Two-dimensional Temperature Research Articles

Insights into Chemical Bonding Modes and Heat Transport at the Molecular Level.

Despite the demand for nanoscale thermal management technologies of material surfaces and interfaces using organic molecules, heat transport properties at the single molecular level remain elusive due to the experimental difficulty of measuring temperature at the nanoscopic scale. Here we show how chemical bonding modes can affect the heat transport properties of single molecules. We focused on four molecular systems: benzylthiol linked to another phenyl group by either a triple (compound 1), double (3), or amide (4) bond and a common linear alkanethiol (2), all of which are nearly identical in molecular length. We prepared binary self-assembled monolayers (SAMs) using 1 as a common reference in combination with 2-4 and investigated their relative heat transport properties using scanning thermal microscopy (SThM). Two-dimensional temperature mapping of the binary SAMs showed that C≡C and C=C bonds provide more effective pathways for heat transport compared to C-C bonds. Since the amide molecule has resonance structures with C=N double bond character, we expected that its heat transport properties would be comparable to those of the thiols containing triple or double bonds. However, the heat transport properties of this molecule prevailed over the others, most likely due to the formation of additional heat transport pathways caused by intermolecular hydrogen bonding. These findings may provide important guidelines for the design of organic materials for nanoscale thermal management.

Multispectral two-dimensional temperature field reconstruction using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm with multiple extreme value optimization

The flame temperature is a crucial parameter in combustion, indicating heat generation and transfer. However, determining the correct temperature becomes challenging when flame emissivity is unknown. This article presents a multispectral 2D temperature field reconstruction method using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm, combined with multivariate extreme-value optimization. This method establishes an objective function based on the correlation between the true temperature and spectral data. The objective function was minimized by adjusting the emissivity, enabling the reconstruction of 2D temperature and emissivity images without assuming an emissivity model. Calibration with a multispectral camera yielded the spectral response coefficients, and three-time spline interpolation was used to verify the calibration data. The reconstructed 2D temperature field showed a mean absolute error (MAE) of 4.61 and structural similarity (SSIM) of 0.995. The reconstructed emissivity image had an MAE range of 0.04 to 0.053 and an SSIM range of 0.897 to 0.915. The system, tested on a butane flame, showed a temperature range of 1001 K to 1356 K, with an average temperature of 1194 K and emissivity values ranging from 0.3166 to 0.8621. The results align with the expected combustion process and radiation characteristics distribution of the butane flame.

Photoacoustic thermal-strain measurement towards noninvasive and accurate temperature mapping in photothermal therapy

Photothermal therapy is a promising tumor treatment approach that selectively eliminates cancer cells while assuring the survival of normal cells. It transforms light energy into thermal energy, making it gentle, targeted, and devoid of radiation. However, the efficacy of treatment is hampered by the absence of accurate and noninvasive temperature measurement method in the therapy. Therefore, there is a pressing demand for a noninvasive temperature measurement method that is real-time and accurate. This article presents one such attempt based on thermal strain photoacoustic (PA) temperature measurement. The method was first modelled, and a circular array-based photoacoustic photothermal system was developed. Experiments with Indian ink as tumor simulants suggest that the temperature monitoring in this work achieves a precision of down to 0.3 °C. Furthermore, it is possible to accomplish real-time temperature imaging, providing accurate two-dimensional temperature mapping for photothermal therapy. Experiments were also conducted on human fingers and nude mice, validating promising potentials of the proposed method for practical implementations.

