Thermal Conductivity Of Solid Phase Research Articles

On the relative contribution of solid-phase heat transfer in 3D printed baffled logpile catalyst structures

Recently introduced 3D printed baffled logpile catalyst structures provide increased fluid-phase convective heat transfer thanks to a cross-flow regime, leading to a favorable trade-off between heat transfer and pressure drop in fixed bed reactors. The role of the solid-phase heat transfer was not yet addressed, which is the purpose of the current work. Specifically, 3D computational fluid dynamics simulations were used to map the heat transfer — pressure drop trade-off for nine different structures as a function of the superficial velocity and the solid-phase thermal conductivity. It was found that for structures without baffles, the solid-phase heat transfer dominates even at low solid-phase thermal conductivity (0.25Wm−1K−1). As the baffle gap spacing decreases, the fluid-phase contribution becomes increasingly more relevant for the baffled structures, underlining the added value of the baffles. The performance parameters were correlated to facilitate design considerations for reactors with 3D printed catalyst internals (in the range 3<Rep<18). An exemplary reaction case was also presented, through which it is shown that the conversion of the steam methane reforming process can be increased through the use of the baffled structures, further demonstrating the process intensification potential.

Significance of the natural convection to the heat transfer of porous media: A pore-scale study

Heat conduction in porous media is generally accompanied by the natural convection of the fluid within the pores driven by the temperature gradient. However, the criterion to determine the critical pore size of porous media where the natural convection cannot be neglected remains elusive. In this study, a pore-scale model is established to investigate the contributions of natural convection on the effective thermal conductivity (ETC) of porous media, which takes the reconstructed microstructures as the geometry input. We thus examine the effects of the porosity, thermal conductivity of the fluid and solid phases, and heating direction on the critical pore size where the natural convection starts to work. The results show that the critical pore size decreases with increasing porosity and heating temperature, but increases with the rise in the thermal conductivity of solid phase. Moreover, the critical pore size is significantly lower for the lateral heating, compared with the bottom heating. Finally, we proposed a new formula as an indicator to determine the significance of natural convection to the heat transfer in porous media.

Transient Thermal Performance of Phase-Change Material Infused in Cellular Materials Based on Different Unit Cell Topologies

Abstract Phase change material (PCM) employment in thermal management and energy storage applications is limited due to their inherently low thermal conductivity. Significant enhancement in the thermal performance of PCMs can be obtained when infused in porous media with high porosity and high solid-phase thermal conductivity. Earlier studies typically employ high porosity aluminum foams obtained via a conventional manufacturing process, commonly known as foaming. A typical representative unit cell of metal foams obtained via foaming process can be of tetrakaidecahedron shape. The conventional manufacturing process of high porosity metal foams offers limited flexibility over unit cell shape, porosity, and pore density. Metal additive manufacturing advancements have the potential to address this manufacturing limitation and provides freedom in the above design domain. To this end, we have explored four different unit cell topologies, viz., octet, tetrakaidecahedron, face-diagonal cube, and cube, for their role in enhancing the transient thermal performance when infused with PCMs. An enthalpy-porosity method has been employed to model the phase-change process for wide range of variables. It has been found that the presence of solid media results in significant enhancement in PCM's thermal performance, and the Octet-shaped unit cell outperformed the other unit cell topologies explored in this study.

Volumetric solar carbon dioxide receiver designs with geometric parameters optimized in combination

Porous volumetric solar receivers with carbon dioxide as the working fluid can simultaneously harvest solar energy and utilize carbon dioxide. This means they hold promise for next-generation solar thermal power applications. The optimization of porous receivers has been performed in many works with their geometric parameters optimized using an exhaustive method. Such methods are computationally intensive and their deduced design guidelines are not consistent. This work presents a distinct design method where geometric parameters (porosity, pore size, and length) are combined into three heat transfer parameters (volumetric convection coefficient, effective solid-phase thermal conductivity and optical thickness), so that they are optimized in combination. The optimization objective is the combination of a large volumetric convection coefficient, a large effective solid-phase thermal conductivity and an optimal optical thickness. The corresponding combination of parameters is a small pore size, a small length and a moderate porosity. Guided by this criterion, the best combination is 0.4 mm pore size, 4 mm length and 0.85 porosity, which result in a corresponding thermal efficiency of 71.5%. This combination is consistent with that from the exhaustive method and the optimization complexity for the developed method is reduced by two dimensions.

