The Effect of Variable Viscosities on Micropolar Flow of Two Nanofluids

2016 ◽  
Vol 71 (12) ◽  
pp. 1121-1129 ◽  
Author(s):  
S. Nadeem ◽  
Z. Ahmed ◽  
S. Saleem
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Particle Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Rotational Inertia ◽  
Physical Parameters ◽  
Particle Volume ◽  
Viscosity Parameter ◽  
Similarity Transformations

AbstractA study of nanofluids is carried out that reveals the effect of rotational inertia and other physical parameters on the heat transfer and fluid flow. Temperature-dependent dynamic viscosity makes the microrotation viscosity parameter and the micro inertia density variant as well. The governing nonlinear partial differential equations are converted into a set of nonlinear ordinary differential equations by introducing suitable similarity transformations. These reduced nonlinear differential equations are then solved numerically by Keller-box method. The obtained numerical and graphical result discloses many interesting behaviour of nanofluids. It is seen that the temperature gradient decreases with the increase in viscosity parameter. Also, it is observed that with the fixed values of micropolar parameter and viscosity parameter, the velocity gradient near the wall increases with increasing values of solid particle volume fraction parameter. A suitable comparison of results is also presented in this study.

scholarly journals Unsteady flow over an expanding cylinder in a nanofluid containing gyrotactic microorganisms

2016 ◽  
Vol 94 (5) ◽  
pp. 466-473 ◽  
Author(s):  
Hui Chen ◽  
Hongxing Liang ◽  
Tianli Xiao ◽  
Heng Du ◽  
Ming Shen
Keyword(s):  
Differential Equations ◽  
Unsteady Flow ◽  
Shooting Method ◽  
Schmidt Number ◽  
Volume Fraction ◽  
Dual Solutions ◽  
Physical Parameters ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Fifth Order

In this paper, an analysis is made for the unsteady flow due to an expanding cylinder in a nanofluid that contains both nanoparticles and gyrotactic microoganisms with suction. The nonlinear system of partial differential equations is transformed into high-order nonlinear ordinary differential equations using similarity transformations, and then solved numerically using a shooting method with fourth-fifth-order Runge–Kutta integration technique. The influences of significant physical parameters on the distributions of the velocity, temperature, nanoparticle volume fraction, as well as the density of motile microorganisms are graphically presented and discussed in detail. It is found that dual solutions exist for both stretching and shrinking cases and the range of dual solutions increases with the strength of the expansion. The results also indicate that larger bioconvection Peclet number and smaller Schmidt number lead to an increased concentration of microorganisms and thicker boundary layer thickness.

scholarly journals Axisymmetric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. Nadeem ◽  
Abdul Rehman ◽  
K. Vajravelu ◽  
Jinho Lee ◽  
Changhoon Lee
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Flow ◽  
Finite Radius ◽  
Similarity Transformations ◽  
Moving Cylinder ◽  
Micropolar Nanofluid ◽  
Homotopy Analysis ◽  
Flow Phenomena

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

scholarly journals On Unsteady Three-Dimensional Axisymmetric MHD Nanofluid Flow with Entropy Generation and Thermo-Diffusion Effects

2017 ◽  
Author(s):  
Mohammed Almakki ◽  
Sharadia Dey ◽  
Sabyasachi Mondal ◽  
Precious Sibanda
Keyword(s):  
Nusselt Number ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Three Dimensional ◽  
Linearization Method ◽  
Physical Parameters ◽  
Particle Volume ◽  
Nanofluid Flow

We investigate entropy generation in unsteady three-dimensional axisymmetric MHD nanofluid flow over a non-linearly stretching sheet. The flow is subject to thermal radiation and a chemical reaction. The conservation equations were solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasilinearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account when the nanofluid particle volume fraction on the boundary in passively controlled. The results show that as the Hartman number increases, both the Nusselt number and the Sherwood number decrease whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with the physical parameters.

Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc

2019 ◽  
Vol 234 (3-4) ◽  
pp. 83-97 ◽  
Author(s):  
Fatema Tuz Zohra ◽  
Mohammed Jashim Uddin ◽  
Md Faisal Basir ◽  
Ahmad Izani Md Ismail
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Engineering Application ◽  
Rotating Disc ◽  
Partial Differential ◽  
Similarity Transformations ◽  
Wide Range

Microfluidic-related technologies and micro-electromechanical systems–based microfluidic devices have received applications in science and engineering fields. This article is the study of a mathematical model of steady forced convective flow past a rotating disc immersed in water-based nanofluid with microorganisms. The boundary layer flow of a viscous nanofluid is studied with multiple slip conditions and Stefan blowing effects under the magnetic field influence. The microscopic nanoparticles move randomly and have the characteristics of thermophoresis, and it is being considered that the change in volume fraction of the nanofluid does not affect the thermo-physical properties. The governing equations are nonlinear partial differential equations. At first, the nonlinear partial differential equations are converted to system of nonlinear ordinary differential equations using suitable similarity transformations and then solved numerically. The influence of relevant parameters on velocities, temperature, concentration and motile microorganism density is illustrated and explained thoroughly. This investigation indicated that suction provides a better medium to enhance the transfer rate of heat, mass and microorganisms compared to blowing. This analysis has a wide range engineering application such as electromagnetic micro pumps and nanomechanics.

scholarly journals A Finite Element Simulation of the Active and Passive Controls of the MHD Effect on an Axisymmetric Nanofluid Flow with Thermo-Diffusion over a Radially Stretched Sheet

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 207 ◽  
Author(s):  
Bagh Ali ◽  
Xiaojun Yu ◽  
Muhammad Tariq Sadiq ◽  
Ateeq Ur Rehman ◽  
Liaqat Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Volume Fraction ◽  
Axisymmetric Flow ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Partial Differential Equations ◽  
Similarity Transformations ◽  
Element Method

The present study investigated the steady magnetohydrodynamics of the axisymmetric flow of a incompressible, viscous, electricity-conducting nanofluid with convective boundary conditions and thermo-diffusion over a radially stretched surface. The nanoparticles’ volume fraction was passively controlled on the boundary, rather than actively controlled. The governing non-linear partial differential equations were transformed into a system of nonlinear, ordinary differential equations with the aid of similarity transformations which were solved numerically, using the very efficient variational finite element method. The coefficient of skin friction and rate of heat transfer, and an exact solution of fluid flow velocity, were contrasted with the numerical solution gotten by FEM. Excellent agreement between the numerical and exact solutions was observed. The influences of various physical parameters on the velocity, temperature, and solutal and nanoparticle concentration profiles are discussed by the aid of graphs and tables. Additionally, authentication of the convergence of the numerical consequences acquired by the finite element method and the computations was acquired by decreasing the mesh level. This exploration is significant for the higher temperature of nanomaterial privileging technology.

scholarly journals Effects of Non-Uniform Heat Generation/Absorption and Radiation on Hydromagnetic Dissipative Flow over a Porous Nonlinear Stretching Surface with Heat and Mass Fluxes

2019 ◽  
Vol 24 (4) ◽  
pp. 36-52
Author(s):  
S.P. Anjali Devi ◽  
M. Agneeshwari
Keyword(s):  
Differential Equations ◽  
Heat Generation ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Iteration Scheme ◽  
Published Data ◽  
Physical Parameters ◽  
Similarity Transformations ◽  
Uniform Heat ◽  
Nonlinear Stretching

Abstract Forced convective heat and mass transfer flow of hydromagnetic, radiating and dissipative fluid over a porous nonlinear stretching sheet in the presence of non-uniform heat generation/absorption is investigated numerically. The system of nonlinear partial differential equations governing the physical problem is reduced to nonlinear ordinary differential equations by means of suitable similarity transformations and are solved numerically using Nachtsheim Swigert shooting iteration scheme together with fourth order Runge Kutta method. The effects of various physical parameters on velocity, temperature and concentration distributions are depicted graphically. The important findings of this study exhibited that the effect of non-uniform heat generation/absorption parameter and radiation parameter have significant role in controlling thermal boundary layer thickness and temperature. Numerical values of the skin friction coefficient, temperature and concentration at the wall are shown in a tabular form. A comparison is made with previously published data which results in good agreement.

