scholarly journals Marangoni convection in layers of water-based nanofluids under the effect of rotation

2021 ◽  
Vol 19 (1) ◽  
pp. 1029-1046
Author(s):  
Abeer H. Bakhsh ◽  
Abdullah A. Abdullah
Keyword(s):  
Marangoni Convection ◽  
Volume Fraction ◽  
Steady State Solution ◽  
Horizontal Layer ◽  
Brownian Diffusion ◽  
Nanoparticle Volume Fraction ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Modified Model ◽  
Conservation Condition

Abstract A linear stability analysis is performed for the onset of Marangoni convection in a horizontal layer of a nanofluid heated from below and affected by rotation. The top boundary of the layer is assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition while the bottom boundary is assumed to be a rigid surface with fixed temperature. The motion of the nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. A modification model is used in which the effects of Brownian diffusion and thermophoresis are taken into consideration by new expressions in the nanoparticle mass flux. Also, material properties of the nanofluid are modelled by non-constant constitutive expressions depending on nanoparticle volume fraction. The steady-state solution is shown to be well approximated by an exponential distribution of the nanoparticle volume fraction. The Chebyshev-Tau method is used to obtain the critical thermal and nanoparticle Marangoni numbers. Different stability boundaries are obtained using the modified model and the rotation.

A revised model for the effect of nanoparticle mass flux on the thermal instability of a nanofluid layer

2021 ◽  
Vol 54 (1) ◽  
pp. 488-499
Author(s):  
Ozwah S. Alharbi ◽  
Abdullah A. Abdullah
Keyword(s):  
Mass Flux ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Steady State Solution ◽  
Horizontal Layer ◽  
Brownian Diffusion ◽  
Stationary Mode ◽  
Nanoparticle Volume Fraction ◽  
Conservation Condition ◽  
Rayleigh Benard

Abstract A revised model of the nanoparticle mass flux is introduced and used to study the thermal instability of the Rayleigh-Benard problem for a horizontal layer of nanofluid heated from below. The motion of nanoparticles is characterized by the effects of thermophoresis and Brownian diffusion. The nanofluid layer is confined between two rigid boundaries. Both boundaries are assumed to be impenetrable to nanoparticles with their distribution being determined from a conservation condition. The material properties of the nanofluid are allowed to depend on the local volume fraction of nanoparticles and are modelled by non-constant constitutive expressions developed by Kanafer and Vafai based on experimental data. The results show that the profile of the nanoparticle volume fraction is of exponential type in the steady-state solution. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau method. The critical values of the thermal Rayleigh number are calculated for several values of the parameters of the problem. Moreover, the critical eigenvalues obtained were real-valued, which indicates that the mode of instability is via a stationary mode.

scholarly journals Modified Model for Binary Nanofluid Convection with Initial Constant Nanoparticle Volume Fraction

2017 ◽  
Vol 10 (5) ◽  
pp. 1387-1395 ◽  
Author(s):  
J. Sharma ◽  
U. Gupta ◽  
V. Sharma ◽  
◽  
◽  
...  
Keyword(s):  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Modified Model

Examination of carbon-water nanofluid flow with thermal radiation under the effect of Marangoni convection

2017 ◽  
Vol 34 (7) ◽  
pp. 2330-2343 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Muhammad Usman ◽  
Kamran Afaq ◽  
Muhammad Hamid ◽  
Wei Wang
Keyword(s):  
Boundary Layer ◽  
Thermal Radiation ◽  
Least Squares ◽  
Marangoni Convection ◽  
Volume Fraction ◽  
Least Squares Method ◽  
Detailed Comparison ◽  
Convection Boundary Layer ◽  
Nanoparticle Volume Fraction ◽  
Content Type

Purpose The purpose of this study is to analyze the effects of carbon nanotubes (CNTs) in the Marangoni convection boundary layer viscous fluid flow. The analysis and formulation for both types of CNTs, namely, single-walled (SWCNTs) and multi-walled (MWCNTs), are described. The influence of thermal radiation effect assumed in the form of energy expression. Design/methodology/approach Appropriate transformations reduced the partial differential systems to a set of nonlinear ordinary differential equations (ODEs). The obtained nonlinear ODE set is solved via the least squares method. A detailed comparison between outcomes obtained by the least squares method, RK-4 and already published work is available. Findings Nusselt number was analyzed and found to be more effective for nanoparticle volume fraction and larger radiation parameters. Additionally, the error and convergence analysis for the least squares method was presented to show the efficiency of the said algorithm. Originality/value The results reveal that velocity is a decreasing function of suction for both CNTs. While enhancing the nanoparticle volume fraction, an increase for both thermal boundary layer thickness and temperature was attained. The radiation parameter has an increasing function as temperature. Velocity behavior is the same for nanoparticle volume fraction and suction. It was observed that velocity is less in SWCNTs as compared to MWCNTs.

