scholarly journals Gyrotactic micro-organism flow of Maxwell nanofluid between two parallel plates

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yun-Jie Xu ◽  
Muhammad Bilal ◽  
Qasem Al-Mdallal ◽  
Muhammad Altaf Khan ◽  
Taseer Muhammad
Keyword(s):  
Differential Equations ◽  
Fluid Velocity ◽  
Continuation Method ◽  
Nonlinear Partial Differential Equations ◽  
Parallel Plates ◽  
Gyrotactic Microorganisms ◽  
Physical Constraints ◽  
Buoyancy Convection ◽  
Parametric Continuation ◽  
Response Versus

AbstractThe present study explores incompressible, steady power law nanoliquid comprising gyrotactic microorganisms flow across parallel plates with energy transfer. In which only one plate is moving concerning another at a time. Nonlinear partial differential equations have been used to model the problem. Using Liao's transformation, the framework of PDEs is simplified to a system of Ordinary Differential Equations (ODEs). The problem is numerically solved using the parametric continuation method (PCM). The obtained results are compared to the boundary value solver (bvp4c) method for validity reasons. It has been observed that both the results are in best settlement with each other. The temperature, velocity, concentration and microorganism profile trend versus several physical constraints are presented graphically and briefly discussed. The velocity profile shows positive response versus the rising values of buoyancy convection parameters. While the velocity reduces with the increasing effect of magnetic field, because magnetic impact generates Lorentz force, which reduces the fluid velocity.

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 Magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Abdullah Dawar ◽  
Zahir Shah ◽  
Hashim M. Alshehri ◽  
Saeed Islam ◽  
Poom Kumam
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Lewis Number ◽  
Casson Fluid ◽  
Stretching Cylinder ◽  
Concentration Difference ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Homotopy Analysis

AbstractThis study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. $$\beta \to \infty$$ β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. $$\beta = 1.0$$ β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms’ concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

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.

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 MHD heat transfer flow of Casson fluid past a stretching wedge subject to suction and injection

2017 ◽  
Vol 13 (4) ◽  
pp. 637-641 ◽  
Author(s):  
Imran Ullah ◽  
Sharidan Shafie ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Wedge Angle ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Suction Parameter ◽  
Keller Box Method

The steady two dimensional incompressible hydromagnetic boundary layer flow caused by stretching wedge immersed in Casson fluid with heat transfer and suction/injection is investigated numerically. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. Numerical results for local skin friction coefficient are compared with the existing literature and observed in closed agreement with those results. The effects of pertinent parameters on flow fields are displayed graphically and discussed. It is found that velocity decreases with increase of Casson parameter and wedge angle parameter when the wedge is stretching faster than free stream. It is also observed that rate of heat transfer at surface increases with the increase of Prandtl number and Casson fluid parameter. Moreover, with increase of suction parameter the fluid velocity decreases and rate of shear stress increases.

scholarly journals STEADY MHD SLIP FLOW OVER A PERMEABLE STRETCHING CYLINDER WITH THERMAL RADIATION

2021 ◽  
Vol 8 (11) ◽  
pp. 23-36
Author(s):  
Sharad Sinha ◽  
Deepak Kumar ◽  
Anil Sharma
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Stretching Cylinder ◽  
Fourth Order Method

Aim of the paper is to investigate the effects of thermal radiation and velocity slip on steady MHD slip flow of viscous incompressible electrically conducting fluid over a permeable stretching cylinder saturated in porous medium in the presence of external magnetic field. The governing nonlinear partial differential equations are transformed into ordinary differential equations by suitable similarity transformation and solved numerically using Runge-Kutta fourth order method with shooting technique. Effect of various physical parameters on fluid velocity, temperature, skin –friction coefficient and Nusselt number are presented through graphs and discussed numerically.

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.

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