Stability Analysis of a Supercritical Fluid in a Porous Medium Heated from Below

2016 ◽  
Author(s):  
Leonardo Santos de Brito Alves ◽  
Leandro Santos de Barros ◽  
Heitor Herculano de Barros
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Supercritical Fluid

Duality and stability of MHD Darcy–Forchheimer porous medium flow of rotating nanofluid on a linear shrinking/stretching sheet: Buongiorno model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jawad Raza ◽  
Sumera Dero ◽  
Liaquat Ali Lund ◽  
Zurni Omar
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Shrinking Sheet ◽  
Dual Nature ◽  
Content Type ◽  
Great Achievement ◽  
Medium Flow ◽  
Buongiorno Model ◽  
Porous Medium Flow

Purpose The purpose of study is to examine the dual nature of the branches for the problem of Darcy–Forchheimer porous medium flow of rotating nanofluid on a linearly stretching/shrinking surface under the field of magnetic influence. The dual nature of the branches confronts the uniqueness and existence theorem, moreover, mathematically it is a great achievement. For engineering purposes, this study applied a linear stability test on the multiple branches to determine which solution is physically reliable (stable). Design/methodology/approach Nanofluid model has been developed with the help of Buongiorno model. The partial differential equations in space coordinates for the law of conservation of mass, momentum and energy have been transformed into ordinary differential equations by introducing the similarity variables. Two numerical techniques, namely, the shooting method in Maple software and the three-stage Lobatto IIIA method in Matlab software, have been used to find multiple branches and to accomplish stability analysis, respectively. Findings The parametric investigation has been executed to find the multiple branches and explore the effects on skin friction, Sherwood number, Nusselt number, concentration and temperature profiles. The findings exhibited the presence of dual branches only in the case of a shrinking sheet. Originality/value The originality of work is a determination of multiple branches and the performance of the stability analysis of the branches. It has also been confirmed that such a study has not yet been considered in the previous literature.

Darcy-Forchheimer porous medium effect on rotating hybrid nanofluid on a linear shrinking/stretching sheet

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Differential Equations ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Medium Effect ◽  
Hybrid Nanofluid ◽  
Three Dimensional Flow ◽  
Content Type ◽  
Dimensional Flow

Purpose The purpose of this study is to find the multiple branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid perfusing a porous medium over the stretching/shrinking surface. The extended model of Darcy due to Forchheimer and Brinkman has been considered to make the hybrid nanofluid model over the pores by considering the porosity and permeability effects. Design/methodology/approach The Tiwari and Das model with the thermophysical properties of spherical particles for efficient dynamic viscosity of the nanoparticle is used. The linear similarity transformations are applied to convert the partial differential equations into ordinary differential equations (ODEs). The system of governing ODEs is solved by using the three-stage Lobatto IIIa scheme in MATLAB for evolving parameters. Findings The system of governing ODEs produces dual branches. A unique stable branch is identified with help of stability analysis. The reduced heat transfer rate has been shown to increase with the reduced ϕ2 in both branches. Further, results revealed that the presence of multiple branches depends on the ranges of porosity, suction and stretching/shrinking parameters for the particular value of the rotating parameter. Originality/value Dual branches of the three-dimensional flow of Cu-Al2 O3/water rotating hybrid nanofluid have been found. Therefore, stability analysis of the branches is also conducted to know which branch is appropriate for the practical applications. To the best of the authors’ knowledge, this research is novel and there is no previously published work relevant to the present study.

Free convection of a hybrid nanofluid past a vertical plate embedded in a porous medium with anisotropic permeability

2019 ◽  
Vol 30 (8) ◽  
pp. 4083-4101 ◽  
Author(s):  
Aneela Bibi ◽  
Hang Xu ◽  
Qiang Sun ◽  
Ioan Pop ◽  
Qingkai Zhao
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Stability Analysis ◽  
Flat Surface ◽  
Saturated Porous Medium ◽  
Heat Energy ◽  
Hybrid Nanofluid ◽  
Anisotropic Permeability ◽  
Content Type ◽  
Hybrid Nanofluids

Purpose This study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended. Design/methodology/approach The generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0. Findings Results show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy. Originality/value Free convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.

scholarly journals Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

2016 ◽  
Vol 21 (4) ◽  
pp. 785-803 ◽  
Author(s):  
B.S. Bhadauria ◽  
M.K. Singh ◽  
A. Singh ◽  
B.K. Singh ◽  
P. Kiran
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Power Series Expansion ◽  
Gravity Modulation ◽  
Internal Heating ◽  
Onset Of Convection ◽  
Fluid Saturated Porous Medium

Abstract In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Onset of convection in a layered porous medium heated from below

1980 ◽  
Vol 96 (2) ◽  
pp. 375-393 ◽  
Author(s):  
R. Mckibbin ◽  
M. J. O'Sullivan
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Homogeneous System ◽  
Onset Of Convection

The formalism required to determine the criterion for the onset of convection in a multi-layered porous medium heated from below is developed using a straightforward linear stability analysis. Detailed results for two- and three-layer configurations are presented. These results show that large permeability differences between the layers are required to force the system into an onset mode different from a homogeneous system.

Sign in / Sign up

Export Citation Format

Share Document