A thermal conductivity model for insulation materials considering the effect of moisture in cold regions

Insulation is an important material for energy conservation and frost heave reduction in cold regions. The thermal conductivity of the insulation materials is usually considered as a constant. However, their thermal performance degenerates due to the absorption of water. To describe the variations of thermal conductivities with water content, a thermal conductivity model for three-phase insulation material was proposed by considering the insulation material's porous and moisture absorption characteristics. A tortuosity correction was introduced to reflect the heat conduction path. Then, the measured results and the existed models were used to evaluate availability of the proposed model. Finally, the quantitative influence of the porosity, water content, and thermal conductivity of solid phase on the thermal conductivity of wet insulation materials was analyzed. The results show that there is close agreement between the predicted results of the new model and the measured ones, with the maximum relative error <15%. The model with tortuosity correction can effectively calculate the thermal conductivities of the insulation materials in a full range of porosity (from 0 to 1). The thermal conductivity decreases with the increase of porosity, but increases with the increase of water content. The solid phase's thermal conductivity has little influence on the thermal conductivity of the insulation materials. The study can provide an effective method to predict the thermal performance variation of the insulation material due to the effect of moisture content in cold regions.

BN white graphene well-dispersed solar salt nanofluids with significant improved thermal properties for concentrated solar power plants

Solar salt is the most commonly used medium for thermal storage and transfer in concentrated solar power (CSP) plants, and the utilization efficiency of solar energy is depended on the thermal properties of solar salt. In this work, atomic-layer-thick hexagonal boron nitride nanosheet (BNNSs, so called white graphene) were obtained and dispersed into solar salt uniformly to produce composites nanofluids. Attributed to the ultra-high thermal conductivity and a large specific surface area of BNNSs, which reduce the thermal resistance, and facilitate forming of more semi-solid boundary layer and nucleation sites, the as-prepared composites nanofluids show superior thermal properties. The properties enhancement mechanism and effects of the mass fraction of BNNSs on the thermal properties of nanofluids was investigated carefully. Compared with the pure solar salt, the solid-phase thermal conductivity, solid-phase and liquid-phase specific heat capacity was elevated by 76.79%, 29.8% and 12.82%, respectively. At the same time, the supercooling degree was significantly decreased from 12.2 °C to 4.7 °C. The enhanced thermal conductivity and specific heat capacity offer significant cost savings, and the reduced supercooling degree prevent phase separation and pipe blockage. Thus, the developed composites nanofluids can be used as a superior medium for CSP plants.

Enhanced Forced Convection through Thin Metal Foams Placed in Rectangular Ducts

This study reports a parametric numerical investigation to elucidate the thermal-hydraulic performance of metal foam for cooling applications. In this study, both spanwise and streamwise size of metal foams having high porosity value of ∼0.95 is varied, along with the solid-phase thermal conductivity and pore-density of metal foams, for both air and water as working fluid flowing at different Reynolds number. Thinner foams (in spanwise) and shorter foams (in streamwise) were found to have highest convective heat transfer coefficient at a certain pumping power, with water-based configurations yielding ∼10 times more heat dissipation at a certain pressure drop when compared to air-based configurations.

The effect of local thermal non-equilibrium on the onset of thermal instability for a metallic foam

Mixed convection in metallic foams modeled with Darcy's law under local thermal non-equilibrium conditions is investigated, where the solid phase thermal conductivity is assumed to be infinitely larger than its fluid phase counterpart. A linear and modal stability analysis was employed to evaluate the convective and absolute instability thresholds as well as their respective cell patterns. This analysis indicates that local thermal non-equilibrium always has a stabilizing effect and the spanwise uniform mode is always the most unstable. At the onset of convective instability, however, the number of equally unstable cell patterns increases with both the aspect ratio and the local thermal non-equilibrium strength.

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.

