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 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.

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
D. A. Nield ◽  
A. V. Kuznetsov
Keyword(s):  
Boundary Condition ◽  
Porous Medium ◽  
Porous Media ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Critical Rayleigh Number ◽  
Nanoparticle Volume Fraction ◽  
Governing Equations ◽  
Medium Layer ◽  
Vertical Throughflow

The model developed in our previous paper (Nield and Kuznetsov, 2011, “The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid,” Transp. Porous Media, 87(3), pp. 765–775) is now revised to accommodate a more realistic boundary condition on the nanoparticle volume fraction. The new boundary condition postulates zero nanoparticle flux through the boundaries. We established that in the new model, oscillatory instability is impossible. We also established that the critical Rayleigh number depends on three dimensionless parameters, and we derived these three parameters from the governing equations. We also briefly investigated the major trends.

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 Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

2017 ◽  
Vol 47 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana ◽  
Dhananjay Yadav
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Mode Analysis ◽  
Brownian Diffusion

Abstract Thermal instability in a horizontal layer of Couple-stress nanofluid in a porous medium is investigated. Darcy model is used for porous medium. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticle is taken to be zero on the isothermal boundaries. Normal mode analysis and perturbation method is employed to solve the eigenvalue problem with the Rayleigh number as eigenvalue. Oscillatory convection cannot occur for the problem. The effects of Couple-stress parameter, Lewis number, modified diffusivity ratio, concentration Rayleigh number and porosity on stationary convection are shown both analytically and graphically.

The stability of viscous flow between rotating cylinders in the presence of a magnetic field

1953 ◽  
Vol 216 (1126) ◽  
pp. 293-309 ◽  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Viscous Flow ◽  
Thermal Instability ◽  
Horizontal Layer ◽  
Rotational Stability ◽  
Marginal Stability ◽  
Inhibiting Effect ◽  
The Stability ◽  
The Magnetic Field

In this paper the theory of the stability of viscous flow between two rotating coaxial cylinders which has been developed by Taylor, Jeffreys and Meksyn is extended to the case when the fluid considered is an electrical conductor and a magnetic field along the axis of the cylinders is present. A differential equation of order eight is derived which governs the situation in marginal stability; and a significant set of boundary conditions for the problem is formulated. The case when the two cylinders are rotating in the same direction and the difference ( d ) in their radii is small compared to their mean (R 0 ) is investigated in detail. A variational procedure for solving the underlying characteristic value problem and determining the critical Taylor numbers for the onset of instability is described. As in the case of thermal instability of a horizontal layer of fluid heated below, the effect of the magnetic field is to inhibit the onset of instability, the inhibiting effect being the greater, the greater the strength of the field and the value of the electrical conductivity. In both cases, the inhibiting effect of the magnetic field depends on the strength of the field ( H ), the density ( ρ ) and the coefficients of electrical conductivity ( σ ), kinematic viscosity ( v ) and magnetic permeability ( μ ) through the same non-dimensional combination Q =μ 2 H 2 d 2 σ/ pv ; however, the effect on rotational stability is more pronounced than on thermal instability. A table of the critical Taylor numbers for various values of Q is provided.

Influences of Zero Mass Flux and Active Conditions on the Predictions of Double Dispersion and Double Diffusive Boundary Layer in Darcy/Non Darcy Nanofluid Flow

2021 ◽  
Vol 57 ◽  
pp. 49-65
Author(s):  
Amina Manel Bouaziz ◽  
M.N. Bouaziz ◽  
A. Aziz
Keyword(s):  
Porous Medium ◽  
Mass Flux ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Mass Transfer Rate ◽  
Flow In Porous Media ◽  
Nanofluid Flow ◽  
Realistic Condition ◽  
Zero Mass ◽  
Flux Condition

Free convective of nanofluid inside dispersive porous medium adjacent to a vertical plate under the effects of the zero mass nanoparticles flux condition and the thermal and solutal dispersions is studied. Buongiorno's model revised is used considering Darcy and non Darcy laminar flows, and isothermal or convective flux outer the wall. Dimensionless governing equations formulated using velocity, temperature, concentration and nanoparticle volume fraction have been solved by finite difference method that implements the 3-stage Lobatto collocation formula. The numerical data obtained with semi or full dispersions cases are compared to predictions made using the non dispersive porous medium. Taking into account the dispersions, the influence of the zero mass nanoparticles flux condition is examined to test the validity of the control active nanoparticle assumption. It is found mainly that the thermal transfers can reach more than 100% in connection with the case where of a semi-dispersion of the porous medium is applied. Realistic condition, i.e. zero mass flux should be addressed for the heat transfer rate rather than the mass transfer rate, discovered markedly different to the active condition. This signifies the importance of considering the zero nanoparticles mass flux and dispersions in the performance characterization of nanofluid flow in porous media.

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.

Sign in / Sign up

Export Citation Format

Share Document