scholarly journals Hydromagnetic Stability of Metallic Nanofluids (Cu-Water and Ag-Water) Using Darcy-Brinkman Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. Ahuja ◽  
U. Gupta ◽  
R. K. Wanchoo
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Darcy Number ◽  
Analytical Investigation ◽  
Brinkman Model ◽  
Free Boundaries ◽  
Weighted Residuals ◽  
Flow Through ◽  
The Stability ◽  
Chandrasekhar Number

Thermal convection of a nanofluid layer in the presence of imposed vertical magnetic field saturated by a porous medium is investigated for both-free, rigid-free, and both-rigid boundaries using Darcy-Brinkman model. The effects of Brownian motion and thermophoretic forces due to the presence of nanoparticles and Lorentz’s force term due to the presence of magnetic field have been considered in the momentum equations along with Maxwell’s equations. Keeping in mind applications of flow through porous medium in geophysics, especially in the study of Earth’s core, and the presence of nanoparticles therein, the hydromagnetic stability of a nanofluid layer in porous medium is considered in the present formulation. An analytical investigation is made by applying normal mode technique and Galerkin type weighted residuals method and the stability of Cu-water and Ag-water nanofluids is compared. Mode of heat transfer is through stationary convection without the occurrence of oscillatory motions. Stability of the system gets improved appreciably by raising the Chandrasekhar number as well as Darcy number whereas increase in porosity hastens the onset of instability. Further, stability of the system gets enhanced as we proceed from both-free boundaries to rigid-free and to both-rigid boundaries.

scholarly journals Chemical Entropy Generation and MHD Effects on the Unsteady Heat and Fluid Flow through a Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal M. Abdel-Rahman Rashed
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Fluid Flow ◽  
Entropy Generation ◽  
Lewis Number ◽  
Heat Transfer Fluid ◽  
Governing Equations ◽  
Flow Through ◽  
Heat And Fluid Flow ◽  
Chemical Reaction Parameter

Chemical entropy generation and magnetohydrodynamic effects on the unsteady heat and fluid flow through a porous medium have been numerically investigated. The entropy generation due to the use of a magnetic field and porous medium effects on heat transfer, fluid friction, and mass transfer have been analyzed numerically. Using a similarity transformation, the governing equations of continuity, momentum, and energy and concentration equations, of nonlinear system, were reduced to a set of ordinary differential equations and solved numerically. The effects of unsteadiness parameter, magnetic field parameter, porosity parameter, heat generation/absorption parameter, Lewis number, chemical reaction parameter, and Brinkman number parameter on the velocity, the temperature, the concentration, and the entropy generation rates profiles were investigated and the results were presented graphically.

Analytical Solution of Forced Convection in a Duct of Rectangular Cross Section Saturated by a Porous Medium

2005 ◽  
Vol 128 (6) ◽  
pp. 596-600 ◽  
Author(s):  
Kamel Hooman ◽  
Ali A. Merrikh
Keyword(s):  
Porous Medium ◽  
Forced Convection ◽  
Cross Section ◽  
Viscosity Ratio ◽  
Rectangular Cross Section ◽  
Darcy Number ◽  
Uniform Heat Flux ◽  
Brinkman Model ◽  
Type Solution ◽  
Series Type

A theoretical analysis is presented to investigate thermally and hydrodynamically fully developed forced convection in a duct of rectangular cross section filled with a hyper-porous medium. The Darcy-Brinkman model was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e., the H boundary condition in the terminology of Kays and Crawford (1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, NY), is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Stability of Hydromagnetic Thermoconvective Flow Through Porous Medium

1973 ◽  
Vol 40 (4) ◽  
pp. 879-884 ◽  
Author(s):  
Prabhamani R. Patil ◽  
N. Rudraiah
Keyword(s):  
Porous Medium ◽  
Viscous Fluid ◽  
Normal Mode ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Thermal Convection ◽  
Stability Region ◽  
Flow Through ◽  
The Stability ◽  
Mode Technique

The stability of the onset of thermal convection of a conducting viscous fluid in a porous medium has been investigated using the linear (normal mode technique) and the non-linear (energy) stability theories. Both the theories show that the stability region is increased to the maximum extent when the usual viscous dissipation is also present in addition to the dissipation due to Darcy’s resistance and Joule heating.

