Steady-state Temperature Profiles Research Articles

Present temperature field characterization and geothermal resource assessment in the Harbin Area, Northeast China

Seven steady-state temperature profiles are logged in the Harbin Area, Northeast China. The temperature data illustrate high conductive thermal gradients with a mean value of 4.78°C/100 m. Temperature maps at depths of 1000, 1500, and 1800 m are represented. The present temperature field is cooling southeastward, with the highest thermal gradients being observed at the junction zone between the Central Depression and the Southeast Uplift of the Songliao Basin. The recoverable heat is calculated using a volumetric method and Monte Carlo simulation. The mean value for recoverable heat from the detailed exploration area around the Harbin Area is 1.052 × 1019 J (3.59 × 1011 t standard coal). Geological controls on the present temperature fields are discussed.

Phonon-electron coupling and nonlocal heat transport in Bi2Te3 nanowires

A hydrodynamical model of heat transfer with phonons and electrons is applied to infer the steady-state temperature profile in a Bi2Te3 nanowire. Our analysis is concerned with systems which allow for different temperatures of phonons and electrons. Along with the approach of kinetic theory, the phonons and the electrons are regarded as a gas-like mixture flowing through the crystal lattice. The coupling between phonons and electrons is taken into account by an additional term in the partial balances of energy of the components of the mixture. The compatibility of the model with the second law of thermodynamics is investigated in view of the requirement of positive entropy production, and of a nonlocal constitutive equation for the entropy flux.

Optimal placement of radiation shields in the displacer of a Stirling engine

The implementation of radiation shields in the displacer assembly of a Stirling engine is an effective way to reduce heat transfer losses. A FEA approach with ANSYS Workbench was utilized to determine the steady-state temperature profile throughout a displacer assembly, as well as the heat transfer from the hot end to the cold end of the displacer to optimize the position of the radiation shields. The results show that the surface finish is a critical aspect of reducing radiation losses since the higher emissivity cases resulted in higher displacer body temperatures and total heat flux to displacer body compared to the lower emissivity cases with the same number of shields and positioning. Even a single shield is capable of significantly reducing the radiation losses present in the displacer. The results also suggest it is more effective to place the shields uniformly along the entire length of the displacer cap. The results also demonstrated that there exits an optimal number of radiation shields that has the lease heat losses.

Optimization of skin cooling by computational modeling for early thermographic detection of breast cancer

The purpose of this study is to enhance the early detection of breast cancer using dynamic infrared (IR) imaging by optimizing thermostimulation with cooling stress to improve thermal contrast. A 2D hemispherical breast model was built to compute steady-state and transient surface temperature profiles for tumors of different size (10–30 mm), depth (6.6–26.6 mm) and location (15°–90°). Larger tumors and tumors closer to the skin surface leave sufficiently large thermal signatures (∼0.6 °C) to be detected by steady state IR imaging. Smaller and deeper tumors in the middle and bottom portion of the gland, with thermal contrasts below 0.1 °C, require dynamic imaging with thermostimulation (cooling) to achieve satisfactory thermal contrast for IR detection. In this paper, we consider cooling times of 15–25 min and cooling temperatures of 5–15 °C to optimize thermal contrast. Cooling penetration depths during the cooling phase for constant temperature cooling at 5 °C, 10 °C and 15 °C were analyzed. To achieve the maximum thermal contrast for deeper and smaller tumors, the tissue should be cooled 5–15 min, and in the maximum thermal contrast of the thermal recovery phase appears after 20–45 min. Effects of tumor size and depth on maximum thermal contrast were analyzed systematically to provide recommendations and guidelines for clinical applications. Thermal signatures computed in this study provide valuable data for inverse reconstruction algorithms that allow the measurement of tumor properties, such as the metabolic heat generation rate.

A unified framework for heat and mass transport at the atomic scale

We present a unified framework to simulate heat and mass transport in systems of particles. The proposed framework is based on kinematic mean field theory and uses a phenomenological master equation to compute effective transport rates between particles without the need to evaluate operators. We exploit this advantage and apply the model to simulate transport phenomena at the nanoscale. We demonstrate that, when calibrated to experimentally-measured transport coefficients, the model can accurately predict transient and steady state temperature and concentration profiles even in scenarios where the length of the device is comparable to the mean free path of the carriers. Through several example applications, we demonstrate the validity of our model for all classes of materials, including ones that, until now, would have been outside the domain of computational feasibility.

