Local Thermal Non-equilibrium Model Research Articles

Optimizing of a metal foam-assisted solar air heater performance: a thermo-hydraulic analysis of porous insert placement.

A numerical assessment of the heat transfer efficacy of a solar air heater (SAH) was carried out. The SAH is supplied with a porous metal foam layer to improve thermal mixing. Both the local thermal non-equilibrium (LTNE) and Darcy-extended Forchheimer (DEF) models were employed to forecast fluid and thermal transport within the partly filled SAH channel. The analysis was performed for various values of dimensionless foam layer lengths ( ), pore densities ( ), and Reynolds numbers ( ) at a fixed value of layer thickness ( ). Based on the position of the porous layer, three distinct arrangements, marked as Case 1, Case 2, and Case 3, were explored. Regarding the parameters examined, the findings indicate a definite improvement in the average Nusselt number ( ), but unfortunately, the friction factor also increases unfavorably. By reducing the length of the porous layer, a reasonable reduction in heat transfer rate and a significant decrease in pressure drop were noticed. The results showed about 26.64%, 48.73%, and 70.74% reductions in pressure drop by reducing the dimensionless foam length from 1 to 0.25, 0.5, and 0.75 respectively for at . On the other side, there are only about 11.05%, 23.11%, and 40.78% reductions in . The exhaustive analysis of the thermal performance of SAH was conducted using the thermal performance factor (TPF), which considers the trade-off between the SAH channel's potential for improved heat transmission and its cost for pressure loss. The TPF may reach a maximum of 2.82 compared to the empty channel when the metal foam layer is inserted with , for , and .

GRAPHITE FOAM STRUCTURES AS AN EFFECTIVE MEANS TO COOL HIGH-PERFORMANCE ELECTRONICS

Due to their unique heat transfer features, graphite foams are used in the current analysis to form heat sinks effective enough to dissipate extreme heat generated within high-performance electronics. The heat sinks proposed are formed from foamed-baffles arranged either in parallel or perpendicular to the coolant paths through the staggered slots in between to alleviate the penalty of pressure drop while maintaining high heat dissipation capability. Two different sorts of dielectric coolants namely, air and the FC-3283 electronic liquid developed by 3MTM, have been utilized to directly dissipate the heat generated. The feasibility of the currently proposed heat sinks has been examined numerically based on the volume averaging concept of porous media employing the local thermal non-equilibrium model to account for interstitial heat exchange between the foam solid matrix and the fluid particles flowing across. A wide range of design parameters has been tested including the heat sink configuration along with structural characteristics of the graphite foam used. It has been found that foam baffles oriented perpendicular to the path of coolant flow can dissipate heat by about 50% better than those parallel to it, but with higher pressure losses. It has also been found that heat dissipation capability, for a certain orientation of baffles, can be improved by up to 100% when the foam pore size is doubled with outstanding saving in pressure losses by up to 300%. The impact of operating conditions, including the coolant flowrate and the heat flux applied, has also been inspected. The currently proposed heat sinks have been found efficient to meet the thermal demands of high-performance electronics and sweep away the extreme heat generated there with reasonable cost of pressure drop, where the proper selection of design parameters in light of the operating conditions applied can prevent the emergence of hot spots entirely. Extreme operating conditions, i.e. with heat density of up to 10W/cm2 for air-cooled heat sinks and 100W/cm2 for those cooled with FC-3283, can be well managed when a heat sink is configured from baffles that are oriented perpendicularly to the coolant flow path and formed of graphite foam having low porosity (∅=0.8) and larger pore size

Numerical Simulation of Chemical Reactive Flow of Boger Fluid Over a Sheet with Heat Source and Local Thermal Non-Equilibrium Conditions

