Steady-state Heat Flow Research Articles

Automatic Image Analysis Method as a Tool to Evaluate the Anisotropy of Autoclaved Aerated Concrete for Moisture and Heat Transport

In this article, the results of studies testing the anisotropy of autoclaved aerated concrete in terms of water and heat transport are presented. Using image analysis techniques, a study was conducted on four different samples of concrete produced in the same process. To ensure the comparability of results, the pictures were taken from a fixed distance with the same lens settings trimmed to a set size. Cross-sectional profiles of the material were examined and were arranged in two directions: perpendicular and parallel to the growth direction occurring in the autoclave. For each block, approximately 4750 objects were obtained, with an average of 2700 objects along the wall and 2050 across it. As a result of the comparative analysis, metrics concerning pores, significantly distinguishing the profile direction, were identified. These included the pore area (area), the maximum and minimum distance between points on the perimeter (Feret, MinFeret), lengths of the major and minor axes of the fitted ellipse (major, minor), and the ratio of the area of selection to its convex hull (solidity). As a reference, standard investigations were conducted for moisture transport using the time domain reflectometry setup and for thermal conductivity values using the steady-state heat flow plate apparatus.

Influence of inhomogeneous magnetic field source location on the intensity of thermomagnetic convection in a closed loop

Purpose. Obtaining information on the influence of the location of the inhomogeneous magnetic field source relative to the heated section of a vertical hydrodynamic loop filled with magnetic fluid on the intensity of convective heat transfer along the loop.Methods. Experiments were carried out using a hydrodynamic loop made of a thin tube of circular cross-section and placed in a vertical plane. Heat source was carried out by a heater on a short vertical section of the loop, and heat removal was implement out by blowing the entire surface of the tube with thermostated air. The source of the magnetic field was the flat pole tips of the ferrite magnetic core, in the gap between which the heater was located. The position of the pole tips relative to the heater varied vertically in the experiments. In the control experiments, the source of the magnetic field was deleted. The circuit was filled with medium concentrated magnetic liquid of the type "magnetite - kerosene - oleic acid". The intensity of steady-state convective heat flow along the tube was calculated from the results of measuring the tube surface temperature by copper-constantane thermocouples. The measurement results were presented in dimensionless form - the relationship between the Nusselt number and Rayleigh number.Results. The unfluctuating mixed, thermomagnetic and gravitational, convection of the magnetic fluid in the loop was observed at any location of the pole tips of the magnetic core relative to the heater. At location of pole tips above the heater, competition of gravitational and thermomagnetic convection was observed, and the heat flux was weak. When the pole tips were placed below the heater, the Nusselt number was 2 - 4 times higher than in the control tests (only gravitational convection) with equal Rayleigh numbers. The highest Nusselt numbers were obtained when the field source was placed in center of the heater.Conclusion. Information on the influence of the relative location of the magnetic field source and the heater on convective heat transfer by magnetic fluid in a hydrodynamic loop is obtained experimentally. The optimal concerning of heat transfer intensity position of the field source was found.

Effective thermal conductivity of LaNi5 powder beds for hydrogen storage: Measurement and theoretical analysis

Accurately measuring and analyzing the effective thermal conductivity of metal hydride beds is critical to design the structure of solid-state hydrogen storage tanks. On the basis of the steady-state radial heat flow method, a measurement cell of effective thermal conductivity was manufactured. The effective thermal conductivities of nonactivated and activated LaNi5 powder beds were measured in helium, nitrogen, and argon atmospheres with the temperature changing from 20 to 60 °C and pressure from 0.1 to 4.0 MPa. Then, the effective thermal conductivities were further analyzed using the Zehner–Schlünder–Damköhler model. Results show that the effective thermal conductivities can be enhanced by increasing gas thermal conductivity, gas pressure, and bed temperature. In addition, the effective thermal conductivities can be accurately predicted using the modified Zehner–Schlünder–Damköhler model considering the Smoluchowski effect (error < ± 5 %). With the use of the modified Zehner–Schlünder–Damköhler model, the contributions of different heat transfer pathways to the entire heat transfer of LaNi5 powder beds were analyzed. Approximately 70 %–91 % of the effective thermal conductivity of LaNi5 powder beds is contributed by the conduction of the particle–gas–particle pathway.

