Convective Instability of the Darcy Flow in a Horizontal Layer With Symmetric Wall Heat Fluxes and Local Thermal Nonequilibrium

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Solid Phase ◽  
Fluid Phase ◽  
Heat Fluxes ◽  
Local Thermal Equilibrium ◽  
Neutral Stability ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Darcy Rayleigh Number

The linear stability of the parallel Darcy throughflow in a horizontal plane porous layer with impermeable boundaries subject to a symmetric net heating or cooling is investigated. The onset conditions for the secondary thermoconvective flow are expressed through a neutral stability bound for the Darcy–Rayleigh number associated with the uniform heat flux supplied or removed from the walls. The study is performed by taking into account a condition of local thermal nonequilibrium between the solid phase and the fluid phase. The linear stability analysis is carried out according to the normal modes' decomposition of the perturbations to the basic state. The governing equations for the disturbances are solved numerically as an eigenvalue problem leading to the neutral stability condition. If compared with the asymptotic condition of local thermal equilibrium, the regime of local nonequilibrium manifests an enhanced instability. This behavior is displayed by lower critical values of the Darcy–Rayleigh number, eventually tending to zero when the thermal conductivity of the solid phase is much larger than the conductivity of the fluid phase. In this special limit, which can be invoked as an approximate model of a gas-saturated metallic foam, the basic throughflow is always unstable to external disturbances of arbitrarily small amplitude.

Heat Transfer in a Porous Electrode of Fuel Cells

2005 ◽  
Vol 128 (5) ◽  
pp. 434-443 ◽  
Author(s):  
J. J. Hwang
Keyword(s):  
Heat Transfer ◽  
Diffusion Layer ◽  
Wall Temperature ◽  
Solid Phase ◽  
Porous Electrode ◽  
Catalyst Layer ◽  
Fluid Phase ◽  
Stanton Number ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium

The thermal-fluid behaviors in a porous electrode of a proton exchange membrane fuel cell (PEMFC) in contact with an interdigitated gas distributor are investigated numerically. The porous electrode consists of a catalyst layer and a diffusion layer. The heat transfer in the catalyst layer is coupled with species transports via a macroscopic electrochemical model. In the diffusion layer, the energy equations based on the local thermal nonequilibrium (LTNE) are derived to resolve the temperature difference between the solid phase and the fluid phase. Parametric studies include the Reynolds number and the Stanton number (St). Results show that the wall temperature decreases with increasing Stanton number. The maximum wall temperatures occur at the downstream end of the module, while the locations of local minimum wall temperature depend on the Stanton numbers. Moreover, the solid phase and the fluid phase in the diffusion layer are thermally insulated as St⪡1. The diffusion layer becomes local thermal nonequilibrium as the Stanton number around unity. The porous electrode is local thermal equilibrium for St⪢1. Finally, the species concentrations inside the catalyst and diffusion layers are also provided.

A Discussion of Transpiration Cooling Problems through an Analytical Solution of Local Thermal Nonequilibrium Model

2006 ◽  
Vol 128 (10) ◽  
pp. 1093-1098 ◽  
Author(s):  
J. H. Wang ◽  
H. N. Wang
Keyword(s):  
Analytical Solution ◽  
Biot Number ◽  
Thermal Conduction ◽  
Porous Plate ◽  
Local Thermal Equilibrium ◽  
Transpiration Cooling ◽  
Thermal Nonequilibrium ◽  
Cooling Effects ◽  
Local Thermal Nonequilibrium ◽  
Hot Surface

To study transpiration cooling problems, an analytical solution of the local thermal nonequilibrium (LTNE) model with the second or third boundary conditions is presented. This solution is obtained through neglecting the thermal conduction of the fluid coolant in porous media. By the analytical solution, two problems are investigated. At first, the parameters which influence transpiration cooling effects are analyzed, and the analysis indicates that the cooling effects are dominated by coolant mass flow rate, the Biot number at the hot surface of porous plate, and the Biot number in the pores. Second, the error caused by the assumption of the local thermal equilibrium (LTE) model is quantitatively discussed, and the variation trend of the LTE error is analyzed. Based on the analytical solution and the error analysis, a quantitative criterion to choose the LTNE or LTE model is suggested, and the corresponding expression is also given in this paper.