On the Steady-State Temperature Rise During Laser Heating of Multilayer Thin Films in Optical Pump–Probe Techniques

In this study, we calculate the steady-state temperature rise that results from laser heating of multilayer thin films using the heat diffusion equation. For time- and frequency-domain thermoreflectance (TDTR and FDTR) that rely on modulated laser sources, we decouple the modulated and steady-state temperature profiles to understand the conditions needed to achieve a single temperature approximation throughout the experimental volume, allowing for the estimation of spatially invariant thermal parameters within this volume. We consider low thermal conductivity materials, including amorphous silicon dioxide (a-SiO2), polymers, and disordered C60, to demonstrate that often-used analytical expressions fail to capture this temperature rise under realistic experimental conditions, such as when a thin-film metal transducer is used or when pump and probe spot sizes are significantly different. To validate these findings and demonstrate a practical approach to simultaneously calculate the steady-state temperature and extract thermal parameters in TDTR, we present an iterative algorithm for obtaining the steady-state temperature rise and measure the thermal conductivity and thermal boundary conductance of a-SiO2 with a 65-nm gold thin film transducer. Furthermore, we discuss methods of heat dissipation to include the use of conductive substrates as well as the use of bidirectional heat flow geometries. Finally, we quantify the influence of the optical penetration depth (OPD) on the steady-state temperature rise to reveal that only when the OPD approaches the characteristic length of the temperature decay does it alter the temperature profile relative to the surface heating condition.

Asymptotic Analysis of a Silicon Furnace Model

Silicon is produced from quartz rock in electrode-heated furnaces by using carbon as a reduction agent. We perform an asymptotic analysis of a heat and mass transfer model of an experimental pilot furnace in order to determine the dominant chemical and thermal behavior of the system. First, by prescribing a steady-state temperature profile in the furnace we explore the leading order reactions in different spatial regions, as well as early time behavior. We are able to obtain asymptotic solutions which compare well with numerical simulations. Utilizing the dominant balances found when the temperature is prescribed, we next reduce the full model to two coupled partial differential equations for the time-variable temperature profile within the furnace and the concentration of solid quartz. These equations account for diffusion, an endothermic reaction, and the external heating input to the system. A moving boundary is found and the behavior on either side of this boundary explored in the asymptotic limit of small diffusion. We note how the simplifications derived may be useful for future models and industrial furnace operation and comment on insights from the model about furnace crust formation.

Kapitza conductance of symmetric tilt grain boundaries of monolayer boron nitride

We use reverse nonequilibrium molecular dynamics simulations to study thermal conductivity of two–dimensional hexagonal boron nitride (h–BN) nanoribbons containing symmetric tilt grain boundaries. The simulations are conducted on periodic h–BN nanoribbons with zigzag and armchair chirality. The effective thermal conductivity of ribbons and Kapitza conductance of grain boundaries are calculated by inducing a constant heat flux along the longitudinal direction of ribbons. The steady state temperature profiles of nanoribbons display jumps at the location of grain boundaries. The temperature jumps monolithically increases with the misorientation angle of grain boundaries indicating that grain boundaries with higher misorientation angle have lower Kapitza conductance. The lower Kapitza conductance is due to higher phonon scattering at grain boundaries which is a result of a higher mismatch between the phonon spectra of grain boundary and grain atoms. Our modeling results also predict that by increasing the length, both Kapitza conductance of grain boundaries and effective thermal conductivity of ribbons increases. Although temperature does not have a significant impact on Kapitza conductance, but by increasing temperature effective thermal conductivity of ribbons decreases.

Improving the effectiveness of heat treatment for insect pest control in flour mills by thermal simulations

The aim of this study was the development of a method to improve the effectiveness of heat treatment (HT) for insect pest control in flour mills by thermal analyses and temperature trend models. Specific attention was paid to surface temperatures of thermal bridges (TBs), which represent HT weakness points because they provide refuge to insects and increase expenditure of electric power due to heat flux loss. Air and TB surface temperatures were monitored in a flour mill during execution of an HT. A first thermal analysis showed that values of indoor air temperatures near TBs were always lower than the computed temperature level that would also guarantee insect mortality on TB surfaces. Since the length of the steady-state air temperature profile was lower than that lethal to all insect vital stages, time series forecasting models based on trend analyses were used to simulate the suitable HT duration. The results highlighted that HT should be increased by 9 h to achieve an air temperature above 45 °C. Finally, to obtain TB surface temperatures lethal to insects, simulations were performed of building interventions capable of reducing sensible heat flux loss through the TBs by using insulating materials. The method described in this paper could help operators define a more suitable HT length and support flour mill owners in decision-making when building interventions to improve heat capacity of the mill envelope should be considered to reduce the power consumption of HT.

