Brinkman ferroconvection

2017 ◽  
Vol 13 (3) ◽  
pp. 366-376
Author(s):  
M. Ravisha ◽  
I.S. Shivakumara ◽  
Gangadhara Reddy R.
Keyword(s):  
Porous Medium ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Shooting Method ◽  
Critical Rayleigh Number ◽  
Content Type ◽  
Vertical Heterogeneity ◽  
Ferromagnetic Convection ◽  
Realistic Boundary Conditions

Purpose The simultaneous effects of local thermal non-equilibrium (LTNE) and vertical heterogeneity in permeability on the onset of ferromagnetic convection in a Brinkman porous medium are analyzed in the presence of a uniform vertical magnetic field. The eigenvalue problem is solved numerically using shooting method for isothermal rigid-ferromagnetic boundaries for various forms of vertically stratified permeability function Γ(z). The effect of vertically stratified permeability is found to either hasten or delay the onset of ferromagnetic convection. The deviation in the critical Rayleigh number between different forms of Γ(z) is found to be not so significant with an increase in the Darcy number. It is observed that the general quadratic variation of Γ(z) has more destabilizing effect on the system when compared to the constant permeability porous medium case. Besides, the influence of LTNE and magnetic parameters on the criterion for the onset of ferromagnetic convection has been assessed in detail. The paper aims to discuss these issues. Design/methodology/approach Ferroconvection in a porous medium has been analyzed considering heterogeneity in the permeability of the porous medium. The resulting eigenvalue problem has been solved numerically using shooting method as well as Galerkin method for realistic boundary conditions. Findings The novelty of the present study lies in understanding the effect of heterogeneity in the permeability of the porous medium on control of ferroconvection in a porous medium. In analyzing the problem, realistic boundary conditions are considered and the resulting eigenvalue problem is solved numerically using shooting method as well as Galerkin method. Originality/value Control of ferroconvection in a porous medium is an important feature in heat transfer-related problems and many mechanisms are being used to understand this aspect in the literature. The novelty of the present study lies in recognizing the effect of heterogeneity in the permeability of the porous medium on control of ferroconvection. This fact has been analyzed in detail for various forms of heterogeneity functions using numerical techniques by considering realistic boundary conditions.

Cattaneo–LTNE porous ferroconvection

2019 ◽  
Vol 15 (4) ◽  
pp. 779-799 ◽  
Author(s):  
Ravisha M. ◽  
I.S. Shivakumara ◽  
Mamatha A.L.
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Free Boundaries ◽  
Content Type ◽  
Darcy Model ◽  
Different Types ◽  
Saturated Porous Layer ◽  
The Galerkin Method

Purpose The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat via a Cattaneo heat flux theory while the fluid phase to transfer heat via usual Fourier heat-transfer law. The flow in the porous medium is governed by modified Brinkman-extended Darcy model. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. The presence of Cattaneo effect introduces oscillatory convection as the preferred mode of instability contrary to the occurrence of instability via stationary convection found in its absence. Besides, oscillatory ferroconvection is perceived when the solid thermal relaxation time parameter exceeds a threshold value and increase in its value is to hasten the oscillatory onset. The effect of different boundary conditions on the instability of the system is noted to be qualitatively same. The paper aims to discuss these issues. Design/methodology/approach The investigators would follow the procedure of Straughan (2013) to obtain the expression for Rayleigh number. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The investigators have used a Galerkin method to obtain the numerical results for rigid-ferromagnetic/paramagnetic boundaries, while the instability of the system is discussed exactly for stress-free boundaries. Findings The Cattaneo–LTNE porous ferroconvection has been analyzed for different velocity and magnetic boundary conditions. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system has been highlighted. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. Originality/value The novelty of the present paper is to combine LTNE and second sound effects in solids on thermal instability of a ferrofluid-saturated porous layer by retaining the usual Fourier heat-transfer law in the ferrofluid. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system is discussed.

Effects of thermal radiation and magnetohydrodynamics on Ree-Eyring fluid flows through porous medium with slip boundary conditions

2019 ◽  
Vol 15 (2) ◽  
pp. 492-507 ◽  
Author(s):  
K. Ramesh ◽  
Sartaj Ahmad Eytoo
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Closed Form ◽  
Parallel Plates ◽  
Slip Boundary Conditions ◽  
Content Type ◽  
Closed Form Solutions ◽  
Slip Boundary

Purpose The purpose of this paper is to investigate the three fundamental flows (namely, both the plates moving in opposite directions, the lower plate is moving and other is at rest, and both the plates moving in the direction of flow) of the Ree-Eyring fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the intention of the study is to examine the effect of different physical parameters on the fluid flow. Design/methodology/approach The mathematical modeling is performed on the basis of law of conservation of mass, momentum and energy equation. The modeling of the present problem is considered in Cartesian coordinate system. The governing equations are non-dimensionalized using appropriate dimensionless quantities in all the mentioned cases. The closed-form solutions are presented for the velocity and temperature profiles. Findings The graphical results are presented for the velocity and temperature distributions with the pertinent parameters of interest. It is observed from the present results that the velocity is a decreasing function of Hartmann number. Temperature increases with the increase of Ree-Eyring fluid parameter, radiation parameter and temperature slip parameter. Originality/value First time in the literature, the authors obtained closed-form solutions for the fundamental flows of Ree-Erying fluid between infinitely parallel plates with the effects of magnetic field, porous medium, heat transfer, radiation and slip boundary conditions. Moreover, the results of this paper are new and original.