Measurement of effective thermal conductivity of composite powders of 2D materials and metals for additive manufacturing

Laser Powder Bed Fusion (LPBF), a promising additive manufacturing technique for composites of 2D materials and metals, requires knowledge of thermophysical properties, such as the thermal conductivity of powder, for process optimization. In this study, we measured the effective thermal conductivity of the most representative Cu-graphene composite powder in the field of heat transfer applications. To measure thermal conductivity, we propose a differential scanning calorimetry (DSC) method to measure the thermal resistances of a powder bed under steady-state heat flow conditions. We observe that the thermal conductivity of a composite powder is 1,000 times lower than that of the bulk metal without 2D material addition; e.g., exhibiting ~ 0.30 W/mK in Cu-1wt.% graphene powder. Furthermore, we discuss powder size and morphology impact on thermal conductivity influencing the number of contact points and thermal contact resistance. Our findings contribute to understanding the thermal conductivity of composite powders in a powder bed and aid in optimizing LPBF processes.

Определение коэффициента теплопроводности деревянных клееных конструкций с учетом макроструктуры и плотности древесины

The paper considers calculated and experimental methods of determining the thermal conductivity coefficient of wooden glued structures. The author shows that when designing the thermal protection of building enclosure structures in the form of CLT-panels or wooden glued laminated timber, one uses reference data on the thermal conductivity coefficient for pine or spruce. In practice, the value of the thermal conductivity coefficient may be less than the reference value; as a consequence, the thickness of the building enclosing structures is overestimated. This is not reasonable in terms of material intensity of construction. When considering wood as an anisotropic material, the peculiarities of the macrostructure and differences in the density of individual layers, as well as the wood species, should be taken into account when determining the parameters of structures. Based on the physical description of the thermal conductivity process and the fundamental laws of heat and mass transfer, the author proposes that it is necessary to adjust the results of calculations to the actual values of the thermal conductivity coefficient of multilayer wooden glued structures. The paper presents the results of experimental determination of the thermal conductivity coefficient of pine and aspen wood using steady-state and unsteady heat flow methods. It is shown that, depending on the density and wood species, experimental values of the thermal conductivity coefficient from 0.102 to 0.115 W·m-1∙K-1 can be obtained.

A new random walk method for simulating heat flow and temperature distribution in three-dimensional discontinuous systems

Numerical methods for analyzing diffusion phenomena involving strong discontinuities and complicated interfaces are of great scientific and technical importance. In this paper, we extend the existing step-balanced random walk, which overcomes the problem of detailed balance of a random walker in three-dimensional (3D), diffusion-tensor discontinuous systems, to particle density (ρ) discontinuous systems, and introduce volumetric heat capacity C and temperature T by considering ρ as heat density, i.e., ρ=CT, to apply it to thermal problems. Two types of thermophysical simulations are demonstrated: one is steady-state heat flow due to a temperature difference at the end surfaces on a two-phase slab model unit cell with periodic boundary conditions; the other is the time variation of temperature distribution due to heat diffusion from a point heat source in a repeated two-phase slab model with no periodic boundary conditions. We see the correct behavior of heat and temperature expected in 3D discontinuous systems composed of two phases with anisotropic thermal conductivity. The applicability to problems other than pure diffusion and the limitations of the method are also discussed.

Dynamic Heat Transfer Simulation in Textile for Practical Application: A Comparative Analysis of Microscopic and Macroscopic Approaches

Heat transfer simulation in textile materials has many practical applications, such as in the design of protective clothing for firefighters, the development of thermal insulation materials, and the optimization of temperature control in textiles for comfort and performance. This paper presents a study on heat transfer simulation in woven fabrics using the Comsol Multiphysics® application. The simulations were carried out for both microscopic (3D) and macroscopic (1D) scales and the heat flux variation was compared with experimental results. The steady-state average heat flow through the textile was determined, and this value was used to calculate the thermal resistance of the woven fabrics. The thermal resistance values obtained were within a deviation range of 4.2% to 6.3% from the values determined according to ISO 11092/1016, thus validating the proposed model. For the transient regime, the microscopic approach proved to be more accurate, the estimated time for the heat flow to reach a certain value depending essentially on the scale approached in the modeling. This finding has particular significance in the field of protective clothing, especially for firefighters exposed to radiant heat sources, where estimating the time for burns to occur is crucial.

