Thermal Equilibrium Hypothesis Research Articles

Numerical Studies on Hydrogen Production from Ammonia Thermal Cracking with Catalysts

To explore and optimize the process of hydrogen production from plasma-assisted ammonia-cracking, a tubular ammonia-cracking on-site hydrogen production device with plasma-assisted ammonia combustion flue gas as the heat source was developed. Using the Temkin–Pyzhev kinetic model and the local thermal equilibrium (LTE) hypothesis, the effects of operating conditions, such as combustion flue gas temperature and ammonia flow rates, on ammonia-cracking efficiency were investigated. The numerical results are quantitatively consistent with the experiment. Ammonia cracking efficiency is notably influenced by the initial combustion gas temperature. When the gas velocity of the cracking system is less than or equal to 0.03 m/s, the cracking rate increases by 63% when the inlet temperature of the heat pipe changes from 700 K to 800 K. The cracking rate of ammonia decreased with the increase of ammonia flow rate, and this trend reached the maximum and began to weaken when the flow rate was 0.3 m/s. Longer catalyst bed length does not always mean higher cracking efficiency; the length of the cracking tube over 0.6 m shows little effect on cracking efficiency. Response surface methodology was used to conduct multi-factor analysis of the three main factors affecting the cracking rate of the cracker, namely, the temperature of the heating tube, the flow rate of flue gas in the heating process, and the inlet flow rate of the catalytic bed. It was found that the flow rate of the catalytic bed was the most significant factor affecting the cracking rate, which could be used as the main control method. The numerical results would provide technical guidance for industrial applications of on-site hydrogen production devices from ammonia decomposition.

Entropy Generation Analysis on a Metal Foam in an Automotive Exhaust Line with Thermoelectric Generator

Abstract In the present paper, an entropy generation analysis on a 2-D steady state problem in convective regime of an aluminum foam partially and totally filled channel with an external TEG element is solved in numerical way. The numerical analyses are accomplished with the assumption of the local thermal equilibrium (LTE) hypothesis in order to model the metal foam and heat transfer inside the channel. The working fluid is exhaust gas characterized by the same properties of the air in correspondence to the TEG upper surface temperature. The TEG is considered as a solid component characterized by an internal energy generation. The thermophysical properties are assumed temperature independent. Ansys-Fluent code is employed in order to resolve the governing equations for exhaust gas, metal foam and TEG. Different exhaust gas mass flow rates on the inlet section are assumed. Several thicknesses of aluminum foam values are employed. The porous media are characterized by a porosity from 0.90 to 0.978 and number of pores per inch (PPI) equal to 5, 10, 20, 40. Results are given in terms of global entropy generations related to the thermal and viscous effects. The total global entropy generation increases with increasing of exhaust gas flow rate for all pore density and porosity values. Bejan number decreases with the increment of mass flow rate and thickness. It increases when the porosity value increases whereas at high mass flow rate and for assigned porosity the values present small difference for different pore density values.

Two-temperature ablative material response model with application to Stardust and MSL atmospheric entries

Ablative material response codes currently in use consider local thermal equilibrium between the solid phases and the pyrolysis gases. For typical entry conditions, this hypothesis may be justified by the fact that the thermal Peclet number within the pores is small, which is a necessary condition for thermal equilibrium in non-reactive materials. However, the validity of this analysis may fall under some circumstances. The thermal Peclet number may become large due to high pyrolysis gas velocities. Additional physical phenomena not accounted for in the Peclet analysis may become non-negligible, such as the change of enthalpy due to chemical reactions. The objective of this study is two-fold. First, a detailed two temperature material response model for porous reactive materials is presented. This model has been implemented and made available in the Porous material Analysis Toolbox based on OpenFOAM (PATO). Second, the model is applied to the Theoretical Ablative Composite for Open Testing (TACOT) in a wide range of conditions to assess the true range of validity of the thermal equilibrium hypothesis. Simulations are carried out on the Stardust and Mars Science Laboratory (MSL) atmospheric entries. The main design variables have been monitored and compared between the two models: temperature evolution and species concentration within the material, pyrolysis gas blowing rate, extension of the pyrolysis zone, and wall recession due to ablation. Results show that under chemical equilibrium conditions, no significant deviation in the monitored quantities are observed, while under chemical non-equilibrium conditions there is a large impact on the species concentration.