A Local Thermal Nonequilibrium Analysis of Silicon Carbide Ceramic Foam as a Solar Volumetric Receiver

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Y. Sano ◽  
S. Iwase ◽  
A. Nakayama
Keyword(s):  
Heat Transfer ◽  
Silicon Carbide ◽  
Pore Diameter ◽  
Solid Phase ◽  
Flow Direction ◽  
Ceramic Foam ◽  
Thermal Nonequilibrium ◽  
Silicon Carbide Ceramic ◽  
Local Thermal Nonequilibrium ◽  
Solar Receiver

A volumetric solar receiver receives the concentrated radiation generated by a large number of heliostats. Heat transfer takes place from the receiver solid phase to the air as it passes through the porous receiver. Such combined heat transfer within the receiver, associated radiation, convection and conduction, are investigated using a local thermal nonequilibrium model. The Rosseland approximation is applied to account for the radiative heat transfer through the solar receiver, while the low Mach approximation is exploited to investigate the compressible flow through the receiver. Analytic solutions are obtained for the developments of air and ceramic temperatures as well as the pressure along the flow direction. The results show that the pore diameter must be larger than its critical value to achieve high receiver efficiency. Subsequently, there exists an optimal pore diameter for achieving the maximum receiver efficiency under the equal pumping power. The solutions serve as a useful tool for designing a novel volumetric solar receiver of silicon carbide ceramic foam.

scholarly journals Effect of Local Thermal Nonequilibrium on the Stability of Natural Convection in an Oldroyd-B Fluid Saturated Vertical Porous Layer

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Natural Convection ◽  
Solid Phase ◽  
Viscoelastic Fluids ◽  
Maxwell Fluid ◽  
Base Flow ◽  
Temperature Fields ◽  
Thermal Nonequilibrium ◽  
Interphase Heat Transfer ◽  
Local Thermal Nonequilibrium ◽  
The Stability

The effect of local thermal nonequilibrium (LTNE) on the stability of natural convection in a vertical porous slab saturated by an Oldroyd-B fluid is investigated. The vertical walls of the slab are impermeable and maintained at constant but different temperatures. A two-field model that represents the fluid and solid phase temperature fields separately is used for heat transport equation. The resulting stability eigenvalue problem is solved numerically using Chebyshev collocation method as the energy stability analysis becomes ineffective in deciding the stability of the system. Despite the basic state remains the same for Newtonian and viscoelastic fluids, it is observed that the base flow is unstable for viscoelastic fluids and this result is qualitatively different from Newtonian fluids. The results for Maxwell fluid are delineated as a particular case from the present study. It is found that the viscoelasticity has both stabilizing and destabilizing influence on the flow. Increase in the value of interphase heat transfer coefficient Ht, strain retardation parameter Λ2 and diffusivity ratio α portray stabilizing influence on the system while increasing stress relaxation parameter Λ1 and porosity-modified conductivity ratio γ exhibit an opposite trend.

Approximate Analysis for Darcy-Flow Convection in Porous Media With Zero Fluid Conduction

2009 ◽  
Author(s):  
Nihad Dukhan
Keyword(s):  
Porous Media ◽  
Solid Phase ◽  
Convection Heat Transfer ◽  
Fluid Phase ◽  
Constant Heat Flux ◽  
Local Thermal Equilibrium ◽  
Electronic Systems ◽  
Air Cooling ◽  
Equilibrium Equations ◽  
Heat Rejection

The heat rejection device is a key component in virtually all electronic systems. New core materials for compact and efficient heat exchangers or heat rejection devices are contemporary porous media including metal and graphite foam. In such materials the solid phase has a relatively high conductivity, especially when the fluid phase has a low conductivity. This condition is realized in air-cooling thermal management systems. Simple models are needed for scientists and engineers who work with these materials. Approximate engineering analysis for the convection heat transfer inside a two-dimensional rectangular porous media subjected to constant heat flux on one side is presented. The analysis sets the conduction in the fluid’s governing equation to zero, and for simplicity assumes Darcian flow. The Darcian flow assumption is valid far enough from the solid boundaries, ant it prevails for most of the cross section. The non-local-thermal equilibrium equations are significantly simplified and solved. The solid and fluid temperatures decay in what looks like an exponential fashion as the distance from the heated base increases. The results are in good qualitative agreement with more complex analytical and numerical results in the literature. The proposed model may prove to be time-savings for design purposes.