Influence of Ag Doping on Thermal Conductivity and Magnetic Levitation of Single Grain YBCO Superconductors for High-Temperature Superconducting Maglev

Ag doping in (RE)Ba2Cu3O7−δ [(RE)BCO] bulk high-temperature superconductors has been recognized as an effective way to improve the mechanical and superconducting properties of REBCO bulk superconductors for practical applications such as high-temperature superconducting (HTS) Maglev. Ag2O nanoparticles doped YBCO samples with different doping amounts (x, x varies from 0∼0.5 wt%) were fabricated by Top-Seeded Melt-Growth method (TSMG). The samples’ steady-state thermal conductivity (λ) and the magnetic levitation force (FL) were measured by a testing platform under a similar condition to the HTS Maglev system. The effects of Ag2O doping on the λ and FL of single domain YBCO bulks have been systematically studied. The λ of the c-axis and the ab-plane were calculated through the steady-state heat flow method. We observed that λ increases distinctly when x ≥0.3 wt%. The doping amount of 0.3 wt% has been evidenced to be the optimal value, of which the λ of the c-axis and ab-plane are approximately 52% and 48% higher than the undoped one respectively. According to the results of the FL measurement, we found FL will increase while the relaxation rate of the FL will decrease by adding trace amounts of Ag2O nanoparticles in comparison to the undoped sample. This observation suggests that Ag-doping is an effective way to enhance thermal conductivity as well as the superconducting properties of YBCO superconductors for practical applications.

Modeling of contact thermal resistance in lateral capillary tube-suction line heat exchangers with experimental validation and investigation

This paper studied the lateral capillary tube-suction line heat exchanger (CTSLHX) with different contact types and different geometries. An improved one-dimensional model of the CTSLHX was established, using the CFD model to derive the contact thermal resistance between the capillary tube and the suction tube. An experimental bench was built to test the steady-state heat transfer and flow performance. It was found that the model predicted 87.6 % and 98.9 % of the measured mass flow rate within the error band of ± 10 % and ± 15 %. The prediction error of the CTSLHX heat transfer effectiveness was within ± 10 %. Parametric effects of different operating conditions and structural parameters on the performance of CTSLHX were investigated. Furthermore, experiments were carried out to study the temperature distribution along the transition section between the exit of the capillary tube and the evaporator. The unique temperature increase reveals that it is beneficial for reducing noise by wrapping a layer of rubber around the second increaser fitting.

Technique and results of determination of vertical variations in rock thermal properties, temperature gradient and heat flow

The paper describes the results of experimental geothermal studies of the formation surrounding Savitskaya-300 well (depth 3555 m) drilled in the Volga-Ural oil and gas basin (Orenburg region, Russia). The work was aimed, firstly, at obtaining geothermal data for basin modeling and, secondly, at improving the instrumental and methodological foundations of experimental studies. Continuous core profiling of the rock thermal conductivity, volumetric heat capacity, and thermal anisotropy was performed on all 2886 recovered core samples with the total length of 329.1 m. Additional measurements were conducted at fluid saturation and elevated temperatures. For non-cored intervals, the rock thermal properties were determined from well-logging data and via measurements on rock cuttings. The studied formation is characterized by high thermal heterogeneity at both the level of strata (horizons) and individual samples. Significant thermal anisotropy up to 1.50–1.66 in the lower part of the well has been observed. To obtain data on vertical variations of equilibrium temperature and its gradient, temperature logging was performed 7 times within the 2 to 186 days of well shut-in. New data on the recovery of temperature and its gradient after drilling are important for the practice of applied and fundamental geothermal surveys. A significant increase in heat flow with depth was established based on the results of temperature gradient and rock thermal conductivity determination for 34 depth intervals. The observed general vertical variation in the whole depth range of the well up to ∼3.3 km depth can be attributed to paleoclimatic effect in the Late Pleistocene-Holocene, while the sharp increase in heat flow at ∼3.3 km within Fransian sediments is possibly due to advective heat transfer by fluid filtration. The apparent heat flow was established to be 84.3 mW⋅m−2 in the lower section of the well, below 3.3 km. The value may be close to the steady-state heat flow value, which is 84% higher than the previous published average data for the studied area.