Heat transfer predictions for helical oscillating heat pipe heat exchanger: Transient condition

The transient temperature profiles of a Helical oscillating heat pipe (HOHP), the heat transfer profiles of the HOHP, and the heat transfer profiles of a HOHP heat exchanger during start-up operation from a numerical model and from an experiment were studied. This article presents the details of a calculation for the HOHP, in which the HOHP has a domain consisting of a pipe wall and a vapor core. The governing equation at the pipe wall and the vapor core of the HOHP was solved by a numerical method. The numerical solution for the transient model in this study was obtained using a finite difference method, and the finite difference method used in this study was the Clank-Nicolson method. The temperature at the pipe wall of the HOHP, the heat transfer of the HOHP, and the heat transfer of the HOHP heat exchanger were plotted as functions of time. The results show that the transient temperature distributions at the pipe wall of the HOHP from the numerical model were successfully compared with the results from the experimental data, which utilizes the concept of temperature distributions during transient operation. The steady state temperature profiles were obtained as a steady temperature was input into the outer wall at the evaporator section of the HOHP. This study also found that the transient heat transfer profiles of the HOHP from the numerical model were successfully compared with the results from the experimental data, which utilizes the concept of heat transfer increments in the HOHP during transient operation. Moreover, it was also found that the transient heat transfer profiles of the HOHP heat exchanger from the numerical model were successfully compared with the results from the experimental data. Therefore, it can be concluded that the numerically validated temperature distributions of the HOHP, the heat transfer of the HOHP, and the heat transfer of the HOHP heat exchanger were successfully simulated in this model.

Production and characterization of the mechanical and thermal properties of expanded polystyrene with recycled material

<p>Three materials were made with mixtures of virgin expanded polystyrene (EPS) grade S3 and recycled material from multipurpose EPS packaging. The latter was subjected to washing and grinding in a blade mill, with percentages by weight of recycled material 10, 15, and 20%. The mechanical properties of these materials were evaluated by testing compressive strength and flexural, impact, and thermal properties using the techniques of differential scanning calorimetry and thermogravimetry. Hot plate and steady state temperature profiles in a non-steady state were simulated with Octave 3.6.4. The results obtained for the three mixtures showed little variation in the properties of compression, impact, glass transition, and thermal diffusivity with respect to the reference material. The regularity of the decline in mass loss as a function of temperature evidences homogeneity in the samples. The flexural strength decreased the maximum failure load compared to the virgin material, and the thermal conductivity exceeded 0.06W/mK, reducing their insulating capacity. These materials can be industrially manufactured in order to produce packaging, caissons, and spheres, among other things.</p>

An effective and efficient numerical method for thermal management in 3D stacked integrated circuits

Three dimensional (3D) integration technology has emerged as a promising solution to improve the performance of microelectronic devices. However, the complex structures and the consequent increase in power density exacerbate the challenge of thermal management in the device with multiple chips. Thus, an effective thermal analysis method is crucial for the reliability of 3D IC device. In this paper, a fast and accurate equivalent approach based on finite element analysis (FEA) was proposed for estimating the equivalent thermal conductivity of 3D IC device, and the proposed numerical model was validated by 3D FEA method. In addition, the estimated equivalent thermal conductivity was employed in thermal analysis of real 3D IC device, whose efficiency significantly outperformed the conventional detailed FE model with comparable accuracy. Furthermore, the effect of the structure and material related parameters on steady-state temperature profiles in 3D stacked packages has been systematically analyzed, including the diameter and pitch of TSVs, the thickness of SiO2, the heat source setting as well as underfill materials, which provides useful insights for thermal management in 3D IC industry.

Inverse method for quantitative characterisation of breast tumours from surface temperature data

Purpose: We introduce a computational method to simultaneously estimate size, location and blood perfusion of the cancerous breast lesion from the surface temperature data.Methods: A 2D computational phantom of axisymmetric tumorous breast with six tissue layers, epidermis, papillary dermis, reticular dermis, fat, gland, muscle layer and spherical tumour was used to generate surface temperature distribution and thereby estimate tumour characteristics iteratively using an inverse algorithm based on Levenberg–Marquardt method. In addition to the steady state temperature data, we modified and expanded the inverse algorithm to include transient data that can be captured by dynamic infra-red imaging. Several test cases were considered for the transient analysis, where the depth, radii and blood perfusion of tumour were varied from 11 to 30 mm, 7 to 11 mm and 0.003 to 0.01 1/s, respectively.Results: Similar steady state temperature profile for different tumours makes it impossible to simultaneously estimate blood perfusion, size and location of tumour using steady state data alone. This becomes possible when transient data are used along with steady state data. For the cases discussed here, the estimates have errors below 1% for tumours with depths less than 20 mm, but for deeper tumours (25 mm) errors can be more than 10%.Conclusions: Combination of transient data and steady state data makes it possible to simultaneously estimate tumour size, location and blood perfusion. Blood perfusion is an indicator of the growth rate of the tumour and therefore its evaluation can possibly lead to the assessment of tumour malignancy.