Numerical Investigation on Natural Convection in Inclined Channels Partially Filled With Asymmetrically Heated Metal Foam

Abstract A numerical study on natural convection in an inclined channel partially filled with open metal foam is investigated in two-dimensional laminar and incompressible and steady-state condition. The upper wall is heated at uniform heat flux, and the lower wall is adiabatic. The governing equations for the metal foam are written assuming the Brinkman–Forchheimer-extended Darcy model and the local thermal equilibrium (LTE) hypothesis. The inclination angle with respect to the horizontal direction ranges between 0 deg and 90 deg. The metal foam structure is homogenous and isotropic and the thermophysical properties are assumed constant with the temperature. The main aim of the present study is to analyze the effect of inclination angle, pore density, and porosity to improve the knowledge on the thermal behaviors of natural convection in partially filled channel with metal foam. Moreover, this study aims to evaluate the possible improvement with respect to the clean inclined channel. Results are presented in terms of velocity and temperature fields, and both temperature and velocity profiles at different significant sections are shown, to obtain a description of the natural convection inside the inclined channel. Finally, average Nusselt number values are evaluated. The presence of metal foam affects the fluid flow in the channel with different motion behaviors. The heat transfer rate increases with the increase in inclination angle, and the average Nusselt number shows different trends for lower and higher Rayleigh numbers, Ra. A significant enhancement is detected for the higher Ra and it depends on the porosity and pore density.

NUMERICAL INVESTIGATION OF FORCED CONVECTION HEAT TRANSFER AROUND AND THROUGH AN ELLIPTICAL POROUS CYLINDER

Convection heat transfer from a heated elliptical porous cylinder in the incompressible and laminar cross-flow is studied numerically. The effects of Darcy number (10<sup>-6</sup> ≤ Da ≤ 10<sup>-2</sup>), aspect ratio (0.2 ≤ AR ≤ 5), Prandtl number (0.7 ≤ Pr ≤ 70), Reynolds number (10 ≤ Re ≤ 40), on the average Nusselt number (Nu), as well as the lift and the drag coefficients are investigated. Two types of thermal boundary conditions for porous cylinder are investigated: uniformly distributed heat source and constant temperature. The fluid flow in the porous medium is numerically simulated by the superficial velocity model. Additionally, the energy equation in the porous medium is simplified by the local thermal equilibrium (LTE) hypothesis. It is concluded that the aspect ratio of the elliptical cylinder has a great influence on the heat transfer and fluid flow characteristics of this problem. Results show that increasing the Darcy number increases the Nusselt number and decreases the drag coefficient of the porous cylinder. Moreover, values of Da smaller than 10<sup>-4</sup> resemble the fluid flow and heat transfer characteristics of the impermeable solid cylinder.

Integral Transform Solution of Porous Medium Models for Heat Sinks Subject to Periodic Heat Loads

Abstract Analysis of the energy transport in thermal microdevices modeled as a porous medium under periodic heat loads is conducted using integral transforms. Coupled eigenvalue problems are employed and a single set of coupled ordinary differential equations conveying all information on the temperature fields in both the solid and fluid phases are reached, allowing for a relatively straightforward treatment of the local thermal nonequilibrium (LTNE) formulation. This characteristic proved instrumental in finding out that the local thermal equilibrium (LTE) hypothesis is inadequate for unsteady problems. The solid phase is shown to have a significant role on inducing thermal lag in the fluid, which may be severe, depending on the dimensions and operational conditions. In general, devices comprised of larger fractions of solid material and with poorer heat transfer characteristics are more prone to having larger thermal lag along them. These conclusions may be relevant to a wide range of applications such as electronics cooling, battery thermal management, solar energy harvesting, among others.