INSTALLATION FOR DETERMINING THE THERMAL CONDUCTIVITY OF PLATES BY THE STATIONARY METHOD

When measuring the thermal conductivity of thermal insulation materials made by powder metallurgy and building porous materials, complications arise due to the fact that heat flows through the samples are commensurate with heat losses. The steady-state heat flow (SSHF) method is simple, does not require sophisticated equipment, and allows determining the thermal conductivity not in the near-surface layer but in the entire sample volume. Its disadvantage is low accuracy and the need to use reference samples. This work aims to develop an installation for measuring the thermal conductivity of largesized samples of low-conductivity material using the steady-state heat flow method with significantly higher accuracy than existing installations using this method. This is achieved by sandwiching the sample, which is a thin square plate of large dimensions, between the heater chamber and the refrigerator. The heating chamber is made of insulating material and its front wall, which is in contact with the sample, is made of the copper plate (which has good thermal conductivity). In the operating mode, the temperature in the heater chamber is maintained equal to the ambient temperature, which allows us to neglect heat losses and assume that in the steady-state mode, the heater power is equal to the heat flux through the sample. The thickness of the sample is much smaller than the size of its side (the sample should be square). This assumption is necessary to use the condition of isotropic temperature distribution in the cross-section of the sample. The refrigerator is filled with water and ice. The isotropic temperature distribution in the sample is ensured by its contact with the copper walls of the heater and refrigerator chamber. The temperature of the heated surface of the sample is measured using a thermocouple inserted through a hole in the front wall of the heater chamber. The proposed design of the installation and its operating conditions make it possible to significantly improve the accuracy of determining the thermal conductivity coefficient and make the error less than 2%.

Heat flow variations in 2 km deep borehole Litoměřice, Czechia

Temperature in 2 km deep borehole Litoměřice, drilled in 2007, was repeatedly logged down to 1700 m in the period 2007 – 2020. We were able to monitor a return of the temperature to the equilibrium temperature-depth profile undisturbed by drilling. The uppermost part of the profile contains signal of the recent warming manifested by a negative temperature gradient close to the surface and a temperature minimum at a depth of about 40 m. The minimum has been migrating downward at a rate of 1.5 – 2 m per year in the period 2015 – 2020.A detailed knowledge of temperature gradient together with thermal conductivity, diffusivity and heat production measurements on the drill-core samples of mica-schist that occurs below 900 m depth enabled us to analyze the heat flow vertical variations in the lithologically homogeneous depth section 900 – 1700 m. We came to the conclusion that temperature-depth profile in this section contains a robust climate signal of the last glacial cycle. The reconstructed ground surface temperature history indicates the magnitude of the last glacial – Holocene warming 13 -15 K and existence of a minimum 15 – 20 ka. The long-term mean ground surface temperature +1 - +2 °C suggests that the borehole site was permafrost free for most of the glacial cycle. Existence of about 100 m deep permafrost is possible in the coldest part of the last glacial.The steady-state surface heat flow has been estimated at 88 mW/m2. The reconstructed ground surface temperature history used as a surface forcing function in a numerical solution of the transient heat conduction equation provided an estimate of the present-day heat flow in the well. The estimate is practically independent from the poorly constrained conductivity of the 900 m thick sedimentary cover. According to it the present-day heat flow is lower than the steady-state one by 20 - 30 mW/m2 in the first hundreds of meters below the surface and still by about 10 mW/m2 at a depth of 1 km.

Theoretical Analysis of the Effects of Exothermic Catalytic Chemical Reaction on Transient Mixed Convection Flow along a Curved Shaped Surface.

The present problem addressed the transient behavior of convective heat and mass transfer characteristics across a curved surface under the influence of exothermic catalytic chemical reactions. The governing non-linear mathematical model wastransformed into a convenient form with the help of a primitive variable formulation. The final primitive formed model wassolved numerically by applying the finite difference method. The analysis of the above said computed numerical data in terms of oscillatory heat transfer, skin friction, and oscillatory mass transfer for various emerging parameters, such as the mixed convection parameter λT, modified mixed convection parameter λc, index parameter n, activation energy parameter E, exothermicparameter β, temperature relative parameter γ, chemical reaction parameter λ, and Schmidt number Sc is plotted in graphical form. An excellent agreement is depicted for oscillatory heat transfer behavior at the large value of activation energy E. The amplitude of heat transfer and prominent fluctuating response in mass transfer with a certain height is found at each value of the index parameter n with a good alteration. An increase in the activation energy led to an increase in the surface temperature, which yielded more transient heat transfer in the above-said mechanism. The main novelty of the current study is that first, we ensured the numerical results for the steady state heat and fluid flow and then these obtained results wereused in the unsteady part to obtain numerical results for the transient behavior of the heat and mass transfer mechanism.

