scholarly journals Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 450
Author(s):  
Pedro Vayssière Brandão ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
Shear Thinning ◽  
Porous Channel ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Transverse Modes ◽  
Ellis Model

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

scholarly journals Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

2021 ◽  
Author(s):  
Pedro Vayssière Brandão ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
Shear Thinning ◽  
Porous Channel ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Transverse Modes ◽  
Ellis Model

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non-Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

scholarly journals Convective to Absolute Instability Transition in a Horizontal Porous Channel with Open Upper Boundary

2017 ◽  
Author(s):  
Antonio Barletta ◽  
Michele Celli
Keyword(s):  
Convective Instability ◽  
Three Dimensional ◽  
Lower Boundary ◽  
Uniform Heat Flux ◽  
Absolute Instability ◽  
Fluid Stream ◽  
Transverse Modes ◽  
Isothermal Wall ◽  
Upper Boundary

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse modes of perturbation. The study of the analytical dispersion relation leads to the conditions for the onset of convective instability as well as to the determination of the parametric threshold for the transition to absolute instability. The results are generalised to the case of three-dimensional perturbations.

Three-Dimensional Natural Convection From Vertical Heated Plates With Adjoining Cool Surfaces

1992 ◽  
Vol 114 (1) ◽  
pp. 115-120 ◽  
Author(s):  
B. W. Webb ◽  
T. L. Bergman
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Control Volume ◽  
Three Dimensional ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Uniform Heat Flux ◽  
Infrared Thermal Imaging ◽  
Transfer Rates ◽  
Thermal Boundary Conditions

Natural convection in an enclosure with a uniform heat flux on two vertical surfaces and constant temperature at the adjoining walls has been investigated both experimentally and theoretically. The thermal boundary conditions and enclosure geometry render the buoyancy-induced flow and heat transfer inherently three dimensional. The experimental measurements include temperature distributions of the isoflux walls obtained using an infrared thermal imaging technique, while the three-dimensional equations governing conservation of mass, momentum, and energy were solved using a control volume-based finite difference scheme. Measurements and predictions are in good agreement and the model predictions reveal strongly three-dimensional flow in the enclosure, as well as high local heat transfer rates at the edges of the isoflux wall. Predicted average heat transfer rates were correlated over a range of the relevant dimensionless parameters.

Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

1996 ◽  
Vol 326 ◽  
pp. 399-415 ◽  
Author(s):  
M. Wanschura ◽  
H. C. Kuhlmann ◽  
H. J. Rath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Onset Of Convection ◽  
Buoyant Convection ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

Baroclinic instability in a reduced gravity, three-dimensional, quasi-geostrophic model

2000 ◽  
Vol 403 ◽  
pp. 1-22 ◽  
Author(s):  
P. RIPA
Keyword(s):  
Kinetic Energy ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
External Potential ◽  
Present System ◽  
Integrals Of Motion ◽  
The Difference

The classical quasi-geostrophic model in an active layer with an arbitrary vertical structure is modified by adding a boundary condition at the interface with a passive (motionless) lower layer: the difference between isopycnal and interface elevations is a Lagrangian constant, so that a particle in this boundary remains there and conserves its density. The new model has the appropriate integrals of motion: in particular, a free energy quadratic and positive definite in the deviation from a state with a uniform flow, made up of the internal and ‘external’ potential energies (due to the displacement of the isopycnals and the interface) and the kinetic energy.Eady's model of baroclinic instability is extended with the present system, i.e. including the effect of the free lower boundary. The integrals of motion give instability conditions that are both necessary and sufficient. If the geostrophic slope of the interface is such that density increases in opposite directions at the top and bottom boundaries, then the basic flow is nonlinearly stable. For very weak internal stratification (as compared with the density jump at the interface) normal modes instability is similar to that of a simpler model, with a rigid but sloping bottom. For stronger stratification, though, the deformation of the lower boundary by the perturbation field also plays an important role, as shown in the dispersion relation, the structure of growing perturbations, and the energetics of the instability. The energy of long growing perturbations is mostly internal potential, whereas short ones have an important fraction of kinetic energy and, for strong enough stratification, external potential.