Linear and non-linear analyses of double-diffusive-Chandrasekhar convection coupled with cross-diffusion in micropolar fluid over saturated porous medium

2020 ◽  
Vol 17 (1) ◽  
pp. 211-236
Author(s):  
Maria Anncy ◽  
Thadathil Varghese Joseph ◽  
Subbarama Pranesh
Keyword(s):  
Porous Medium ◽  
Micropolar Fluid ◽  
Saturated Porous Medium ◽  
Perturbation Technique ◽  
Critical Rayleigh Number ◽  
Series Representation ◽  
Content Type ◽  
Cross Diffusion ◽  
Non Linear ◽  
Double Diffusive

PurposeThe problem aims to find the effects of coupled cross-diffusion in micropolar fluid oversaturated porous medium, subjected to Double-Diffusive Chandrasekhar convection.Design/methodology/approachNormal mode and perturbation technique have been employed to determine the critical Rayleigh number. Non-linear analysis is carried out by deriving the Lorenz equations using truncated Fourier series representation. Heat and Mass transport are quantified by Nusselt and Sherwood numbers, respectively.FindingsAnalysis related to the effects of various parameters is plotted, and the results for the same are interpreted. It is observed from the results that the Dufour parameter and Soret parameter have an opposite influence on the system of cross-diffusion.Originality/valueThe effect of the magnetic field on the onset of double-diffusive convection in a porous medium coupled with cross-diffusion in a micropolar fluid is studied for the first time.

scholarly journals Axisymmetric Natural Frequencies of Statically Loaded Annular Plates

2003 ◽  
Vol 10 (5-6) ◽  
pp. 301-312 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Waleed F. Faris ◽  
Ali H. Nayfeh
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Shooting Method ◽  
Large Deformations ◽  
Natural Frequencies ◽  
Numerical Procedure ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Plate Model ◽  
Annular Plates

We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.

scholarly journals Nonlinear eigenvalue problem in the integral transforms solution of convection-diffusion with nonlinear boundary conditions

2016 ◽  
Vol 26 (3/4) ◽  
pp. 767-789 ◽  
Author(s):  
Renato M Cotta ◽  
Carolina Palma Naveira-Cotta ◽  
Diego C. Knupp
Keyword(s):  
Boundary Condition ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Eigenvalue Problem ◽  
Nonlinear Boundary Conditions ◽  
Content Type ◽  
Convection Diffusion ◽  
Diffusion Problems

Purpose – The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis. Design/methodology/approach – The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials. Findings – An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented. Originality/value – This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.

Double rotations of cylinders on thermosolutal convection of a wavy porous medium inside a cavity mobilized by a nanofluid and impacted by a magnetic field

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Abdelraheem M. Aly ◽  
Shreen El-Sapa
Keyword(s):  
Porous Medium ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Thermosolutal Convection ◽  
Circular Cylinders ◽  
Lagrangian Description ◽  
Content Type ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics

Purpose The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method. Design/methodology/approach The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method. Findings The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity. Originality/value The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

Symmetry group and numerical study of non-Newtonian nanofluid transport in a porous medium with multiple convective boundary and nonlinear radiation

2016 ◽  
Vol 26 (5) ◽  
pp. 1526-1547 ◽  
Author(s):  
Md. Jashim Uddin ◽  
O. Anwar Bég ◽  
Izani Md. Ismail
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Conditions ◽  
Power Law ◽  
Manufacturing Systems ◽  
Free Stream ◽  
Nonlinear Ordinary Differential Equations ◽  
Governing Equations ◽  
Convective Boundary ◽  
Content Type

Purpose – The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical plate in a saturated porous medium taking into account thermal and mass convective boundary conditions numerically. Design/methodology/approach – The governing equations are reduced to a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The transformed equations are then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method with Maple 17 and Adomian decomposition method (ADM) in Mathematica. Findings – The transformed equations are controlled by the parameter: power-law exponent, n; temperature ratio, Tr; Rosseland radiation-conduction, R; conduction-convection, Nc; and diffusion-convection, Nd. Temperature and nanoparticle concentration is enhanced with convection-diffusion parameter as are temperatures. Velocities are depressed with greater power-law rheological index whereas temperatures are elevated. Increasing thermal radiation flux accelerate the flow but to strongly heat the boundary layer. Very good correlation of the Maple solutions with previous stationary free stream and ADM solutions for a moving free stream, are obtained. Practical implications – The study is relevant to high temperature nano-polymer manufacturing systems. Originality/value – Lie symmetry group is used for the first time to transform the governing equations into a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The study is relevant to high temperature nano-polymer manufacturing systems.

scholarly journals Rayleigh-Bénard Convection for Nanofluids for More Realistic Boundary Conditions (Rigid-Free and Rigid-Rigid) Using Darcy Model

2019 ◽  
Vol 4 (1) ◽  
pp. 139-156 ◽  
Author(s):  
Jyoti Ahuja ◽  
Urvashi Gupta
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
Galerkin Approximation ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Realistic Boundary Conditions

In this article, Rayleigh-Bénard convection for nanofluids for more realistic boundary conditions (rigid-free and rigid-rigid) under the influence of the magnetic field is investigated. Presence of nanoparticles in base fluid has introduced one additional conservation equation of nanoparticles that incorporates the effect of thermophoretic forces and Brownian motion and the inclusion of magnetic field has introduced Lorentz’s force term in the momentum equation along with Maxwell’s equations. The solution of the Eigen value problem is found in terms of Rayleigh number by implementing the technique of normal modes and weighted residual Galerkin approximation. It is found that the stationary as well as oscillatory motions come into existence and heat transfer takes place through oscillatory motions. The critical Rayleigh number for alumina water nanofluid has an appreciable increase in its value with the rise in Chandrasekhar number and it increases moderately as we move from rigid-free to both rigid boundaries. The effect of different nanofluid parameters on the onset of thermal convection for two types of boundaries is investigated.

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