In this article, the effect of nonlinear heat source on chemical reactive flow of magnetized Boger fluid over a sheet with Marangoni convection and porous medium is explored. In the modelling, local thermal non-equilibrium (LTNE) conditions and heat sources are taken into account. The unique heat transport for both liquid and solid phases is provided by the LTNE model, which is based on thermal equations. As a result, various temperature profiles are used in this work for both the solid and fluid phases. It is essential for streamlining industrial procedures, improving material processing methods, comprehending biological systems like blood flow for medicine delivery, determining the environmental impact of pollutant dispersion, and increasing the effectiveness of oil and gas transportation. This model supports crucial decision-making processes in numerous disciplines by offering insights into the intricate interplay between reactive fluids, heat transmission, and chemical reactions. The appropriate similarity variables are used to compress the model equation system, and the shooting method and the conventional bvp4c solver are then used to solve the system numerically. Optimal homotopy approach is used to achieve residual errors. There are suggested best estimates for auxiliary variables. Results show that for larger values of the solvent fraction parameter, Boger fluid exhibits an enhanced velocity profile and a declining thermal profile of the liquid phase. The concentration and thermal profiles of both the solid and liquid phases are declined and enhanced the velocity of the Boger fluid for higher values of the Marangoni convection parameter.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection

The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.

LTNE effects on two‐layer configuration with throughflow

AbstractThe effect of throughflow on the beginning of convective motion in a fluid layer overlying a fluid‐saturated porous layer is examined theoretically in this article under the local thermal nonequilibrium model. We considered boundaries to be insulating to temperature perturbations. The normal mode approach is employed to analyze the governing equation for a composite configuration, with the solution sought through the regular perturbation technique to assess linear stability. The critical Rayleigh number, signifying the initiation of stationary convection, has been determined by solving the system of coupled equations. It is found that the system attains stability with increased porosity–conductivity ratios, regardless of the throughflow direction. This stability is consistently observed for depth ratios of 0.1 and 0.2. However, for higher depth ratios (0.5 and 1.0), the system exhibits dual nature stability when throughflow is present. Further, the stability of the system is enhanced by a graphical depiction illustrating how the throughflow parameter, porosity‐scaled conductivity ratio, depth ratio, Darcy number, and Prandtl number collectively influence the onset of convective motion.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.

Numerical Investigation on Transpiration Cooling Performance of Oriented Porous Structure Under Local Block Conditions

With the development of an active thermal protection system (TPS) for hypersonic vehicles, reliability improvement and weight reduction of TPS are key issues to be considered. In this paper, an oriented porous structure (OPS) is proposed to solve the local overheating problem in transpiration cooling. The transpiration cooling performances are investigated in a two-dimensional computational domain using a local thermal nonequilibrium model. The cooling mechanisms of OPS and uniform porous structure (UPS) under local block conditions have been numerically analyzed and compared. The results show that OPS leads to effective cooling of the overheated region by regulating the coolant flow behavior, especially in the case of serious block conditions. The maximum temperature reduction can be up to more than 200 K, and the maximum optimization rate can reach up to 23% compared to UPS. Moreover, OPS consumes less coolant and uses less driving force to deliver coolant when reaching the same peak temperature as OPS. This study shows that OPS has a better thermal protection effect in transpiration cooling, which can improve the reliability of TPSs, and that OPS can also achieve the lightweight of the aircraft.

Thermocapillary convection modes and phase change heat transfer characteristics of three-dimensional metal foam composited phase change materials with different aspect ratios under microgravity

This work aims to investigate the flow, heat transfer and phase change characteristics of porous media composite phase change materials with different aspect ratios in the thermocapillary mode under microgravity. A three-dimensional hydrodynamic model of thermocapillary-enhanced phase change heat transfer in the composite is developed. The model considers the shear stress boundary conditions on the porous free surface, employing the enthalpy-porosity method and the Darcy–Forchheimer model to describe the phase change process and fluid flow within the porous matrix, respectively, and the local thermal non-equilibrium model to describe the transient heat energy transfer between the paraffin and copper foam. The effects of different Marangoni numbers (Ma), aspect ratios (AR), Darcy numbers (Da) and porosities (ε) on the phase change heat transfer are compared. The results show that the increase of Ma from 6 × 104 to 2 × 105 accelerates the thermocapillary effect, and positively affect the thermal transport inside the cavity. The total melting time of the composite is reduced by 22.6 %, the heat storage efficiency is improved by 31.1 %, and secondary vortices appear in the convection zone. The large AR is favorable to the development of thermocapillary convection, but it also causes the reduced temperature gradient and heat transfer area of the heat source as well as the increased heat transfer distance. Compared to AR = 1, the total melting time increased by 34.4 % and 46.9 % for AR of 1.95 and 2.25 at a larger Ma, while the heat storage efficiency decreased by 26.5 % and 33.7 %, respectively. For a fixed ε, the decrease in Da hinders the development of convection, thus weakening the heat transfer and storage performance of the composite, and also causes heat conduction to dominate the phase change process in advance.