Multi-physics modeling of thermochemical heat storage with enhance heat transfer

• A multi-physical model of CaO/Ca(OH) 2 hydration process is simulated. • Thermal conductivity of solid-phase has a significant effect on hydration process. • Relationships between fins and reaction are explored. • Axial fins shorten the exothermic time to 83.4%. Thermochemical heat storage technology is an important component in energy system, and plays a key role in the balance of energy supply and demand. A multi-physics model is constructed to study the hydration process in a tubular reactor, including fluid flow, heat transfer and reaction. Variations of temperature and conversion of CaO are discussed in detailed to reveal exothermic reaction characteristics. Besides, effects of different reaction conditions during hydration are studied, such as porosity, temperature, pressure, flow rate and thermal conductivity. It is found that the low thermal conductivity of solid-phase is the most important factor which limits the reaction. The heat transfer process can be greatly promoted by adding fins, due to the high heat conductivity. However, the relationship between the reactor structure and the performance of the thermochemical heat storage is not quantitatively clear. The present study aims to investigate the impact of the arrangement of fins on the hydration process. Finally, different types of fins with high thermal conductivity are employed in the reactor. Attributing to the fact that the equilibrium temperature is affected by the vapor pressure, thermochemical reactors with different fin configurations have different flow characteristics and pressure drops, leading to different reaction characteristics. It is shown that the exothermic time was reduced to 84.32% (axial fins), 89.97% (radial fins), and 88.71% (spiral fins) of the original, respectively. This study can reveal the coupling relations of multi-physics fields in thermochemical heat storage, and provide theoretical basis for the design of thermochemical heat storage reactors.

Examination on aerogel based on the heat transfer characteristics of nanotechnology

With the rapid development of global industrialization, the research and development of new thermal insulation materials has great social and economic significance for national development and social progress. Due to the porous network structure of nanotechnology, the porosity of aerogel is 80–99.8%, the thermal conductivity can be as low as 0.013 w/(m k) at room temperature. It is the best insulation material by far, it has important value in the fields of aerospace, petrochemical, electric metallurgy, shipbuilding, precision instruments and so on. This paper is based on aerogel nanotechnology materials at home and abroad. In order to solve the problem of the study on heat transfer characteristics based on nanotechnology is not perfect, and the calculation model of solid phase thermal conductivity coefficient and total thermal conductivity of complex nanotechnology structure is not accurate enough. Through a heat transfer calculation method suitable for nanotechnology to conduct more detailed and in-depth research on these issues, introduces and analyzes the development of the equivalent thermal conductivity calculation model of Novel Aerogel nanotechnology insulation material in recent years. And analyzed The heat transfer characteristics and thermal insulation principle of nanotechnology aerogel by using equivalent thermal conductivity calculation model of aerogel nanotechnology insulation material. Research indicates: For aerogel nanotechnology materials, Use heat transfer calculation method aerogel nanotechnology insulation materials can be well calculated using a heat transfer calculation method that suitable for nanotechnology can calculate the equivalent thermal conductivity of aerogel nanotechnology insulation material very well; nanotechnology particles and aerogel meshes and continuous spatial network structures are reason for the very low thermal conductivity of aerogels; The heat transfer of the material is mainly achieved by convection, radiation and heat transfer. So it is possible to reduce the thermal conductivity from the heat transfer path of the material.

Influence of swelling and non-swelling clays on the thermal properties of grouting materials for borehole heat exchangers

Grouting materials for borehole heat exchangers often contain rheological additives. Typically, swelling clays are added to benefit from their thixotropic behavior, helping to adjust the stability and flowability of the grouting suspension. Clay compounds without swelling clay minerals but with similar control effects in case of suspension stability and flowability due to their surface charges and structure are usually not used specifically in such geotechnical applications. However, it is conceivable that the thermal conductivity of a water-saturated grout might be higher with non-swelling clays than with swelling clays due to the higher solid phase thermal conductivity of non-swelling clay minerals. In this work, thermophysical, hydraulic and mechanical properties of geothermal grouts containing swelling or non-swelling clays were investigated. It was aimed not to negatively affect the important grout properties despite the replacement of swelling clays by non-swelling clays. The results of this laboratory study showed an increase in thermal conductivity of 5% by substituting swelling clays with non-swelling clays and can be an approach to further optimize grouting materials.

Advances in the Development of Sol-Gel Materials Combining Small-Angle X-ray Scattering (SAXS) and Machine Learning (ML)

The requirements for new materials are increasing with each new application, which, in most cases, means an enhancement in the complexity of the development process. Nanoporous sol-gel-based materials, especially aerogels, are promising candidates for thermal superinsulation, electrodes for energy conversion and storage or high-end adsorbers. Their synthesis and processing route is complex, and the relationship between the material/processing parameters and the resulting structural and physical properties is not straightforward. Using small-angle X-ray scattering (SAXS) allows for fast structural characterization of both the gel and the resulting aerogel; combining these results with the respective physical properties of the aerogels and using these data as inputs for machine learning (ML) algorithms provide an approach to predict physical properties on the basis of a structural dataset. This data-driven strategy may be a feasible approach to speed up the development process. Thus, the study aimed to provide a proof of concept of ML-based model derivation from material, process and SAXS data to predict physical properties such as the solid-phase thermal conductivity (λs) of silica aerogels from a structural dataset. Here, we used different data subsets as predictors according to different states of synthesis (wet and dry) to evaluate the model performance.