Unsteady Mixed Bioconvection Flow of a Nanofluid Between Two Contracting or Expanding Rotating Discs

2016 ◽  
Vol 71 (3) ◽  
pp. 261-272 ◽  
Author(s):  
Jiao Jiao Li ◽  
Hang Xu ◽  
Ammarah Raees ◽  
Qing Kai Zhao
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Brownian Diffusion ◽  
Physical Parameters ◽  
Nanoparticle Volume Fraction ◽  
Transport Mechanisms ◽  
Rotating Discs ◽  
Complex Nonlinear System ◽  
Passively Controlled Nanofluid Model ◽  
Fully Coupled

AbstractAn investigation is made for a three-dimensional unsteady mixed nano-bioconvection flow between two contracting or expanding rotating discs. The passively controlled nanofluid model in which Brownian diffusion and thermophoresis are considered as the two dominant factors for nanoparticle/base-fluid slip mechanisms is introduced for description of this flow problem. A novel similarity transformation is introduced so that the governing equations embodying the conservation of total mass, momentum, thermal energy, nanoparticle volume fraction, and microorganisms are reduced to a set of five fully coupled ordinary differential equations. Exact solutions are then obtained analytically for this complex nonlinear system. Besides, the influences of various physical parameters on distributions of velocity, temperature, nanoparticle volume fraction, and the density of motile microorganisms, along with the local Nusselt number and the local wall motile microorganisms flux, are presented and discussed. It is expected that this study can provide a theoretical base for understanding the transport mechanisms of unsteady bioconvection in nanofluids.

scholarly journals The onset of Marangoni bio-thermal convection in a layer of fluid containing gyrotactic microorganisms

2021 ◽  
Vol 6 (12) ◽  
pp. 13552-13565
Author(s):  
Latifa I. Khayyat ◽  
◽  
Abdullah A. Abdullah ◽  
Keyword(s):  
Thermal Convection ◽  
Marangoni Number ◽  
Fluid Layer ◽  
Lewis Number ◽  
Horizontal Layer ◽  
Stationary Mode ◽  
Rigid Surface ◽  
Fixed Temperature ◽  
Gyrotactic Microorganisms ◽  
Motile Gyrotactic Microorganisms

<abstract><p>The problem of the onset of Marangoni bio-thermal convection is investigated for a horizontal layer of fluid containing motile gyrotactic microorganisms. The fluid layer is assumed to rest on a rigid surface with fixed temperature and the top boundary of the layer is assumed to be a free non deformable surface. The resulting equations of the problem constitute an eigenvalue problem which is solved using the Chebyshev tau numerical method. The critical values of the thermal Marangoni number are calculated for several values of the bioconvection Péclet number, bioconvection Marangoni number, bioconvection Lewis number and gyrotaxis number. The results of this study showed that the existence of gyrotactic microorganisms increases the critical thermal Marangoni numbers. Moreover, the critical eigenvalues obtained were real-valued indicating that the mode of instability is via a stationary mode, however oscillatory mode is possible for some ranges of the parameters values.</p></abstract>

scholarly journals Thermophoresis and suction/injection roles on free convective MHD flow of Ag–kerosene oil nanofluid

2020 ◽  
Vol 7 (3) ◽  
pp. 386-396
Author(s):  
Himanshu Upreti ◽  
Alok Kumar Pandey ◽  
Manoj Kumar
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Mass Transfer Rate ◽  
Brownian Diffusion ◽  
Particle Volume ◽  
Ohmic Dissipation ◽  
Surface Mass

Abstract In this article, the mass and heat transfer flow of Ag–kerosene oil nanofluid over a cone under the effects of suction/injection, magnetic field, thermophoresis, Brownian diffusion, and Ohmic-viscous dissipation was examined. On applying the suitable transformation, PDEs directing the flow of nanofluid were molded to dimensionless ODEs. The solution of the reduced boundary value problem was accomplished by applying Runge–Kutta–Fehlberg method via shooting scheme and the upshots were sketched and interpreted. The values of shear stress and coefficients of heat and mass transfer were attained for some selected values of governing factors. The obtained results showed that when the amount of surface mass flux shifts from injection to the suction domain, the heat and mass transfer rate grew uniformly. However, they have regularly condensed with the rise in the magnitude of the magnetic field and particle volume fraction. Several researches have been done using cone-shaped geometry under the influence of various factors affecting the fluid flow, yet, there exists no such investigation that incorporated the response of viscous-Ohmic dissipation, heat absorption/generation, suction/blowing, Brownian diffusion, and thermophoresis on the hydro-magnetic flow of silver-kerosene oil nanofluid over a cone.

scholarly journals Molecular-Theory of High Frequency Dielectric Susceptibility of Nematic Nanocomposites

Crystals ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 970
Author(s):  
Mikhail A. Osipov ◽  
Alexey S. Merekalov ◽  
Alexander A. Ezhov
Keyword(s):  
Plasmon Resonance ◽  
High Frequency ◽  
Volume Fraction ◽  
Simple Expression ◽  
Dielectric Anisotropy ◽  
Dielectric Susceptibility ◽  
Nanoparticle Volume Fraction ◽  
Effective Polarizability ◽  
Dielectric And Optical Properties ◽  
Analytical Expressions

A molecular-statistical theory of the high frequency dielectric susceptibility of the nematic nanocomposites has been developed and approximate analytical expressions for the susceptibility have been obtained in terms of the effective polarizability of a nanoparticle in the nematic host, volume fraction of the nanoparticles and the susceptibility of the pure nematic phase. A simple expression for the split of the plasmon resonance of the nanoparticles in the nematic host has been obtained and it has been shown that in the resonance frequency range the high frequency dielectric anisotropy of the nanocomposite may be significantly larger than that of the pure nematic host. As a result, all dielectric and optical properties of the nanocomposite related to the anisotropy are significantly enhanced which may be important for emerging applications. The components of the dielectric susceptibility have been calculated numerically for particular nematic nanocomposites with gold and silver nanoparicles as functions of the nanoparticle volume fraction and frequency. The splitting of the plasmon resonance has been observed together with the significant dependence on the nanoparticle volume fraction and the parameters of the nematic host phase.

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