A Unified Approach to Two-Dimensional Brinkman-Bénard Convection of Newtonian Liquids in Cylindrical and Rectangular Enclosures.

A unified model for the analysis of two-dimensional Brinkman-Bénard/Rayleigh-Bénard/ Darcy-Bénard convection in cylindrical and rectangular enclosures (CE/RE) saturated by a Newtonian liquid is presented by adopting the local thermal non-equilibrium (LTNE) model for the heat transfer between fluid and solid phases. The actual thermophysical properties of water and porous media are used. The range of permissible values for all the parameters is calculated and used in the analysis. The result of the local thermal equilibrium (LTE) model is obtained as a particular case of the LTNE model through the use of asymptotic analyses. The critical value of the Rayleigh number at which the entropy generates in the system is reported in the study. The analytical expression for the number of Bénard cells formed in the system at the onset of convection as a function of the aspect ratio, So, and parameters appearing in the problem is obtained. For a given value of So it was found that in comparison with the case of LTE, more number of cells manifest in the case of LTNE. Likewise, smaller cells form in the DBC problem when compared with the corresponding problem of BBC. In the case of RBC, fewer cells form when compared to that in the case of BBC and DBC. The above findings are true in both CE and RE. In other words, the presence of a porous medium results in the production of less entropy in the system, or a more significant number of cells represents the case of less entropy production in the system. For small and finite So, the appearance of the first cell differs in the CE and RE problems.

Development and validation of a local thermal non-equilibrium model for high-temperature thermal energy storage in packed beds

High-temperature thermal energy storage (TES) in packed beds is gaining interest for industrial energy recovery. The wide range of temperature distributions causes significant variations in thermophysical properties of the fluid and solid phases, leading to inaccuracies of classical TES models and heat transfer correlations. The objective of this work is to develop and validate a detailed but pragmatic model accounting for high-temperature effects. Based on a literature survey spanning over several communities interested in high-temperature porous media, we propose a generic local thermal non-equilibrium model for granulate porous media accounting for conservation of mass, momentum and energy (two-equation temperature model). The effective parameters needed to inform the model are the effective thermal conductivities of the different phases and the heat transfer coefficient. An experimental-numerical inverse analysis method is employed to determine these parameters. A dedicated experimental facility has been designed and built to study a model granulate made of glass bead of 16 mm diameter. Experiments are conducted using the Transient Single-Blow Technique (TSBT) by passing hot air (ranging from 293 K to 630 K) through cold particles at various mass flow rates, covering a Reynolds number range of 58 to 252. The new model was implemented in the Porous material Analysis Toolbox based on OpenFoam (PATO) used to compute the transient temperature fields. Two optimization algorithms were employed to determine the parameters by minimizing the error between experimental and simulated temperatures: a Latin Hypercube Sampling (LHS) method, and a local optimization method Adaptive nonlinear least-squares algorithm (NL2SOL). The results indicate that the value of heat transfer coefficient hv in the two-equation model falls in the range of 1.0 × 104∼1.93× 104 W/(m3 K) under the given conditions. The axial dispersion gas thermal conductivity was found to be around 5.9 and 67.1 times higher than the gas thermal conductivity at Peclet numbers of around 55 and 165, respectively. Furthermore, two improved correlations of Nusselt number (Nu=2+1.54Re(T)0.6Pr(T)1/3) and of axial dispersion gas thermal conductivity (kdis,∥=0.00053Re(T)2.21Pr(T)⋅kg) are proposed and validated for a range of Reynolds number from 58 to 252. The overall approach is therefore validated for the model granulate of the study, opening new perspectives towards more precise design and monitoring of high-temperature TES systems.