Numerical investigation on a thermoelectric generator in an exhaust automotive line with convergent metal foam

In the present paper, a 2-D steady state convective heat transfer problem in a convergent channel partially filled with aluminum foam with an external thermoelectric generator (TEG) component is numerically solved. The channel is characterized by a length equal to 272 mm and by a height of 60 mm. The TEG has the dimensions equal to 65 mm and 8.5 mm. The investigation is executed considering the Darcy-Forchheimer-Brinkman assumption and the local thermal equilibrium (LTE) hypothesis for modelling the metal foam. The exhaust gas is considered to have the same properties of the air in corresponding to the assigned temperature of the upper surface of the thermoelectric generator. The thermophysical properties are temperature independent and the thermoelectric generator is studied as a solid with an internal energy generation. The governing equations for gas, porous media and thermoelectric generator are solved by finite volume method using the Ansys-Fluent code. Different configurations of convergent metal foam are analyzed. The aluminum foams are characterized by 5 PPI and porosity equal to 0.905, 0.946 and 0.971. Results are presented in terms of temperature distributions, thermoelectric efficiency, power density, and the Energy Performance Ratio (EPR) for different gas flow rates and aluminum foam configurations. Furthermore, a comparison with the use of the same foam samples characterized by a constant section is showed for the same system. From the comparison, it is possible to deduce how the configuration with convergent channel has a more uniform temperature profile than the geometry with constant section.

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.

Steady-State Thermal-Hydraulic Analysis of Steam Generator with Axial Economizer Based on Node Method

Based on the one-dimensional flow hypothesis, heat transfer hypothesis, and two-phase thermal equilibrium hypothesis, a lumped parameter method and a distributed parameter method are used to establish a one-dimensional steady-state thermal-hydraulic analysis model of the steam generator with axial economizer. Using C++ language programming, the calculation results are compared with the design values of the thermal-hydraulic parameters of a typical steam generator with axial economizer. The results show that the relative error of most of the overall parameter calculation results is within 3%, which verifies the rationality of the model. The analysis of the temperature, cavitation share, pressure and other parameters of the steam generator along the direction of the measured fluid flow trend consist well with the results of thermal hydraulics and qualitative mechanism analysis, indicating that the model and solution method established in this paper can accurately predict the steady-state thermal hydraulic parameter distribution of the steam generator with axial economizer.

Hybrid solutions for thermally developing flows in channels partially filled with porous media

A new approach based on the Generalized Integral Transform Technique is advanced to deal with convective heat transfer in partially porous channels under local thermal nonequilibrium (LTNE) formulation. A semi-infinite partially porous parallel plates channel configuration is used to illustrate the semi-analytical solution methodology. The proposed eigenfunction expansion is based on a novel coupled multilayer eigenvalue problem which results in similar accuracy and computational performance in comparison to the expansions employed in solving the formulation under the local thermal equilibrium (LTE) hypothesis. Results from the LTE and LTNE formulations are then critically compared to explore the validity of the former in the present configuration. It is observed that the LTE formulation results may significantly overestimate the Nusselt number, leading to overly optimistic heat transfer predictions. Finally, an analysis of the effect of each parameter in the difference between the temperatures in the solid and fluid phases of the porous medium and in the Nusselt number is carried out, offering guidance for the design of heat transfer devices.

Why adult mayflies ofCloeon dipterum(Ephemeroptera:Baetidae) become smaller as temperature warms

AbstractWe reared Cloeon dipterum from egg hatch to adult at 10 constant temperatures (12.1–33.5°C) to test 3 hypotheses (thermal equilibrium hypothesis, temperature size rule [TSR], and O2- and ca...

High-resolution spectroscopy of giant stars in the open clusters IC 4651 and IC 4725

Open clusters are important astrophysical laboratories to study the stellar formation and evolution and to verify the disk structure of the Milky Way. We present calculations of stellar atmospheric parameters and s-process abundances for nine giant stars in the galactic open clusters IC 4651 and IC 4725. These objects have their memberships confirmed from dynamic studies and chemical analysis. The high-resolution spectra are available in the FEROS ESO archive. We have applied a line by line analysis relative to Juno solar spectrum to determine the stellar atmospheric parameters and chemical abundances of Y II, Zr I, La II, Ce II, and Nd II under the local thermal equilibrium hypothesis. The obtained results were compared to the literature values. The derived s-process abundance pattern agrees with the most recent behaviors reported for giant stars in galactic open clusters.