Transverse Heterogeneity Effects in the Dissipation-Induced Instability of a Horizontal Porous Layer

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Linear Stability ◽  
Porous Layer ◽  
Normal Modes ◽  
Lower Boundary ◽  
Boussinesq Approximation ◽  
Darcy Law ◽  
Main Task ◽  
Heterogeneity Effects ◽  
Upper Boundary

The linear stability of a parallel flow in a heterogeneous porous channel is analyzed by means of the Darcy law and the Oberbeck–Boussinesq approximation. The basic velocity and temperature distributions are influenced by the effect of the viscous dissipation, as well as, by the boundary conditions. A horizontal porous layer bounded by impermeable and infinitely wide walls is considered. The lower boundary is assumed to be thermally insulated, while the upper boundary is assumed to be isothermal. A transverse heterogeneity for the permeability and for the thermal conductivity is taken into account. The main task of this work is to investigate the role of this heterogeneity in changing the threshold for the onset of instability. A linear stability analysis by means of the normal modes method is performed. The onset of instability against oblique rolls is studied. The eigenvalue problem is solved numerically.

Natural Convection in a Porous Medium: Effects of Confinement, Variable Permeability, and Thermal Boundary Conditions

1976 ◽  
Vol 98 (1) ◽  
pp. 42-48 ◽  
Author(s):  
R. J. Ribando ◽  
K. E. Torrance
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Natural Convection ◽  
Lower Boundary ◽  
Horizontal Layer ◽  
Temperature Fields ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Variable Permeability ◽  
Real Fluids

Two-dimensional numerical calculations are reported for natural convection of a fluid in a porous, horizontal layer heated from below. Effects of the following parameters are examined: rigid (impermeable) and constant-pressure (permeable) upper boundaries; isothermal and uniform heat flux at the lower boundary; and permeabilities which are constant, or which vary with depth to simulate compaction of a porous medium or property variations of real fluids within the medium. Steady-state results are presented for the heat flux distribution on the upper surface, as well as for flow and temperature fields in the interior.

Flow Over a Sudden Expansion in an Annular Pipe: Steady Axisymmetric Flow and its Stability

2016 ◽  
Author(s):  
Behnaz Beladi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Linear Stability ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Normal Modes ◽  
Staggered Grid ◽  
Sudden Expansion ◽  
Algebraic Equations ◽  
Neutral Curves ◽  
Implicitly Restarted Arnoldi ◽  
Annular Pipe

The stability of the axisymmetric incompressible Newtonian flow in an annular pipe suddenly expanding radially inward is investigated. The axisymmetric steady basic flow is discretized using primitive variables and second-order finite volumes on a staggered grid. The resulting algebraic equations are solved by Newton–Raphson iteration. A three-dimensional global linear stability analysis is performed. The solutions to the linear stability problem are represented by normal modes. The generalized eigenvalue problem is solved using an implicitly restarted Arnoldi algorithm which is provided by the ARPACK library and a Cayley transformation. Stability boundaries have been computed for a range of parameters varying the outlet radius ratio. The physical instability mechanisms are studied by a an posteriori analysis of the kinetic energy transferred between the basic state and the critical mode. Neutral curves and critical modes are presented and the instability mechanisms are discussed.

Computational and Experimental Study of Enhanced Laminar Flow Heat Transfer in Three-Dimensional Sinusoidal Wavy-Plate-Fin Channels

2003 ◽  
Author(s):  
Jiehai Zhang ◽  
Arun Muley ◽  
Joseph B. Borghese ◽  
Raj M. Manglik
Keyword(s):  
Heat Transfer ◽  
Flow Behavior ◽  
Computational Simulation ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Staggered Grid ◽  
Uniform Heat Flux ◽  
Complex Flow ◽  
Constant Property ◽  
Fin Efficiency

Enhanced heat transfer characteristics of low Reynolds number airflows in three-dimensional sinusoidal wavy plate-fin channels are investigated. For the computational simulation, steady state, constant property, periodically developed, laminar forced convection is considered with the channel surface at the uniform heat flux condition; the wavy-fin is modeled by its two asymptotic limits of 100% and zero fin efficiency. The governing equations are solved numerically using finite-volume techniques for a non-orthogonal, non-staggered grid. Computational results for velocity and temperature distribution, isothermal Fanning friction factor f and Colburn factor j are presented for airflow rates in the range of 10 ≤ Re ≤ 1500. The numerical results are further compared with experimental data, with excellent agreement, for two different wavy-fin geometries. The influence of fin density on the flow behavior and the enhanced convection heat transfer are highlighted. Depending on the flow rate, a complex flow structure is observed, which is characterized by the generation, spatial growth and dissipation of vortices in the trough region of the wavy channel. The thermal boundary layers on the fin surface are periodically disrupted, resulting in high local heat fluxes. The overall heat transfer performance is improved considerably, compared to the straight channel with the same cross-section, with a relatively smaller increase in the associated pressure drop penalty.

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