A new pool boiling heat transfer correlation for wetting dielectric fluids on metal foams

Porous structures, as metal foams, can enhance the heat transfer performance. For a safe industrial application, a predictive model for both heat transfer coefficient and maximum heat flux is required. But, there is no correlation for dielectric fluids on metal foams available in the literature. This work aims to develop a correlation based on dimensional analysis for metal foam surfaces in pool boiling with different dielectric fluids. The model takes into account the porous heating surface characteristics (porosity, pore diameter, and thickness), the working fluid thermophysical properties, and its interaction. The model was developed based on the experimental database obtained by the authors and validated with the open literature database. Two metal foams with different characteristics were used for carrying out the pool boiling tests with two different working fluids: HFE-7100 and ethanol. The newly developed correlation predicted well the database with an average error equal to 10.8% where 93.8% within the error range of ± 30%. To the maximum heat flux, the average error was 13.6% where 100% within the error range of ± 30%. The pore diameter and thickness play an important role in both models. The porosity and solid-phase thermal conductivity from the metal foam change the porous medium thermal conductivity, which influences the heat transfer coefficient (HTC). Finally, the properties of the working fluid also influence the predictive model, mainly the latent heat of vaporization, liquid thermal conductivity, and saturation temperature.

An effective thermal conductivity model of rocks considering variable saturation and pore structure: Theoretical modelling and experimental validations

The effective thermal conductivity (ETC) of rocks is crucial for many geological and engineering applications and projects. In this study, a three-component ETC model was proposed, which includes seven parameters, that are, the thermal conductivities of water (λw), gas (λg) and solid phase (λs), the porosity (φ), the coefficient of shape factor (n), the weighted harmonic parameter (η) and saturation degree (Sr). The methods to establish the parameters of the proposed model were described with validation carried out using several experiments including X-ray diffraction (XRD) test, porosity test and thermal conductivity test. Comparisons performed indicated that the new proposed model was flexible enough to reflect the variation of the ETC with saturation degree. Furthermore, the sensitivity analysis and grey correlation analysis were given in examining the effect of the parameters included in the model. The results showed that: 1) The parameter sensitivity analysis and grey correlation analysis of ETC show that the ETC is most sensitive to the thermal conductivity of solid phase (λs), followed by coefficient of shape factor (n), weighted harmonic parameter (η) and saturation degree (Sr), and less sensitive to the porosity (φ). 2) When the pore shape of the porous media is irregular or the thermal conductivity ratio of the continuous phase and discontinuous phase is larger than 100, n is a key parameter that can tremendously influence the value of ETC. 3) Although the change of η does not influence the maximum and minimum values of ETC, it can greatly affect the variation of ETC when 0 < Sr < 1.

Reduced thermal conductivity of nanoparticle packed bed by hybrid design

Nanoparticle packed bed (NPB) as a kind of promising thermal insulation material (TIM) has drawn widely concern because of their lightweight and ultra-low thermal conductivities (k). In this paper, breaking through the conventional wisdom that the TIM adopts the amorphous morphology, we develop the hybrid NPB (h-NPB) with the crystal morphology for thermal insulating application. The hybrid design of crystal nanoparticle benefits the reduced k together with the enhanced mechanical strength. The lowest effective thermal conductivity (ke) as low as 0.018 W m−1 K−1 is achieved in (3:7) h-NPB, which is inferior to the k of the free air and most prevalent TIMs. The mechanism can be understood by the quite low solid-phase thermal conductivity (ks), negligible thermal conductivity of the confined air (ka) and small radiative thermal conductivity (kr). Neglecting the ka, the minimum ke occurs at the porosity where domination role changes from ks to kr. In addition, an excellent mechanical strength, nearly 40-50 % compared to bulk silica, is harvested in silica h-NPB, guaranteeing the practical application. This study is expected to supply some information for the design of next generation TIM characterized with the lightweight, high strength and low k.