Analysis of effective thermal conductivity of pebble bed by artificial neural network and its computational and experimental verification

While dealing with a solid-type ceramic breeding blanket for a fusion reactor, it is critical to determine the basic and thermal properties of the functional material in the form of a pebble bed. In the form of pebbles, lithium ceramics serve as the tritium breeder material in the fusion blanket. Effective thermal conductivity (keff) is one of the important thermal properties for the design and useful parameter to determine the performance of the blanket component. Artificial Neural Networks (ANN) are a popular machine learning technique for tuning between input and output parameters. These networks can learn from examples (data set) and apply them when a homogeneous event arises, making them able to work through genuine-time events. Hence, it can save a lot of time and money for doing repetitive experiments and high-end simulations. This will aid in the creation of a huge database on the pebble bed's keff, which will be useful in the design and development of fusion blankets. The findings of simulations and experiments are compared to those predicted by the ANN model for the pebble bed's thermal conductivity.At IPR, a test setup for experiments has been developed using the steady-state and axial heat flow approach. keff of Li2TiO3 has been measured for the pebbles of diameter of 0.8–1.2 mm having packing fraction of ∼62% and using helium environment at different temperatures ranging from 100 °C to 600 °C at constant atmospheric pressure. keff has been compared with pebble bed of stainless steel pebbles of different diameters (1, 2, 3, 1&3, & 2&3 mm) as well. DDPM-DEM model has been used to generate the pebble bed and ANSYS-CFD simulations using FLUENT have been performed to validate the results. The projected values using ANN are within 5% of the results obtained from simulations and experiments. The details of the DDPM-DEM and ANN models, FLUENT simulations, and experimental results will be discussed in this paper.

COMPARATIVE THERMAL PERFORMANCE ANALYSIS OF ROOFTOPS WITH ELEVATED CEILING CONFIGURATION

In this study, thermal performance of different pitched roofs with elevated ceiling configuration is analyzed and compared. Three different ceiling shapes, viz., cathedral, barrel-vault and A-frame, at the same pitch angle and ceiling material, under winter heating are examined numerically by solving the steady-state air and heat flow problems simultaneously. In all the roofs, the airflow fields show counter-rotating recirculating cells. The multicellular flow field promotes uniform temperature distribution within the enclosures. Heat loss to the attic from the space below increases with the closeness of the hot ceiling to the cold inclined walls. In the A-frame roof, there is uniform convective heat transfer. But in the cathedral and barrel-vault roofs, near the bottom corners, conductive heat exchange predominates. In all, the thermal performance of the barrel-vault is least while that of the cathedral is best. This observation is useful on the application of insulation when using such ceiling shapes.

Interaction of phonons with spherical nanoparticles embedded densely in simple crystalline matrix. Case of nitrogen-palladium nanocomposite

The results of experimental investigations of thermal conductivity of nanocomposites built of palladium spherical nanoparticles embedded in the structure of crystalline nitrogen are presented in this paper. The investigations were carried out on the samples containing the Pd nanospheres of diameters of 6, 8, 10, 12, 18, and 24 nm at the palladium fraction amounting to 15% of the nanocomposite volume. The measurements were performed with a steady-state heat flow method in the temperature interval of 2–35 K. For the analysis of the experimental results, the relaxation time approximation in the frame of the thermal conductivity Debye model was used. The analysis shows that the nitrogen matrix phonons can effectively interact with spherical nanoparticles in, at least, four different mechanisms. Two of those mechanisms, a diffuse scattering by the boundary of two media (which are the matrix and the material of the nanoparticle) and an oscillating resultant of interaction of nanoparticle phonons with the matrix phonons, result in a decrease of the nanocomposite thermal conductivity. The remaining two mechanisms would be considered nonthermal resistive scattering processes: The first of them is the specular scattering of the matrix phonons by the matrix and the nanoparticle material interface. The second one is a forward scattering, in which the matrix phonon penetrates the nanoparticle and afterward penetrates another one without any resistive interaction with phonons of the crystalline matrix. The analysis shows that the nonresistive processes are significantly more frequent in the investigated nanocomposites than the resistive ones. Such a conclusion is in perfect agreement with the results of the analysis of the phonon mean free path in the nitrogen crystal-palladium nanospheres composite.