Comparison between Two Local Thermal Non Equilibrium Criteria in Forced Convection through a Porous Channel

Two criteria are used and compared to investigate the local thermal equilibrium assumption in a forced convection through a porous channel. The first criterion is based on the maximum local temperature difference between the solid and fluid phases, while the second is based on the average of the local differences between the temperature of the solid phase and the fluid phase. For this purpose, the momentum and energy equations based on the Darcy-Brinkman-Forchheimer and the local thermal non equilibrium models are solved numerically using the finite volume method. The analysis focused on searching thermophysical parameters ranges which validate local thermal equilibrium hypothesis. Thus, by using the two criteria, the obtained results mainly revealed that this local thermal equilibrium assumption is verified for low thermal conductivity ratio and Reynolds number values and for high interstitial Biot number and porosity, while it is unfavorably affected by the high values of Prandtl number. However, it is also found that the parameters ranges corresponding to the local equilibrium validity depends on the selected local thermal non equilibrium criterion.

Mathematical description of heat and mass transfer during deep bed drying: Effect of product shrinkage on bed porosity

The global behaviour of a deep bed dyer is studied. The system is considered as a porous media at the macroscopic scale. A model based on heat and mass balance is applied to the different components of the system and coupled to the drying kinetic, which is based on experimental data. Moreover, the local thermal equilibrium (LTE) hypothesis is used. It allows reducing the obtained set of differential equations, which is resolved numerically. The studied system obliges to use variable thermo-physical properties of the heated air. Also, shrinkage effect is taken into consideration; it makes diameter of the product, bed porosity and air velocity changes during all the process. Simulation permits to follow the evolution of humidity and temperature variations of the dried product and the drying air with respect to time and space. The results show that drying is performed with non-homogeneous and different manners; as first layers are yet dried and have attained the temperature of the heated air; last ones are still at ambient conditions. The pick up efficiency gives more information about the performance of the dryer and the distribution of the obtained energy inside it. Temperature and humidity of the air influence considerably the results and then the behaviour of the presented drying system.

Models and validation of particulate debris coolability with the code MC3D-REPO

This paper presents MC3D-REPO which is a multidimensional code dealing with boiling – including the presence of non-condensable gases – in porous media. Use is made of the thermal equilibrium hypothesis between components, so, for reactor applications, it can only be used for the prediction of dry out. Validations against analytical solutions for simplified problems are presented, as well as comparisons with two different types of experiments. The first one deals with the cooling of a heated container located in initially saturated sand and the second one concerns the coolability of a bed of heated steel balls.

A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow Over an Array of Square Rods

Interfacial heat transfer coefficients in a porous medium modeled as a staggered array of square rods are numerically determined. High and low Reynolds k-ϵ turbulence models are used in conjunction of a two-energy equation model, which includes distinct transport equations for the fluid and the solid phases. The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal nonequilibrium assumption. Macroscopic time-average equations for continuity, momentum, and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). The numerical technique employed for discretizing the governing equations is the control volume method. Turbulent flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.

The influence of stream water temperature on size and weight of caddisflies (Insecta, Trichoptera) along the Breitenbach 1983-1991