Numerical Assessment of Heat Transfer and Entropy Generation of a Porous Metal Heat Sink for Electronic Cooling Applications

In the present study, the thermal performance of an electronic equipment cooling system is investigated. The heat sink used in the current cooling system consists of a porous channel with a rectangular cross-section that is assumed to be connected directly to the hot surface of an electronic device. In this modeling, a fully developed flow assumption is used. The Darcy–Brinkman model was used to determine the fluid flow field. Since using the local thermal equilibrium (LTE) model may provide results affected by the error in metal foams, in the present research, an attempt has first been made to examine the validity range of this model. The local thermal non-equilibrium (LTNE) model taking into account the viscous dissipation effect was then used to determine the temperature field. To validate the numerical solution, the computed results were compared with other studies, and an acceptable agreement was observed. Analysis of the temperature field shows that if the fluid–solid-phase thermal conductivity ratio is 1 or the Biot number has a large value, the difference between the temperature of the solid phase and the fluid phase decreases. Moreover, the effect of important hydrodynamic parameters and the porous medium characteristics on the field of hydrodynamic, heat, and entropy generation was studied. Velocity field analysis shows that increasing the pore density and reducing the porosity cause an increase in the shear stress on the walls. By analyzing the entropy generation, it can be found that the irreversibility of heat transfer has a significant contribution to the total irreversibility, leading to a Bejan number close to 1. As a guideline for the design of a porous metal heat sink for electronic equipment, the use of porous media with low porosity reduces the total thermal resistance and improves heat transfer, reducing the total irreversibility and the Bejan number. Moreover, the increasing of pore density increases the specific porous surface; consequently, it reduces the total irreversibility and Bejan number and improves the heat transfer.

A cylindrical self-consistent modelling of vegetal wools thermal conductivity

In recent years, the fight against climate change has come to the fore. In this scope, the use of vegetal wools, which can store carbon dioxide, is particularly relevant for developing greenbuilding solutions. Moreover, considering their high porosity levels, the thermal performances of these materials can compete with conventional insulators ones. These performances are related to the microscale vegetal fibres specificities that are used in the wool manufacturing process. So, a self-consistent modelling approach is developed in order to model the vegetal wools thermal properties as a function of their microscale parameters. To do that, a simplifying assumption assimilates the fibres to a representative elementary volume based on a biphasic (including solid and fluid phases) cylindrical inclusion. This model has been validated in the specific case of a flow perpendicular to the fibres by comparison with experimental characterisations performed on four materials in real hygrothermal conditions and with data from literature. Thanks to a parametric analysis, it is finally shown that for high porosity values (>95%), vegetal wools thermal properties present interesting values regardless of the solid phase thermal conductivity.

Enhancement of solid-phase thermal conductivity and specific heat of solar salt through addition of MWCNT: new observations and implications for thermal energy storage

Solid-phase thermophysical properties of solar salt (a mixture of NaNO3 and KNO3) influence the performance of sensible heat and latent heat thermal energy storage systems. Solar salt’s lower thermal conductivity imparts kinetic limitation during the discharge cycle and hence its thermal conductivity needs to be enhanced. This work is aimed at studying the influence of MWCNT incorporation on the improvement of solid-phase thermophysical properties of solar salt. Accordingly, experiments were carried out to study the influence of method of MWCNT-solar salt preparation, MWCNT concentration and temperature on solid-phase specific heat and thermal conductivity. Our results reveal that 0.5 wt% MWCNT-solar salt composite prepared by ultrasonication and milling for an appropriate time lead to 18.3% enhancement in the solid-phase thermal conductivity and 18% enhancement in the solid-phase specific heat. In addition, the total energy storage capacity over the temperature range of 50–270 °C (including solid–liquid phase change) is amplified by 11.5%. These results augur well for deployment of the MWCNT-solar salt composite in the thermal energy storage system as a storage medium.

Pulsed laser melting of bismuth telluride thermoelectric materials

While laser melting, deposition, and annealing of semiconductor thin films are well-established, pulsed laser processing of bulk semiconductor material powders has been minimally investigated. This work investigates nanosecond pulsed laser melting of bismuth telluride, a common thermoelectric material. Using both experimental and computational modeling methods, a process window was determined in which melting is achieved before ablation occurs. The process window was determined for Bi2Te3 powder compacts, with melt depths on the order of 20–100 μm. The melted region had a fine-grained, columnar microstructure and showed typical selective laser melting defects such as microcracking. Stroboscopic imaging was used as an in situ imaging technique to observe molten pool features, revealing a teardrop-shaped molten pool with little resolidification between pulses. A simplified thermal model of the nanosecond pulsed laser melting process was developed, and two models for the solid phase thermal conductivity were used to investigate the impact of thermal conductivity on the size, shape, and duration of the molten pool. The results demonstrate the narrow process window available for pulsed laser processing of bulk bismuth telluride powders, and the discussion includes thermal management approaches possible for reducing defects such as microcracking.