Thermal mixing and structure of the jet in swirling crossflow

The dilution zone in modern aero-engine combustors is characterized by a strong swirling mainstream with weak transverse jets. This characteristic brings new challenges in homogenizing the temperature distribution at the combustor exit. Therefore, it is imperative to understand the temperature penetration and mixing process of the jet in swirling crossflow (JISCF). This investigation provides new insight in the temperature mixing process for a JISCF in nozzle exit diameter (D) at 7.4, 10.7, and 14 mm and jet to mainstream velocity ratio (VR) from 2.0 to 6.6. The temperature mixing process was measured in a specially designed optical assessable three-dome model gas turbine combustor by planar 1-methylnaphthalene (1-MN) tracer laser-induced fluorescence thermometry. A detailed quantitative measurement of temperature distribution is achieved through the spectral red shift in the fluorescence of 1-MN as the temperature increase. This diagnostic was employed to provide the first two-dimensional temperature distribution for the JISCF. The results showed that the swirling crossflows induce strong spanwise thermal advection, forming secondary low-temperature regions downstream. Generally, the flow structure and mixing process are governed by the interaction of jet and swirling flow. The jet flow parameters, including velocity ratio and diameter, changed the flow structures by changing the interaction between jet and swirling flow. Statistical results and proper orthogonal decomposition (POD) analyses showed a strong anisotropic mixing process in the downstream of the jet.

Background radiation compensation calibration method for film cooling infrared temperature measurement based on BP neural network

The precise non-contact temperature measurement method is essential for studying gas turbine component heat transfer. While infrared thermal imaging provides high-resolution two-dimensional temperature fields, errors arise from the measurement environment's complexity, emissivity variations, and reflection radiation effects. This study utilizes BP neural networks to correct infrared radiation on gas film cooled plates. By modeling background radiation and analyzing infrared emission processes, factors influencing temperature distribution are identified. Experimental data from uncooled plate are used for network training. Experimental measurements were conducted on uncooled plates to obtain training data. A BP neural network was established based on Planck's law and the radiation transmission process to relate the mainstream temperature to the background radiation. Calibration analysis was performed based on experimental data from the cooled plate, achieving the restoration of the two-dimensional temperature field under multiple operating conditions and significantly reducing measurement errors. This method comprehensively considers the entire process of radiation transmission, thereby eliminating background radiation embedded in the infrared images. The obtained measurement results vividly depict the real temperature distribution, offered significant support for gas turbine engineering applications.

Comprehensive experimental thermal analysis of single bubble nucleation in vertical flow boiling: Whole field temperature and microlayer dynamics

Nucleate boiling, an important heat transfer phenomenon, holds significance in the thermal management of numerous engineering applications. Understanding and predicting its heat transfer characteristics are vital for system optimization. The formation of a microlayer, resulting from rapid bubble growth on a heater substrate, subsequently facilitates further bubble growth through evaporation playing a critical role in overall bubble dynamics. This study examines the intricate relationship between bubble and microlayer dynamics and their impact on heat transfer rates. Experimental work is conducted for varying heat fluxes using rainbow schlieren deflectometry (RSD) and thin-film interferometry (TFI) in tandem for simultaneous mapping of key parameters: bubble dynamics, microlayer dynamics, and two-dimensional temperature field in vertical flow boiling. The analysis of these parameters has provided significant insights into some fundamental aspects of boiling. Firstly, this study emphasizes that the bubble growth rate models need to take into initial microlayer thickness in accurately predicting bubble growth dynamics. The iteratively obtained constant Ceff (describing the initial microlayer thickness) for bubble growth models matches well the value of Ceff obtained experimentally from thin film interferograms. Additionally, this study also validates the applicability of the kinetic theory-based model in predicting the evaporative heat transfer coefficient during the initial stage of flow boiling, while demonstrating that the accommodation coefficient is ∼0.04 for the investigated range of heat fluxes. Subsequently, using the experimentally obtained evaporative heat transfer coefficient, further insights are provided into the dry patch dynamics. Experimental dry patch dynamics were in good agreement with theoretical predictions up to the rewetting phase. The results also indicate a substantial contribution of microlayer evaporation, constituting approximately 34 % of the total heat flux.