New models for heat flux splitting at the boundary of a porous medium: three energy equations for nanofluid flow under local thermal nonequilibrium conditions

2014 ◽  
Vol 92 (11) ◽  
pp. 1312-1319 ◽  
Author(s):  
M. Nazari ◽  
M.J. Maghrebi ◽  
T. Armaghani ◽  
Ali J. Chamkha
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Medium ◽  
Solid Phase ◽  
Solid Matrix ◽  
Fluid Temperature ◽  
Transfer Coefficients ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Energy Equations

One of the challenging points in the simulation of a nanofluid flowing through a porous medium is modeling the surface heat flux in the presence of nanoparticles and internal solid matrix. The question is how much energy is absorbed by the solid phase, fluid phase, and particles at the surface of imposing heat flux? To reach a suitable answer, a local thermal nonequilibrium approach (including three energy equations) is presented in this paper and three heat flux models are proposed for the first time. The proposed models are compared and analyzed. The effects of interstitial heat transfer coefficients on the heat transfer in a porous channel are completely studied. The fluid temperature distributions and heat transfer rate obtained by homogenous and nonhomogenous approaches (for the proposed models) are completely studied and compared. The results show that the nonhomogeneous approach experiences larger Nusselt number than the homogeneous one for all the recommended heat flux models.

Finite Darcy–Prandtl Number and Maximum Density Effects on Gill's Stability Problem 

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
S. B. Naveen ◽  
B. M. Shankar ◽  
I. S. Shivakumara
Keyword(s):  
Rayleigh Number ◽  
Prandtl Number ◽  
Wave Mode ◽  
Density Variation ◽  
Maximum Density ◽  
Time Dependent ◽  
Wave Number ◽  
Neutral Stability ◽  
The Stability ◽  
Darcy Rayleigh Number

Abstract The simultaneous effect of a time-dependent velocity term in the momentum equation and a maximum density property on the stability of natural convection in a vertical layer of Darcy porous medium is investigated. The density is assumed to vary quadratically with temperature and as a result, the basic velocity distribution becomes asymmetric. The problem has been analyzed separately with (case 1) and without (case 2) time-dependent velocity term. It is established that Gill's proof of linear stability effective for case 2 but found to be ineffective for case 1. Due to the lack of Gill's proof for case1, the stability eigenvalue problem is solved numerically and observed that the instability sets in always via traveling-wave mode when the Darcy–Prandtl number is not larger than 7.08. The neutral stability curves and isolines are presented for different governing parameters. The critical values of Darcy–Rayleigh number corresponding to quadratic density variation with respect to temperature, critical wave number, and the critical wave speed are computed for different values of governing parameters. It is found that the system becomes more stable with increasing Darcy–Rayleigh number corresponding to linear density variation with respect to temperature and the Darcy–Prandtl number.

The effect of rotation on double diffusive convection: perspectives from linear stability analysis

2021 ◽  
Author(s):  
Yu Liang ◽  
Jeffrey R. Carpenter ◽  
Mary-Louise Timmermans
Keyword(s):  
Stability Analysis ◽  
Rayleigh Number ◽  
Arctic Ocean ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Rayleigh Number ◽  
Heat Fluxes ◽  
The Arctic ◽  
Diffusive Convection ◽  
The Arctic Ocean

AbstractDiffusive convection can occur when two constituents of a stratified fluid have opposing effects on its stratification and different molecular diffusivities. This form of convection arises for the particular temperature and salinity stratification in the Arctic Ocean and is relevant to heat fluxes. Previous studies have suggested that planetary rotation may influence diffusive-convective heat fluxes, although the precise physical mechanisms and regime of rotational influence are not well understood. A linear stability analysis of a temperature and salinity interface bounded by two mixed layers is performed here to understand the stability properties of a diffusive-convective system, and in particular the transition from non-rotating to rotationally-controlled heat transfer. Rotation is shown to stabilize diffusive convection by increasing the critical Rayleigh number to initiate instability. In the rotationally-controlled regime, a −4/3 power law is found between the critical Rayleigh number and the Ekman number, similar to the scaling for rotating thermal convection. The transition from non-rotating to rotationally-controlled convection, and associated drop in heat fluxes, is predicted to occur when the thermal interfacial thickness exceeds about 4 times the Ekman layer thickness. A vorticity budget analysis indicates how baroclinic vorticity production is counteracted by the tilting of planetary vorticity by vertical shear, which accounts for the stabilization effect of rotation. Finally, direct numerical simulations yield generally good agreement with the linear stability analysis. This study, therefore, provides a theoretical framework for classifying regimes of rotationally-controlled diffusive-convective heat fluxes, such as may arise in some regions of the Arctic Ocean.

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