A new LTNE analysis process for predicting the steady-state temperature distribution in a fixed bed of randomly packed mono-sized rough spheres based on pore-scale simulations

A new analysis process for the LTNE (local thermal non-equilibrium) model to solve for steady-state, fully-developed convection in mono-sized-sphere packed bed is proposed to predict the temperature distribution inside a fixed bed. For an actual mono-sized-sphere packed bed, the voidage lies between those of the regularly arranged beds of FCC, BCC, and SC. Through an interpolation/extrapolation process based on the pore-scale computation results of the SC, BCC, and FCC packings, the heat transfer parameters of a randomly packed bed can be calculated. To reliably estimate the local heat transfer rate, the regional mass flow rates in a packed bed are accurately predicted first. Then, the regional solid-phase thermal conduction can be independently evaluated without interference from the regional fluid-solid convection heat transfer. Additionally, a finite-thickness wall is constructed into the computational model to significantly improve the accuracy of the predicted radial temperature profiles. With realistic temperature self-adjustment within the wall, there is no need to set unrealistic boundary conditions of either isothermal, isoflux or their combinations at the outer face of the porous zone, as many conventional methods in the literature do. The solution process and necessary parameters are summarized into flowcharts. Finally, the accuracy of the new LTNE analysis process in predicting the temperature distribution throughout the packed bed is validated with the literature experiment. In contrast, the conventional methods fail to provide the correct trend of the temperature variation.

Entropy generation minimization of hybrid nanofluid mixed convection flow in lid-driven square enclosure with heat-generating porous layer on inner walls

PurposeThis study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe3O4/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.Design/methodology/approachThe dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.FindingsThe roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.Originality/valueThe analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

Outlining the impact of discrete filling of metal foams on thermodynamic performance

The desire of this paper is to present the numerical analysis of thermodynamic performance of high porosity metal foams with discrete filling inside the horizontal pipe. The heater is embedded on the pipe’s circumference and is assigned with known heat input. To enhance heat transfer, aluminum metal foam of 10 PPI (pores per inch) with porosity 0.95 is filled into the pipe. In filling, two kinds of arrangements are made. In the first arrangement, the metal foam is filled adjacent to the inner wall of the pipe (Model (1–3)), and in the second arrangement, the metal foam is located at the center of the pipe (Model (4–6)). So, six different models are inspected for different fluid velocities (0.7–7 m/s) under turbulent flow conditions. Darcy Extended Forchheimer (DEF) is combined with local thermal non-equilibrium (LTNE) models for estimating the flow features and heat transfer via metal foams and initially validated with experimental outcomes. The application of the second law of thermodynamics via metal foams is the novelty of current investigation. In the study, the thermal performance is assessed in terms of heat transfer enhancement ratio and heat transfer performance ratio, and the thermodynamic performance is evaluated based on exergy and irreversibility analysis. In the analysis, the parameters like mean exergy based Nusselt number (Nue), heat transfer and flow frictional irreversibility are considered for the evaluation. The overall thermal performance and exergy transfer found higher in Model (1–3) than the Model (4–6) respectively. The flow and heat transfer irreversibility found less in Model (1–3) than the Model (4–6) respectively. The superior thermodynamic performance is obtained from the metal foam filled cases than from the clear pipe. In that, Model-2 suits the best configuration for designing the thermal system.

Latent heat thermal energy storage in a shell-tube design: Impact of metal foam inserts in the heat transfer fluid side

The improvement of heat transfer in latent heat thermal energy storage (LHTES) system is a crucial task. In the current study, the impact of diverse metal foam (MF) layer arrangements on heat transfer fluid (HTF) within a shell-tube LHTES is explored. Six distinct cases (A-F) with varied MF coverage percentages and layer dimensions were assessed. The local thermal non-equilibrium model was utilized to take into account the PCM and MF temperatures. The finite element method was used for solving the partial differential equations. The impact of MF configurations and inlet pressures (250 Pa, 500 Pa, and 750 Pa) on the thermal energy storage/release was addressed. Cases A-C, featuring a 50 % MF concentration, exhibit shorter melting times than Cases DF, with decreasing MF concentrations. A higher MF concentration improves the melting process due to increased thermal conductivity and lower thermal resistance on the HTF side. Cases DF, with a centralized MF layer and decreasing concentrations from 25 % to 6.25 %, display progressively shorter melting times, suggesting that a lower MF concentration leads to more efficient melting. Solidification times also decrease with increasing inlet pressures across all cases. Reynolds numbers, influenced by average HTF tube outlet velocity, vary substantially across cases and inlet pressure differences. Cases A-C demonstrate similar Reynolds numbers for each inlet pressure difference, while Cases DF show a more pronounced increase in Reynolds numbers as the MF layer is reduced and flow resistance drops. Cases A (50 % MF layer) and F (6.5 % MF layer) provide the quickest charging and discharging times due to their unique combination of MF layer properties and inlet pressures. The study highlights the need to consider MF layer composition and inlet pressure when designing optimal LHTES systems for efficient energy storage/release.