In-Fiber Hybrid Structure Sensor Based on the Vernier Effect for Vector Curvature and Temperature Measurement

A vector curvature and temperature sensor based on an in-fiber hybrid microstructure is proposed and experimentally demonstrated. The proposed scheme enables the dimensions of the Fabry–Perot and Mach–Zehnder hybrid interferometer to be adjusted for the formation of the Vernier effect by simply changing the length of a single optical fiber. The sensor is fabricated using a fiber Bragg grating (FBG), multimode fiber (MMF), and a single-hole dual-core fiber (SHDCF). The sensor exhibits different curvature sensitivities in four vertical directions, enabling two-dimensional curvature sensing. The temperature and curvature sensitivities of the sensor were enhanced to 100 pm/°C and −25.55 nm/m−1, respectively, and the temperature crosstalk was minimal at −3.9 × 10−3 m−1/°C. This hybrid microstructure sensor technology can be applied to high-sensitivity two-dimensional vector curvature and temperature detection for structural health monitoring of buildings, bridge engineering, and other related fields.

Spatially Resolved Quantum Sensing with High-Density Bubble-Printed Nanodiamonds.

Nitrogen-vacancy (NV-) centers in nanodiamonds have emerged as a versatile platform for a wide range of applications, including bioimaging, photonics, and quantum sensing. However, the widespread adoption of nanodiamonds in practical applications has been hindered by the challenges associated with patterning them into high-resolution features with sufficient throughput. In this work, we overcome these limitations by introducing a direct laser-writing bubble printing technique that enables the precise fabrication of two-dimensional nanodiamond patterns. The printed nanodiamonds exhibit a high packing density and strong photoluminescence emission, as well as robust optically detected magnetic resonance (ODMR) signals. We further harness the spatially resolved ODMR of the nanodiamond patterns to demonstrate the mapping of two-dimensional temperature gradients using high frame rate widefield lock-in fluorescence imaging. This capability paves the way for integrating nanodiamond-based quantum sensors into practical devices and systems, opening new possibilities for applications involving high-resolution thermal imaging and biosensing.

Latitudinal Asymmetry in the Dayside Atmosphere of WASP-43b

We present two-dimensional near-infrared temperature maps of the canonical hot Jupiter WASP-43b using a phase-curve observation with JWST NIRSpec/G395H. From the white-light planetary transit, we improve constraints on the planet’s orbital parameters and measure a planet-to-star radius ratio of 0.15883−0.00053+0.00056 . Using the white-light phase curve, we measure a longitude of maximum brightness of 6.9−0.°5+0.°5 east of the substellar point and a phase-curve offset of 10.0−0.°8+0.°8 . We also find a ≈4σ detection of a latitudinal hotspot offset of −13.4−1.°7+3.°2 , the first significant detection of a nonequatorial hotspot in an exoplanet atmosphere. We show that this detection is robust to variations within planetary parameter uncertainties, but only if the transit is used to improve constraints, showing the importance of transit observations to eclipse mapping. Maps retrieved from the NRS1 and NRS2 detectors are similar, with hotspot locations consistent between the two detectors at the 1σ level. Our JWST data show brighter (hotter) nightsides and a dimmer (colder) dayside at the shorter wavelengths relative to fits to Spitzer 3.6 and 4.5 μm phase curves. Through comparison between our phase curves and a set of general circulation models, we find evidence for clouds on the nightside and atmospheric drag or high metallicity reducing the eastward hotspot offset.

