Lack Of Local Thermal Equilibrium Research Articles

Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Local thermal equilibrium (LTE) is a frequently-employed hypothesis when analysing convection heat transfer in porous media. However, investigation of the non-equilibrium phenomenon exhibits that such hypothesis is typically not true for many circumstances such as rapid cooling or heating, and in industrial applications involving immediate transient thermal response, leading to a lack of local thermal equilibrium (LTE). Therefore, for the sake of appropriately conduct the technological process, it has become necessary to examine the validity of the LTE assumption before deciding which energy model should be used. Indeed, the legitimacy of the LTE hypothesis has been widely investigated in different applications and different modes of heat transfer, and many criteria have been developed. This paper summarises the studies that investigated this hypothesis in forced, free, and mixed convection, and presents the appropriate circumstances that can make the LTE hypothesis to be valid. For example, in forced convection, the literature shows that this hypothesis is valid for lower Darcy number, lower Reynolds number, lower Prandtl number, and/or lower solid phase thermal conductivity; however, it becomes invalid for higher effective fluid thermal conductivity and/or lower interstitial heat transfer coefficient.

A comparative study on heat transfer characterization of sodium alginate-based carbon nanotubes in a non-Newtonian fluid flow using a new local thermal nonequilibrium formulation

The current study elucidates the mass and heat transfer characteristics of Casson nanofluid flow over a stretching sheet in a porous medium (PM) subject to a lack of local thermal equilibrium (LTNE). The LTNE model is based on the energy balance of both solid and fluid phases. Hence, distinctive thermal profiles for both the fluid and solid phases are employed in this study. Further, owing to exceptional high intrinsic conductance performance, Carbon nanotubes (CNT’s) show great potential to increase the thermal conductivity. In this connection, CNT’s (single and multi-wall) are considered as suspended nanoparticles in the base fluid sodium alginate (SA). The equations of modeled physical problem are reduced by using a proper transformation, which are then numerically tackled by using the classical Runge-Kutta (RK) process with the shooting technique. The impact of the flow parameters on the thermal, concentration and velocity profiles along with skin friction, Nusselt and Sherwood numbers is explored and interpreted graphically. The results reveal that, SWCNT-sodium alginate Casson nanoliquid show improved heat transfer for growing values of porosity parameter. The fluid and solid phase thermal profiles of MWCNT-sodium alginate Casson nanoliquid is strongly stimulated by growing values of porosity-modified conductivity ratio parameter.

Emergence of kinetic behavior in streaming ultracold neutral plasmas

We create streaming ultracold neutral plasmas by tailoring the photoionizing laser beam that creates the plasma. By varying the electron temperature, we control the relative velocity of the streaming populations, and, in conjunction with variation of the plasma density, this controls the ion collisionality of the colliding streams. Laser-induced fluorescence is used to map the spatially resolved density and velocity distribution function for the ions. We identify the lack of local thermal equilibrium and distinct populations of interpenetrating, counter-streaming ions as signatures of kinetic behavior. Experimental data are compared with results from a one-dimensional, two-fluid numerical simulation.

Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

The effects of lack of local thermal equilibrium between the solid phase and the fluid phase are taken into account for the convective stability analysis of a horizontal porous layer. The layer is bounded by a pair of plane parallel walls which are impermeable and such that the lower wall is subject to a uniform flux heating, while the upper wall is isothermal. The local thermal non-equilibrium is modelled through a two-temperature formulation of the energy exchange between the phases, resulting in a pair of local energy balance equations: one for each phase. Small-amplitude disturbances of the basic rest state are envisaged to test the stability. Then, the standard normal mode procedure is adopted to detect the onset conditions of convective rolls. Beyond the Darcy-Rayleigh number, playing the role of order parameter for the transition to instability, the relevant dimensionless parameters are the inter-phase heat transfer parameter and the thermal conductivity ratio. The disturbance governing equations, formulated as an eigenvalue problem, are solved numerically by a shooting method. Results are reported for the neutral stability curves and for the critical values for the onset of instability.

