluid subjected to a magnetic field with suction/blowing through the disk is studied. The nonlinear ordinary differential equations resulting from the balance of momentum and mass are discretised by a finite-difference method and numerically solved by means of an iteration method in which, by a coordinate transformation, the semi-infinite physical domain is converted to a finite calculation domain. In order to solve the fourth-order nonlinear differential equations, asymptotic boundary conditions at infinity are augmented. The manner in which various material parameters affect the structure of the boundary layer is delineated. It is found that the suction through the disk and the magnetic field tend to thin the boundary layer near the disk for both the Newtonian fluid and the fourth-grade fluid, while the blowing causes a thickening of the boundary layer with the exception of the fourth-grade fluid under strong blowing. With the increase of the higher-order viscosities, the boundary layer has the tendency of thickening.

scholarly journals Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

2016 ◽  
Vol 26 (8) ◽  
pp. 2370-2392 ◽  
Author(s):  
Ioan Pop ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Norfifah Bachok ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Content Type

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Influence of induced magnetic field and slip conditions on convective Prandtl fluid flow over a stretching surface with homogeneous and heterogeneous reactions

2020 ◽  
Vol 17 (1) ◽  
pp. 127-147 ◽  
Author(s):  
R. Meenakumari ◽  
P. Lakshminarayana ◽  
K. Vajravelu
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heterogeneous Reactions ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Content Type ◽  
Homogeneous And Heterogeneous Reactions ◽  
Moderate Magnetic Field

PurposeThe aim of the present paper is to investigate the homogeneous and heterogeneous reactions on Prandtl fluid flow at a stretching sheet with an induced magnetic field and slip boundary conditions.Design/methodology/approachThe governing equations include the continuity, induced magnetic field, momentum, energy and homogeneous–heterogeneous equations. Initially, with suitable similarity variables, the governing partial differential equations and converted into a system of ordinary differential equations. Then, the nonlinear ordinary differential equations are solved by a shooting technique with the help of the BVC5C Matlab package.FindingsThe results of the present investigation are presented through graphs for different values of the various parameters. The authors observed that the large values of the stretching ratio and the induced magnetic parameters are moderate magnetic field, velocity and temperature primarily. Also, the authors found the more velocity and temperatures by boosting the slip parameters.Originality/valueIn addition, the values of the skin friction and the rate of heat transfer for various values of physical parameters are tabulated and deliberated in detail.

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