In-situ two-dimensional temperature measurements using x-ray fluorescence spectroscopy in laminar flames with high silica particle concentrations

X-ray fluorescence spectroscopy (XRF) was used to measure temperatures and study mixing, for the first time in silica particle synthesis flames. Hexamethyldisiloxane (HMDSO) and trimethylsilanol (TMSO) were the particle precursors. A multi-element diffusion burner was used to produce a flat methane flame, and the precursors, dilute in inert gas, were injected via a central jet. Krypton was the fluorescent medium at 3.2 % concentration by volume. Scans with Kr in the central flow and not in the main flow were made to assess the mixing effects between the central and main gas flows. When HMDSO or TMSO were added, a secondary diffusion flame formed between the jet and the main methane flame. The results revealed a dramatic change in the centerline temperature profile of the jet gases when HMDSO or TMSO were added. The main methane flame stoichiometry also affected the temperature profiles. The results show HMDSO and TMSO reactions are initiated in a low-temperature and low-oxygen concentration region of the jet where thermal decomposition is not expected to be significant. Reaction of the particle precursors is therefore attributed to radical transport from the main methane flame. In the current work, particle number densities of up to 270 g/m3 locally are estimated. Thus, the study also demonstrates the capability of the XRF technique for high spatial fidelity measurements in flames with high concentrations of condensed-phase particles, leveraging the attribute that the XRF signal is generally not impacted by condensed-phase interferences. The observations and data obtained in this study inform likely reaction pathways for this important class of siloxane compounds.

The Discrete, Fractional Order Model of a Two-Dimensional Temperature Field using Grünwald-Letnikov Definition

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow to estimate the orders of the model. Theoretical considerations are validated using exprimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length.

Two-dimensional temperature measurements in laser-induced air plasma

Two-dimensional temperature measurements in laser-induced air plasma

Instantaneous thermometry imaging using two-photon laser-induced fluorescence.

Measuring temperature in complex two-phase flows is crucial for understanding the dynamics of heat and mass transfer. In this Letter, we introduce a novel, to the best of our knowledge, optical approach based on the combination of two-photon laser-induced fluorescence (2p-LIF) imaging and two-color laser-induced fluorescence (2CLIF) for instantaneous temperature mapping of complex liquid media. Using Kiton Red (KR) and Rhodamine 560 (R560), a temperature sensitivity of 1.54%/∘C has been achieved over a range of 17-60°C. The monitoring of two-dimensional transient temperature dynamics in the heating and degassing of water shows the efficiency of the 2p-2CLIF. This new approach contributes to the toolkit of optical temperature measurement techniques, providing a robust solution for studying transient scattering media and high-speed two-phase flows.

Temperature field reconstruction based on femtosecond laser prepared of multiwavelength fibre bragg grating array

Temperature field measurements are of great significance in industrial production, scientific research, and other fields. Contact temperature measurements usually achieve high spatial resolution by increasing the layout density of the sensors. However, in practical applications, achieving high-density sensor placement is often difficult. Therefore, when the number of sensors is limited, it is necessary to perform function fitting or interpolation of the temperature of the sampling points to reconstruct the temperature field distribution. This study proposed a temperature field reconstruction method based on femtosecond laser prepared multiwavelength fibre Bragg grating (FBG) array. A multiwavelength FBG array was prepared using the femtosecond laser phase mask method combined with stress stretching, and applied for measuring the temperature field distribution in a tubular high-temperature furnace. Cubic spline interpolation and backpropagation (BP) neural networks were used to construct two-dimensional temperature field models for the temperature field distribution data measured by the FBGs, and the prediction accuracies of the two models were compared. The test results show that the root mean square error of the temperature field distribution constructed using the BP neural network is 0.7333 °C, which is approximately 23.18% of the predicted results of the cubic spline interpolation model, indicating that it is a high-precision temperature field reconstruction method.

Multi-View Synthesis of Sparse Projection of Absorption Spectra Based on Joint GRU and U-Net