Investigating the impact of modeling assumptions and closure models on the steady-state prediction of solar-driven methane steam reforming in a porous reactor

In this work, the effect of different modeling assumptions and closure models — frequently considered in the literature of solar thermochemical reactors and closely-related areas — is investigated. The application of different modeling assumptions and closure models may strongly affect the results accuracy and compromise a meaningful comparison across literature works. The following is herein investigated: (i) the role of upstream and downstream fluid regions to the two-phase reactor region; (ii) relevance of species and gas-phase thermal diffusion mechanisms; (iii) reaction heat accounted for in gas- or solid-phase energy balance equations; (iv) local thermal equilibrium (LTE) vs. local thermal non-equilibrium (LTNE) models; (v) model dimension (one-dimensional vs. two-dimensional axisymmetric models); (vi) local volumetric convection heat transfer correlations; and (vii) effective solid thermal conductivity correlations. The relevance of this work extends well beyond the current application (methane steam reforming in a volumetric solar reactor), since similar models and assumptions have also been widely applied for predicting the performance of volumetric solar absorbers and dry reforming solar reactors. The results show that an upstream fluid region should be considered while applying inlet first-type boundary conditions and diffusion transport in the corresponding governing equations to ensure full-conservation and simultaneously to account for developing profiles upstream the reactor inlet section. For the operating conditions considered, species diffusion and gas-phase heat conduction are particularly relevant at the reactor centerline but with a negligible integral effect. A significant difference in the reactor performance is observed while accounting for the reaction heat from surface reactions in the solid- or gas-phase energy balances — for the lowest inlet gas velocity herein considered, the thermochemical efficiency (methane conversion) is approximately equal to 70.8% (76.3%) and 77.3% (84.7%) assigning the reaction heat to the gas- and solid-phase energy balances, respectively. LTE model results are strikingly different from the results obtained with the LTNE model considering the reaction heat accounted for in the gas-phase energy balance but not significantly different from the results computed with the LTNE model with the reaction heat assigned to the solid-phase energy balance. One-dimensional reactor modeling provided with an average concentrated solar heat flux value results in a similar average performance as that given by a two-dimensional model but fails to predict the high temperatures observed at reactor centerline — for the lowest inlet gas velocity, the difference between the maximum solid temperatures predicted by one- and two-dimensional models is about 340K.

Prediction and control of elevated temperatures within landfills under aeration and recirculation based on the thermal non-equilibrium model

Aeration is an effective approach to sustainable landfilling but may lead to elevated temperatures within landfills, resulting in landfill fires or explosions. Therefore, aeration is usually combined with leachate recirculation to control the elevated temperatures within landfills. To predict landfill temperatures during aeration and recirculation, a local thermal non-equilibrium model is developed considering the heat generation of biodegradation, the heat removal due to evaporation and leachate-gas flow, and the effects of the capillary. The solver is implemented in OpenFOAM based on the finite volume method and validated against a waste-column experiment and an in-situ aeration test. The simulation results demonstrate that the assumption of local thermal equilibrium will distinctly overestimate the temperature, maximally by 15 °C in the studied case. The model is then used to simulate a typical aerobic landfill unit to investigate the formation of explosive gas mixtures and elevated temperatures under different operating conditions. The simulation results of gas composition suggest that aeration will not result in explosive gas within landfills. A reasonable recirculation method for temperature control with corresponding operating parameters under a group of values of aeration pressure (2000–4000 Pa) and recirculation rate (0.0001–0.0008 m/s) are proposed, which can provide some guides for the design of an aeration and recirculation combined system. For a given total volume of added leachate, a higher recirculation rate does not always mean better cooling, and the cooling effect of continuous recirculation is better than that of intermittent recirculation.

