Onset of Convection in a Porous Medium Layer Saturated With an Oldroyd-B Nanofluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
J. C. Umavathi ◽  
J. Prathap Kumar
Keyword(s):  
Porous Medium ◽  
Volume Fraction ◽  
Momentum Equation ◽  
Nanoparticle Volume Fraction ◽  
Oscillatory Convection ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Fourier Series Method ◽  
Medium Layer ◽  
Linear And Nonlinear

A linear and nonlinear stability analysis of a viscoelastic fluid in a porous medium layer saturated by a nanofluid with thermal conductivity and viscosity dependent on the nanoparticle volume fraction is studied. To simulate the momentum equation in porous media, a modified Darcy model has been used. To describe the rheological behavior of viscoelastic nanofluids, an Oldroyd-B type constitutive equation has been used. The onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the truncated representation of Fourier series method is used to find the transient heat and mass transfer.

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.

scholarly journals Effect of anisotropy on the onset of convection in rotating bi-disperse Brinkman porous media

2021 ◽  
Author(s):  
Florinda Capone ◽  
Roberta De Luca ◽  
Giuliana Massa
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Nonlinear Stability ◽  
Linear Instability ◽  
Combined Effects ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Linear And Nonlinear ◽  
The Stability

AbstractThermal convection in a horizontally isotropic bi-disperse porous medium (BDPM) uniformly heated from below is analysed. The combined effects of uniform vertical rotation and Brinkman law on the stability of the steady state of the momentum equations in a BDPM are investigated. Linear and nonlinear stability analysis of the conduction solution is performed, and the coincidence between linear instability and nonlinear stability thresholds in the $$L^2$$ L 2 -norm is obtained.

scholarly journals Mixed convection over a horizontal circular cylinder embedded in porous medium immersed in a nanofluid with convective boundary conditions at lower stagnation point: A numerical solution

2018 ◽  
Vol 189 ◽  
pp. 02004
Author(s):  
Sarif Norhafizah Md ◽  
Sallhe Mohd Zuki ◽  
Roslinda Nazar
Keyword(s):  
Porous Medium ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Bottom Surface ◽  
Nanoparticle Volume Fraction ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Convective Parameter

This study aims to examine the effect of governing parameters on the flow and heat transfer of the steady mixed convection flow embedded in porous medium with convective boundary conditions. The resulting system of nonlinear partial differential equations is solved numerically. The special case at the lower stagnation point of the cylinder is observed and the case where bottom surface of the cylinder is heated by convection from hot fluids is considered. Numerical solutions are obtained for the velocity, temperature and nanoparticle volume fraction profiles for two values of governing parameters namely convective parameter γ and Lewis number Le. It is found that as the convective parameter γ increases, velocity profile, temperature and nanoparticle volume fraction profile also increases.

scholarly journals Study of heat and mass transfer control inside channel partially filled with a porous medium using nanofluids

2019 ◽  
pp. 460-460 ◽  
Author(s):  
Hamida Ben ◽  
Mohamed Massoudi ◽  
Riadh Marzouki ◽  
Lioua Kolsi ◽  
Mohammed Almeshaal ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Solid Phase ◽  
Pure Water ◽  
Vertical Wall ◽  
Vertical Channel ◽  
Porous Wall ◽  
Nanoparticle Volume Fraction

The steady mixed convection of heat and mass transfer inside and outside a porous vertical wall is numerically studied. The porous wall, placed in a vertical channel, contains a solid phase, a nanofluid phase (Water-Al2O3 or Water-Cu) and gas phase. The effect of several physical quantities such as nanoparticle volume fraction, ambient temperature and initial nanofluid saturation on heat and mass transfer were investigated. Results reveal that the temperature of porous medium is decreased considerably with nanoparticle volume fraction. It has been also found that the heat and mass transfer are dramatically reduced using Water-Alumina nanofluid when compared with pure water.

A nonlinear-stability analysis of second-order fluid in porous medium in presence of magnetic field

Analysis ◽  
2005 ◽  
Vol 25 (2) ◽  
Author(s):  
Lanxi Xu
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Boundary ◽  
Second Order ◽  
Nonlinear Stability Analysis ◽  
Onset Of Convection ◽  
Medium Permeability ◽  
Lyapunov’S Second Method ◽  
Chandrasekhar Number

AbstractNonlinear stability of the motionless state of the second-order fluid in porous medium in presence of magnetic field is studied by the Lyapunov’s second method. Through defining a Lyapunov function we will prove the inhibiting effect of the magnetic field on the onset of convection. If the Chandrasekhar number is below a computable constant depending on system parameters, we even prove the coincidence of linear and nonlinear stability boundary. Moreover, the medium permeability has a destabilizing effect.

Horton-Rogers-Lapwood Convection in a Binary Nanofluid Saturated Rotating Porous Layer

2014 ◽  
Author(s):  
Shilpi Agarwal ◽  
Puneet Rana
Keyword(s):  
Porous Medium ◽  
Base Fluid ◽  
Oscillatory Convection ◽  
Binary Fluid ◽  
Salty Water ◽  
Diffusive Convection ◽  
Medium Layer ◽  
Dimensional Parameters ◽  
Rayleigh Numbers ◽  
Double Diffusive

Double-diffusive convection in a horizontal rotating porous medium layer saturated by a nanofluid, for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water, is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Brinkman model is used for the porous medium. The Rayleigh numbers’ for stationary and oscillatory convection have been obtained in terms of various non-dimensional parameters. Several results are obtained as limiting cases of the present study.

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