Tunable diode laser absorption spectroscopy (TDLAS) technology, combined with chromatographic imaging algorithms, is commonly used for two-dimensional temperature and concentration measurements in combustion fields. However, obtaining critical temperature information from limited detection data is a challenging task in practical engineering applications due to the difficulty of deploying sufficient detection equipment and the lack of sufficient data to invert temperature and other distributions in the combustion field. Therefore, we propose a sparse projection multi-view synthesis model based on U-Net that incorporates the sequence learning properties of gated recurrent unit (GRU) and the generalization ability of residual networks, called GMResUNet. The datasets used for training all contain projection data with different degrees of sparsity. This study shows that the synthesized full projection data had an average relative error of 0.35%, a PSNR of 40.726, and a SSIM of 0.997 at a projection angle of 4. At projection angles of 2, 8, and 16, the average relative errors of the synthesized full projection data were 0.96%, 0.19%, and 0.18%, respectively. The temperature field reconstruction was performed separately for sparse and synthetic projections, showing that the application of the model can significantly improve the reconstruction accuracy of the temperature field of high-energy combustion.

A new conceptual model of the Travale (Italy) enhanced geothermal system: Insights from electromagnetic geothermometry

The paper presents an electromagnetic geothermometer-based two-dimensional temperature model for the Travale (Italy) enhanced geothermal system derived from magnetotelluric and temperature data. Joint analysis of the temperature and electrical resistivity models made feasible a new self-consistent conceptual model of this site, which agrees with available geological data and previous geophysical results. It explains the nature of seismic reflection horizons detected in 1978 and unusual seismicity distribution in depth which could not be properly addressed earlier without temperature predicting beyond boreholes. It is concluded that the heat source feeding this system may be a granitic intrusion located at a depth below 4 km, which corresponds to the isotherm of 600 °C. A sharp temperature gradient above this intrusion forms a contact thermo-metamorphic halo in the depth range of 3–4 km. Assessment of the released fluid volume fraction from the electrical resistivity model indicates that the general amount of thermo-metamorphic and magmatic fluids in the rock-dominated Travale geothermal system is negligible. It is concluded that meteoric waters are the main source of fluids penetrating along normal faults up to 3 km. Despite some supercritical fluids of thermo-metamorphic origin could circulate in the system below this depth, their amount is hardly sufficient for economically justified exploration drilling. The results of the study indicate that building the temperature model of the geothermal area is crucially important for the exploration of enhanced geothermal systems.

Study on Sunlight Temperature Field of Steel Box Arch Ribs in Irregular Arch Bridges

Due to their excellent thermal conductivity and sensitivity to temperature changes, special attention should be paid to the influence of temperature on steel-structure bridges. The temperature effect is complex, especially for unstable steel arch bridges with complex structural forms. This paper proposes an approximate method that measures the three-dimensional temperature field of the symmetrical arch rib with the two-dimensional temperature field of multiple sections. In addition, it converts the complex radiant intensity calculation of the special-shaped steel box arch rib into the calculation of numerous planar radiant intensities. It uses the ANSYS Workbench to establish the three-dimensional transient thermal analysis finite element model of the No. 2 steel box arch rib. The influence of seasons and arch rib direction on the temperature field of steel box arch ribs and the stress and deformation of steel box arch ribs under non-linear temperature effects were analyzed. The results show that the temperature changes in different seasons significantly impact the temperature changes in the arch ribs. The change in the azimuth angle of the arch rib has a significant impact on the temperature difference between the web plates on both sides of the arch rib; under the influence of the temperature field at the most unfavorable time in summer and winter, symmetrical stress concentration occurs in the arch foot area. Furthermore, the maximum vertical displacement is 13.9 mm and 10.8 mm, respectively. Finally, when the angle is 40°, the maximum temperature difference between the web plates on both sides is 6.9 °C.