A nonlinear stability analysis in a double-diffusive magnetized ferrofluid with magnetic-field-dependent viscosity saturating a porous medium

2009 ◽  
Vol 87 (6) ◽  
pp. 659-673 ◽  
Author(s):  
Sunil ◽  
Amit Mahajan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nonlinear Stability ◽  
Stability Result ◽  
Darcy Number ◽  
Linear Instability ◽  
Nonlinear Stability Analysis ◽  
Field Dependent ◽  
Magnetized Ferrofluid ◽  
Mfd Viscosity

A rigorous nonlinear stability result is derived by introducing a suitable generalized energy functional for a magnetized ferrofluid layer heated and soluted from below with magnetic-field-dependent (MFD) viscosity saturating a porous medium, in the stress-free boundary case. The mathematical emphasis is on how to control the nonlinear terms caused by the magnetic-body and inertia forces. For ferrofluids, we find that there is possibility of existence of subcritical instabilities, however, it is noted that, in case of a non-ferrofluid, the global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of the magnetic parameter, M3; solute gradient, Sf; Darcy number, Da; and MFD viscosity parameter, δ; on the subcritical instability region has also been analyzed.

scholarly journals A revised model of "Steady laminar natural convection of nanofluid under the impact of magnetic field on 2-D cavity with radiation" [AIP advances 9, 065008 (2019); https://doi.org/10.1063/1.5109192]

2020 ◽  
Vol 24 (1 Part A) ◽  
pp. 421-425
Author(s):  
Hossam Nabwey
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Natural Convection ◽  
Darcy Number ◽  
Porous Media Flow ◽  
Governing Equations ◽  
Laminar Natural Convection ◽  
The Impact ◽  
Published Paper ◽  
Steady Laminar

This discussion exhibits the major scientific errors on the recent published paper, entitled "Steady Laminar Natural Convection of Nanofluid Under the Impact of Magnetic Field on 2-D Cavity with Radiation" and their corrections indifferently. In Saleem et al. [1], the authors stated in both of abstract and problem assumptions that the non-Darcy model is used for the porous medium, while the porous terms are incompatible with this assumption. In addition, the authors used a non-inclined geometry in their investigation, but the governing equations are conflicting with this hypothesis. Further, the used range of the Darcy number is between 10?2-102 and this range is very large and did not represent the porous media flow. All of these observations make the mathematical formulations and the obtained results of Saleem et al. [1] are wrong. In the following sections, these scientific errors and their corrections will be presented minutely.

scholarly journals The convective instability of a Maxwell–Cattaneo fluid in the presence of a vertical magnetic field

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200494
Author(s):  
I. A. Eltayeb ◽  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Prandtl Number ◽  
Critical Rayleigh Number ◽  
Free Boundaries ◽  
Governing Equations ◽  
Horizontal Scale ◽  
Temperature Relation ◽  
Magnetic Prandtl Number ◽  
Zero Values ◽  
Chandrasekhar Number

We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell–Cattaneo (MC) heat flux–temperature relation. We extend the work of Bissell ( Proc. R. Soc. A 472, 20160649 (doi:10.1098/rspa.2016.0649)) to non-zero values of the magnetic Prandtl number p m . With non-zero p m , the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number Q confirms that the MC effect becomes important when C Q 1/2 is O (1), where C is the MC number. In this regime, we derive a scaled system that is independent of Q . When CQ 1/2 is large, the results are consistent with those derived from the governing equations in the limit of Prandtl number p  → ∞ with p m finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large p m regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For Q  ≫ 1 and small values of p , we show that the critical Rayleigh number is non-monotonic in p provided that C  > 1/6. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading-order results.

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