Basic natural convection in a vertical porous layer differentially heated from its sidewalls subject to lack of local thermal equilibrium

A vertical porous layer subject to lack of local thermal equilibrium and differentially heated from its sidewalls experiences extremely different conditions when it is heated via a constant heat flux, rather than via a hot temperature imposed on the sidewall. For a start the steady state basic temperatures of the fluid and solid differ, as distinct from the corresponding case of imposed temperature on the sidewall when both fluid and solid temperatures are identical and linear at steady state and the lack of local thermal equilibrium (LaLotheq) can manifest itself at transients or when the basic temperature profiles stated above become unstable. In addition, in the case of heating via a constant heat flux the steady state basic temperatures of the fluid and solid are not only distinct but also nonlinear. The analytical derivation of these nonlinear solutions for the basic natural convection in a vertical porous layer differentially heated from its sidewalls, subject to lack of local thermal equilibrium and heating via a constant heat flux is presented and the results analyzed over a wide range of parameter space. In general it is shown that the lack of local thermal equilibrium destroys the symmetry of the problem via deviatoric terms in the solutions.

Heating of saturated porous media in practice: Several causes of local thermal non-equilibrium

In recent years the industrial applications of porous materials has shown a growing relevance. Most of the technological thermal processes in porous media involve time-dependent thermal conditions. Therefore, the temperature at each point of the material also changes in time. In order to correctly carry out the technological process, it becomes necessary to know the temperature distribution inside the material. This is a problem of heat conduction in a fluid saturated porous media subject to a lack of local thermal equilibrium (LTNE). The purpose of this paper is to elucidate the several causes of LTNE, even in steady or quasi steady heat transfer processes in saturated porous media, and to evaluate the influence of structural characteristic of porous media and the presence of surfactant in the saturating liquid phase.

Finite Péclet number forced convection past a sphere in a porous medium using a thermal nonequilibrium model

We study the finite-Peclet number forced convective heat transfer from a uniform temperature sphere placed in otherwise uniform fluid stream within a porous medium. A numerical study is undertaken to determine how the lack of local thermal equilibrium between the phases affects temperature fields of the two phases and the respective rates of heat transfer from the sphere. On the upstream side of the sphere the temperature field extends further from the sphere in the solid phase than it does for the fluid phase, but the opposite is true on the downstream side.

Equivalence between dual-phase-lagging and two-phase-system heat conduction processes

We show the equivalence between the dual-phase-lagging heat conduction and the Fourier heat conduction in two-phase systems subject to lack of local thermal equilibrium. This provides an additional tool for studying the two heat-conduction processes and shows the possibility of thermal oscillation and resonance in two-phase-system heat conduction, a phenomenon observed experimentally. Such thermal waves and possibly resonance come from the macroscale coupled conductive terms.

On the paradox of heat conduction in porous media subject to lack of local thermal equilibrium

An apparent paradox that appears in problems of heat conduction in porous media subject to lack of local thermal equilibrium (LaLotheq) that was introduced by Vadasz [Transport in Porous Media 59 (2005) 341–355] is reformulated and resolved. This apparent paradox relates to a combination of Dirichlet and insulation boundary conditions and leads the solution towards local thermal equilibrium (Lotheq).

Exclusion of oscillations in heterogeneous and bi-composite media thermal conduction

Analysis of Fourier heat conduction in heterogeneous and bi-composite media (e.g. porous media, fluid suspensions, etc.) subject to Lack of Local Thermal Equilibrium (LaLotheq) reveals a condition for thermal oscillations and resonance to be possible. This paper shows that this condition cannot be fulfilled because of physical constraints leading to the exclusion of thermal waves and resonance.