Multi-dimensional investigation of ceiling jet temperature characteristics beneath curved ceiling produced by fire in the utility tunnel

To study the temperature profile beneath the curved ceiling from a multi-dimensional perspective, an experimental investigation was conducted in utility tunnels with two different sizes, and a series of models were established to predict a two-dimensional longitudinal temperature profile and transverse temperature attenuation in this study. The prediction models for the two-dimensional longitudinal temperature profile were developed by modeling the vertical temperature distribution, thermal boundary layer thickness, Gaussian thermal layer thickness and maximum longitudinal temperature attenuation. Through the experimental validation on two sizes, it is found that the proposed prediction model can express the longitudinal temperature profile from a two-dimensional view within the relative error range of 20%. Besides, the prediction model for transverse temperature attenuation was established by the definition of characteristic tilt angle, and the three detailed expressions of this model were proposed according to different types of ceiling jets after impingement. The proposed prediction model for transverse temperature attenuation was also validated, and the verification results showed that the relative error of the transverse temperature attenuation prediction model can be controlled within a 25%. The developed prediction models in this study can be applied in the fire protection engineering of utility tunnels.

Analytical Confirmation of the Calculated Dependencies for Heat Exchange in a Plate Recuperator when Humidifying the Auxiliary Flow

The relevance of the study is related to the need to ensure maximum reduction of energy consumption while ensuring the calculated parameters of the indoor climate in buildings under the Law of the Russian Federation “On Energy Saving...” and the updated version of SP 131. The purpose of the study is to obtain an approximate analytical expression of this dependence, which makes it possible to additionally confirm the results of field and numerical experiments previously performed by the authors for this flow treatment scheme. The objective of the study is to build a simplified mathematical model of the processes of changing the heat and humidity state of the air in the recuperator, identify the main factors affecting the increasing multiplier to the coefficient of temperature efficiency of the device and obtain the necessary numerical coefficients in formulas linking the desired and initial parameters. The general equation of thermal balance and heat transfer for the heat exchanger as a whole is used, including the integral characteristics of the apparatus in a dimensionless form, as well as standard techniques of algebraic transformations. An approximate analytical expression is obtained for an increasing multiplier to the coefficient of thermal efficiency of the recuperator taking into account the additional cooling of the inflow due to the heat consumption for evaporation. It is shown that the general structure of this ratio coincides with the one found by the authors earlier by processing the results of numerical modeling of a two-dimensional temperature field in a heat exchanger, taking into account experimental data on the amount of moisture carried away, which confirms their correctness and reliability.

ANALYTICAL SOLUTION OF THE DIFFERENTIAL EQUATION OF HEAT CONDUCTIVITY FOR DAMAGED THERMAL INSULATION OF PIPELINES

For heat supply systems of Ukraine, the determination and forecasting of thermal energy losses during the transportation of heat carrier is an urgent problem. The thermal lines of the heating networks are long and its insulation is damaged. Installation of heat energy metering devices at all sources and all consumers (i.e. buildings) without exception allows determining and forecasting real heat losses in the heat network, but this is a difficult task, not all consumers and sources are actually covered by heat consumption accounting. The task of determining heat losses is also relevant for energy management systems of heat supply systems, energy companies and industry. The solution to the problem is proposed by a separate mathematical modeling of the temperature state of the section of the damaged insulating layer with the determination of the heat flow through it. It is proposed to solve the problem by the method of analytical solution of the differential equation of heat conduction with boundary conditions of the third kind. With the uniform distribution of characteristic damages along the total length of the pipeline, knowing the limits of damage influence, the share of insulation damage and the number of damages on the pipeline, it is possible to determine the real heat flow from the outer surface of the pipelines, including coefficient of increase of heat losses on the section of the heat pipe in relation to those determined by regulatory documents. Traditionally, one-dimensional models or determinations of the two-dimensional temperature field and actual heat fluxes in a cross-section to the axis of a characteristic damaged section of insulation are considered. But this does not take into account the two-dimensionality of the temperature field of the damaged layer of insulation along the length (that is, along the axis) of the pipeline. Therefore, the purpose of this work is to develop a methodology for determining heat losses through pipelines, taking into account the damage to their insulation and the distribution of characteristic damages along the length. The following simulation was carried out for one of the areas. Also, experimental and numerical studies using the finite difference method in combination with the method of running variable directions for similar models confirmed the coincidence of the analytical solution of the proposed model and the finite difference model within the permissible error.