Natural Convection in a Newtonian Nanoliquid-Saturated Porous Enclosure with Local Thermal Non-Equilibrium Effect

Buoyancy-driven convective flow and heat transfer characteristics in a Newtonian nanoliquid-saturated porous square enclosure are analyzed numerically using a local thermal non-equilibrium model. An enclosure’s horizontal walls are considered free–free and adiabatic, and the vertical walls are free–free isothermal boundaries. The dimensionless governing equations are solved using a central finite difference scheme with second-degree accuracy, and the results are in satisfactory agreement with the earlier works. The impact of various parameters on streamlines and isotherms is analyzed and depicted graphically. The effect of Darcy number, thermal Rayleigh number, and the ratio of thermal conductivities slow down the liquid flow. The temperature distribution is maximum at sidewalls and diminishes the amount of heat transport. The opposite phenomenon is observed for the solute Rayleigh number and interphase transfer coefficient of liquid-particle phases. For large values of interphase heat transfer coefficients, liquid-solid and liquid-particle are said to be in the local thermal equilibrium phase. The amount of heat transfer increases with an increasing interphase heat transfer coefficient and the ratio of the phases’ thermal conductivities. Results of local thermal equilibrium situation can be obtained as the particular case of the study. The amount of heat transfer is maximum in the local thermal non-equilibrium situation, and enhanced by 0.09% compared with the local thermal equilibrium situation. Heat transport is 0.74% less in the sparsely packed porous medium compared with the low-porosity medium.

Numerical analysis of the heat transfer enhancement by using metal foam

Forced convection heat transfer in metal foam pipe under uniform heat flux was investigated numerically. Water has been used as the fluid medium in numerical simulations with copper metal foam. The test sample used metal foam for four cases (A, B, C, and D) by using varying thicknesses of foam along the pipe. In case (A), the pipe was completely filled with metal foam; in case (B), the pipe was partially embedded with metal foam and close to the wall; in case (C), the pipe was partially filled in the section's center; and in case (D), the pipe was partially filled in the form of three sections along the pipe. The foam employed in this study has a porosity of 0.90 and pore density ranges from (10–40) PPI. The fluid and energy transfers are simulated using the Forchheimer-extended Darcy equation and the local thermal non-equilibrium (LTNE) model. The simulation is performed using the commercial software FLUENT with specific boundary conditions. Turbulence was taken into account using the k- ε model. The results reveal that when the pipe is filled partially with metallic foam as indicated in case B, the Nusselt ratio rises due to the velocity gradient and temperature distribution is more homogenous inside the pipe led to enhancement in overall heat transfer. Also, the metallic foam 40PPI has a highly Nusselt number ratio, with a big value equal to 5.5 in case B due to the highly conductive surface area of heat transfer from the wall heated to the fluid. Additionally, the pipe in case A was completely filled with metallic foam, resulting in a bigger pressure drop than in the other cases, which increases flow resistance. The metal foam in case C, which is centered in the pipe's center, has the lowest pressure drop measurement. The 10PPI metallic foam exhibits the highest performance factor when compared to other metallic foam.

Experimental investigation on the validity of the local thermal equilibrium assumption in ablative-material response models

Thermal Protection Systems (TPS) material response models rely on the assumption of local thermal equilibrium (LTE) between the solid phase and the gas phase. This assumption was challenged and investigated by several authors but a sufficiently precise knowledge of heat transfer coefficients in TPS materials was lacking to reach final conclusions. The objective of this work is to contribute to filling this gap by providing a literature review of available data in other communities (thermal energy storage, heat exchangers) and by performing an experimental characterization of Calcarb, a commercial carbon preform used for manufacturing thermal protection systems. Heat transfer within Calcarb was studied experimentally in the Through-Thickness and in the In-Plane directions for Reynolds numbers of 1 to 4 - representative of the TPS application - using the transient single-blow technique. Numerical parameter estimation was performed using the Porous material Analysis Toolbox based on OpenFoam (PATO) and the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA). The heat transfer coefficient hv is found to be greater than or equal to 108 W/(m3K) and the LTE assumption is shown to be valid in the conditions of the experiment. To assess the validity of the LTE assumption for other conditions, the above bound of hv may now be used in combination with a local thermal non-equilibrium model.