Explicit Conditions for Local Thermal Equilibrium in Porous Media Heat Conduction

Based on the traditional formulation of heat transfer in porous media it is demonstrated that Local Thermal Equilibrium (Lotheq) applies generally for any boundary conditions that are a combination of constant temperature and insulation. The resulting consequences are being analysed and discussed. Among these consequences it is shown that the linear relationship between the average temperature difference of the two phases and the heat transferred over the fluid-solid interface is inappropriate for use in connection with conditions of Lack of Local Thermal Equilibrium (La Lotheq).

Lack of oscillations in Dual-Phase-Lagging heat conduction for a porous slab subject to imposed heat flux and temperature

This study shows that the physical conditions necessary for thermal waves to materialize in Dual-Phase-Lagging porous media conduction are not attainable in a porous slab subject to a combination of constant heat flux and temperature (Neumann and Dirichlet) boundary conditions. It is demonstrated that the approximate equivalence between Dual-Phase-Lagging (DuPhlag) heat conduction model and the Fourier heat conduction in porous media subject to Lack of Local Thermal Equilibrium (La Lotheq) that suggested the possibility of thermal oscillations and resonance reveals a condition that cannot be fulfilled because of physical constraints.

Absence of Oscillations and Resonance in Porous Media Dual-Phase-Lagging Fourier Heat Conduction

The approximate equivalence between the dual-phase-lagging heat conduction model and the Fourier heat conduction in porous media subject to lack of local thermal equilibrium suggested the possibility of thermal oscillations and resonance. The present investigation demonstrates that the physical conditions necessary for such thermal waves and, possibly resonance, to materialize are not attainable in a porous slab subject to constant temperature conditions applied on the boundaries.

Understanding spectroscopy with a view to rationalizing spectrochemical analysis: an abysmal adventure or a realistic ideal?

This paper presents a view on the creation, transfer, and use of knowledge that constitutes or should constitute the basis of spectrochemical analysis methods. This view is projected on a communication network of “spheres” of which physics, spectrochemical physics, methodology development, instrument development, and applications development form the nuclei. According to the author's definition, the knowledge created in the sphere of methodology development is based partly on parametric studies of sources or atomizers, partly on analytical or spectroscopic approaches inherent in and characteristic of spectrochemical methodology development. On the other hand, methodology development is understood to derive a rational backing from an indispensable interaction with spectrochemical physics and physics. Methodology development is argued to occupy a crucial and central position in the communication network because it searches for concrete answers to generally analytical or spectrochemical questions and provides these answers by building up systematic knowledge that is directly usable in both instrument and applications development. This philosophy and the pertinent question raised in the title of this paper are discussed in a concrete context by reviewing and analyzing the developments in three domains of spectrochemical analysis: inductively coupled plasma (ICP) atomic emission spectrometry (AES), spark AES, and glow discharge (GD) spectroscopy. The pivot position of methodology development is illustrated by the developments of both ICP-AES and GD-AES, where methodology development has substantially contributed to the implementation of rational approaches. This situation is contrasted with the development of spark AES, where a vast reservoir of profound fundamental knowledge has been acquired but has also been locked up in an ebony tower, because there has been little or no demand from the side of instrument manufacturers for a rationalization of spark-AES analysis. This has created a “spark-AES methodology gap”, which, for various reasons discussed, is not likely to be bridged in the future. GD spectroscopy is shown to cope with a rather fundamental handicap: the lack of local thermal equilibrium in GDs. The further rationalization of GD spectroscopy is concluded therefore to require an essential expansion of spectrochemical physics using basic input from physics and the implementation of approaches not yet very common in the spectrochemical field. On the whole, the author expresses his concern not so much about the unavailability of knowledge that would help rationalizing spectrochemical analysis, but about the proper transfer of this knowledge to the recipients. In particular, the author emphasizes the need for making fundamental knowledge in the circuits of methodology development and spectrochemical physics better consumable, not only to applied analysts but also to chemometricians in order to prevent the proliferation of artificial intelligence that rests on practice only but lacks a really rational basis.