scholarly journals Dusty Nanofluid Past a Centrifugally Stretching Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wubshet Ibrahim ◽  
Dachasa Gamachu
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Velocity Profile ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Stretching Surface ◽  
Particle Volume ◽  
Magnetic Field Parameter ◽  
The Magnetic Field

This communication reports, the flow of Cu-water dusty nanofluid past a centrifugally stretching surface under the effect of second order slip and convective boundary conditions. The coupled nonlinear ordinary differential equations are get hold of from the partial differential equations which are derived from the conservation of momentum and energy of both nanofluid and dusty phases. Then, using apt resemblance transformation these ordinary differential equations were altered into a dimensionless form and then solved by bvp5c solver in Matlab software. The variation in velocity and temperature profiles of fluid and dusty phases for different parameters are thrash out in depth by figures and tables. The outcomes exhibit that the velocity profile of both fluid and dusty phases boot as the values of the dust particle volume fraction parameter is enlarged. Besides, the magnetic field parameter has similar effect on the velocity profile of both fluid and dusty phases. Also, the results illustrated that temperature profile of both Cu-water nanofluid and dusty particle phases are improved within an enhancement in the values of the temperature relaxation parameter, Cu-particle volume fraction, and Biot number. The results also confirm that for greater values of the magnetic field parameter the values of skin friction coefficient are enlarged for all values of the velocity ratio parameter.

Numerical study of heat transfer and Hall current impact on peristaltic propulsion of particle-fluid suspension with compliant wall properties

2019 ◽  
Vol 33 (35) ◽  
pp. 1950439 ◽  
Author(s):  
M. M. Bhatti ◽  
Rahmat Ellahi ◽  
A. Zeeshan ◽  
M. Marin ◽  
N. Ijaz
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Hall Current ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
Particle Volume Fraction ◽  
Mathematical Formulation ◽  
Solid Particles ◽  
Particle Volume ◽  
The Impact

In this paper, the effects of heat transfer and Hall current on the sinusoidal motion of solid particles through a planar channel has been discussed. The walls of the channel are considered as compliant under the effects of magnetohydrodynamics. The mathematical formulation has been performed using energy equation, momentum equation, and Ohm’s law. The modeled equations are further modified by taking the assumption of a zero Reynolds number and long wavelength. Numerical shooting technique has been employed to solve the nonlinear differential equations. The impact of all the emerging parameters such as wall rigidity, wall tension, mass characterization, Hall parameter, Hartmann number, Weissenberg number, particle volume fraction, Prandtl number, and Eckert number, respectively. Particularly, we discussed their effects on velocity and temperature profile.

scholarly journals Magnetohydrodynamic Effects in Mixed Convection Copper-Water Nano Fluid Flow at Lower Stagnation Point on a Sliced Sphere

CFD Letters ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 21-31
Author(s):  
Basuki Widodo ◽  
Adhi Surya Nugraha ◽  
Dieky Adzkiya ◽  
Mohd Zuki Salleh
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Copper Particle ◽  
Particle Volume ◽  
Nano Fluid ◽  
Determining Factors

The study of simulation and applications of mathematics in fluid dynamics continues to grow along with the development of computer science and technology. One of them is Magnetohydrodynamics (MHD) which is closely related to its implementation in engineering and industry. And given the importance of magnetic fluid flow has attracted researchers to study and explore its benefits and uses in the industrial field, especially in convective flow and heat transfer processes. This paper therefore considers mathematical modeling on mixed convection MHD viscous fluid flow on the lower stagnation point of a magnetic sliced sphere. The study began with transforming the governing equations which are in dimensional partial differential equations to non-dimensional ordinary differential equations by using the similarity variable. The resulting similarity equations are then solved by the Keller-Box scheme. The characteristics and effects of the Prandtl number, the sliced angle, the magnetic parameter, and the mixed convection parameter are analyzed and discussed. The results depicted that the uniform magnetic field produced by Lorentz force and slicing on the sphere act as determining factors for the trend of nano fluid movement and controlling the cooling rate of the sphere surface. In addition, the viscosity depends on the copper particle volume fraction.

Sign in / Sign up

Export Citation Format

Share Document