Competing hypotheses that try to relate population size, individual weight, and water temperature in running waters were tested. Female and male dry weight and specimen numbers of eleven caddisfly species (Trichoptera) collected from 1983 to 1991 in four emergence traps along the Breitenbach (Germany) were related to site specific water temperatures. Water temperature along the stream showed the classical pattern, almost constant near the source and increasing annual variability downstream. Temperature sum (dd = degree days) increased downstream; sums of the last three, six and nine months had a clear seasonality, twelve months sums were almost constant. Greatest upstream-downstream differences occurred in autumn and winter. Comparison of Trichoptera was based on yearly abundance and weight data. Females were heavier in all species but Potamophylax cingulatus. Among sites, weight differences were not detected for Apatania fimbriata. Silo pallipes, Tinodes rostocki, Plectrocne-mia conspersa and for P. cingulatus (♂) and Rhyacophila fasciata (♂) at least in stream sections where they occurred regularly and abundantly. Weight differences were usually significant only between the uppermost or the lowermost, and the remaining sites along the stream. Sericostoma personatum exhibited an almost site by site weight increase downstream. Drusus annulatus (♂, ♀), R. fasciata (9) and P. cingulatus (♀) were lightest at the downstream site, where only R. fasciata occurred regularly. C. villosa (♂, ♀). Potamophylax luctuosus (♂), S. personatum (♂) and Agapetus fuscipes (♂) were lightest at the uppermost site. No single hypothesis explained all results. High individual and population success (high weight or abundance) as predicted by the 'Thermal Equilibrium Hypothesis' occurred in D. annulatus, P. cingulatus and P. luctuosus. In contrast, high abundance and low weight occurred in C. villosa and S. personatum. Individual success seems to depend on a specific fit of genetic pre-adaptations, appropriate physiographical and ecological conditions, and competitive ability; it is not necessarily connected with population success.

Interfacial heat transfer coefficient for non-equilibrium convective transport in porous media

The literature has documented proposals for macroscopic energy equation modeling for porous media considering the local thermal equilibrium hypothesis and laminar flow. In addition, two-energy equation models have been proposed for conduction and laminar convection in packed beds. With the aim of contributing to new developments, this work treats turbulent heat transport modeling in porous media under the local thermal non-equilibrium assumption. Macroscopic time-average equations for continuity, momentum and energy are presented based on the recently established double decomposition concept (spatial deviations and temporal fluctuations of flow properties). Interfacial heat transfer coefficients are numerically determined for an infinite medium over which the fully developed flow condition prevails. The numerical technique employed for discretizing the governing equations is the control volume method. Preliminary laminar flow results for the macroscopic heat transfer coefficient, between the fluid and solid phase in a periodic cell, are presented.

Gondwanan mesotherms and cosmopolitan eurytherms: effects of temperature on the development and survival of Australian Chironomidae (Diptera) from tropical and temperate populations

In temperate regions of the northern hemisphere, where stream thermal regimes fluctuate seasonally and predictably, temperature has a role in niche segregation and maintenance of patterns of lotic diversity and distribution, as described by the ‘Thermal Equilibrium Hypothesis’. In Australia, the role of temperature in regulating patterns of diversity and distribution has been obscure, as seasonal variation in stream temperatures can be exceeded by stochastic fluctuation in flow. The thermal responses of five lotic Chironomidae (Diptera) species, contrasting in biogeographic (evolutionary) history, from warm tropical and cool temperate Australian populations, were investigated. All species, including postulated cool-stenotherms, showed broadly eurythermic developmental and morphological responses, and maintained both survivorship and oocyte production at elevated temperatures despite reductions in overall body size. There were subtle differences among species according to biogeographic affinity, with tolerances of Gondwanan species, which were narrower than those of cosmopolitan species, best characterised as ‘mesothermic’, but there was little divergence between populations. These results have implications for the understanding of diversity and distribution of Australian chironomids, and indicate that applicability of the Thermal Equilibrium Hypothesis to Australian lotic faunas may be limited.

Proposal for Theoretical Improvement of Semi-Physical Forest Fire Spread Models Thanks to a Multiphase Approach: Application to a Fire Spread Model Across a Fuel Bed

This paper is devoted to the improvement of semi-physical fire spread models. In order to improve them, a theoretical approach based on the multiphase concept was carried out. The multiphase approach which considers the finest physical phenomena involved in fire behaviour was reduced by making several assumptions. This work led us to a simplified set of equations. Among these, a single equation for the thermal balance was obtained by using the thermal equilibrium hypothesis. This approach has been applied to the improvement of our semi-physical model in order to take into account increasing wind influence. The predictions of the improved model were then compared to experimental data obtained for fire spread conducted across pine needle fuel beds. To this end, different slope values and varying wind velocities were considered. The experimental tendency for the variation of the rate of spread was predicted. Indeed, it increases with increasing wind velocity for a given slope as well as for a given wind with increasing slope.