Nonequilibrium thermal transport in the two-mode qubit-resonator system

Nonequilibrium thermal transport in circuit quantum electrodynamics emerges as one interdisciplinary field, due to the tremendous advance of quantum technology. Here, we study steady-state heat flow in a two-mode qubit-resonator model under the influence of both the qubit-resonator and resonator-resonator interactions. The heat current is suppressed and enhanced by tuning up resonator-resonator interaction strength with given weak and strong qubit-resonator couplings respectively, which is cooperative contributed by the eigen-mode of coupled resonators and qubit-photon scattering. Negative differential thermal conductance and significant thermal rectification are exhibited at weak qubit-resonator coupling, which are dominated by cycle transition processes. Moreover, the heat flow through the resonator decoupled from the qubit can be dramatically enhanced via the resonator-resonator interaction, which is attributed by the generation of eigen-mode channels of resonators.

Comparative Study of Analytic and Numerical Solutions of Steady-state Temperature Distribution on Semi-circular Plate Using Laplace Equation

In this paper numerical methods have been used to solve two dimensional steady state heat flow problem in polar coordinates with Dirichlet boundary conditions inside a semi-circular plate and the work focuses on the numerical methods for solving Laplace equation; finite difference schemes and Gauss elimination method. The numerical solution is compared with exact solution of the same problem. Finally, we analyze the absolute error in different number of iterations to check the accuracy of schemes.

Thermal conductivity of niobium and thermally sprayed copper at cryogenic temperature

We have developed a test facility dedicated to thermal conductivity k(T) measurements at low temperature. These experimental devices allow the test of four samples simultaneously during each run. The measurements are performed using steady-state axial heat flow method with a careful control of heat leaks to the surrounding. The apparatus was successfully used for measuring k(T) (Temperature T in the range: 1.5 K - 10 K) of niobium and other materials used for the fabrication of Superconducting Radio Frequency (SRF) cavities. We have tested the following samples: 1) niobium samples from different supplier (as received or/and after various high temperature Heat Treatments (HT)), 2) thermally sprayed copper coatings. The resulting experimental data are presented and compared to the experimental results previously reported by other groups and theoretical values. As expected heat treatment have a strong impact on k(T) and in particular on the phonons peak at T∼2K. More precisely, HT @ 1200°C with Ti gettering improves the Nb Residual Resistance Ratio (RRR) by a factor of 3 and consequently k(T). Finally, the correlation between the niobium RRR and the thermal conductivity. at T=4.2 K is confirmed in good agreement with the Wiedemann-Franz law

Determination on the thermal conductivity and thermal contact resistance of thin composite phase change films as a thermal interfacial material

Sub-millimeter thick phase change material (PCM) composites have been utilized in the thermal management of micro-electronics serving as a novel thermal interfacial material. However, there is a lack of appropriate measuring methods and precise data for the thin-film PCM composites' intrinsic thermal conductivity, as well as the thermal contact resistance (TCR) at interfaces between those thin-films and metal. In this work, the out-of-plane thermal conductivity of thin-film PCM35, which is a paraffin composite showing the melting point of 35 °C, was first gauged through the commercialized transient plane source (TPS) method, followed by a correction process to deduct the TCR between thin films/temperature sensor interfaces. The direct TPS readings were corrected based on the proportional relation between samples’ thickness and inherent thermal resistance. An improved steady-state heat flow apparatus designed for thin-walled samples was then utilized to examine the reliability of the corrected TPS technique, with a relative deviation between them being only ∼7%. In order to test the applicability of the corrected TPS method, the thermal conductivities of thin polytetrafluoroethylene films were also determined. Furthermore, the TCR between thin PCM35 film and thin 1060Al plate was identified by performing the improved steady-state apparatus. The contribution of overheated PCM35 film on fitting the interfacial voids and reducing the TCR were elucidated, which can guide the thermal design with the use of such thin-film PCMs.