Phonon and electron temperature and non-Fourier heat transport in thin layers

We present a thermodynamic model of heat conductor which allows for different temperatures of phonons and electrons. This model is applied to calculate the steady-state radial temperature profile in a circular thin layer. The compatibility of the obtained temperature profiles with the second law of thermodynamics is investigated in view of the requirement of positive entropy production and of a nonlocal constitutive equation for the entropy flux.

A numerical model for transient simulation of porous wicked heat pipes by lattice Boltzmann method

A numerical model based on an analytical lumped vapor assumption was proposed for highly efficient simulation of transient performances of heat pipes. The wick is modeled as fully thawed porous medium in which both the Darcian and non-Darcian effects are considered. The evaporation and condensation rates of the working substance are calculated locally as a function of not only the liquid–vapor interface temperature but also the vapor state properties by the kinetic theory. The coupled equations for liquid flow and heat conduction in/between components of the heat pipe are solved by a thermal lattice Boltzmann algorithm. Validation of the model is conducted by reproducing representative cases from the literature and then comparing the present results with their experimental and theoretical data. It turns out that both the transient temperature variation and the steady-state temperature and pressure profiles are in accordance with the literature results. The vapor velocity profile inferred from the evaporation rates is also found to be sufficiently accurate, which even gives a more reasonable estimate than the reference in comparison. In order to further improve the simulation efficiency of the code, non-uniform lattice and parallel algorithm are incorporated, based upon which the lumped vapor model achieves a speed over 50 times faster than the plain model with complete vapor consideration. The present model could serve as an efficient tool for quick evaluation of transient heat pipe behaviors and for assisting parametric studies of heat pipes.

Plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation

Optical localized heating in the nanoscale has recently attracted great attention due to its unique small hot spot size with high energy. However, the hot spot size is conventionally constrained by the diffraction limit. Plasmonic localized heating can provide solutions to this limitation in nanoscale patterning, cancer treatment, and data storage. Plasmonic approaches to overcome the diffraction limit in hot spot size have mainly utilized the excitation of surface plasmon or localized surface plasmon resonance. However, achieving plasmonic localized heating by the excitation of magnetic polariton has not been researched extensively yet. In this work, we numerically investigated the optical response of a nanoscale metamaterial composed of a gold nanowire array and a gold film separated by an ultrathin polymer spacer using ANSYS High Frequency Structural Simulator. A strong absorption peak at the wavelength of 760 nm was exhibited, and the underlying physical mechanism for the strong absorption was verified via the local electromagnetic field distribution to be magnetic resonance excitation. An inductor-capacitor circuit model was used to predict the magnetic resonance wavelength and compare with the numerical results for varied geometrical parameters. Volume loss density due to the strong local optical energy confinement was transferred as heat generation to an ANSYS thermal solver to obtain the local temperature profile. The steady state temperature profile shows an average temperature of 145 °C confined in a local area as small as 33 nm within the spacer, with a full-width at half-maximum of 50 nm along the x-direction. Moreover, the temperature rise from ambient drops to half its maximum value at a distance of 5 nm from the top of the spacer along the z-direction. This clearly demonstrates plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation. Furthermore, the transient temperature profile shows that the system reached steady state within ∼0.36 μs.

Experimental and numerical study of a printed circuit heat exchanger

Printed circuit heat exchangers (PCHEs) are promising to be employed in very-high-temperature gas-cooled reactors (VHTRs) due to their high robustness for high-temperature, high-pressure applications and high compactness. PCHEs typically serve as intermediate heat exchangers (IHXs) that isolate the secondary loop from the reactor’s primary system and hence must be sufficiently robust to maintain the system integrity during normal and off-normal conditions. In addition, the performance of the PCHE-type IHX could considerably affect the nuclear power plant overall operation since any transients on the secondary side would be propagated back to the reactor’s primary coolant system via the IHX. It is therefore imperative to understand how the PCHE would dynamically respond to a variety of transients. In the current study, experiments were first conducted to examine the steady-state thermal performance of a reduced-scale straight-channel PCHE. A dynamic model benchmarked in a previous study was then used to predict the steady-state and transient behavior of the PCHE. The steady-state temperature profiles of the working fluids on both the hot and cold sides and in the solid plates of the heat exchanger were obtained, which served as the initial condition for the transient simulations. The detailed dynamic response of the straight-channel PCHE, subject to inlet temperature variations, helium mass flow variations, and combinations of the two, was simulated and analyzed. In addition, two sets of transient tests, one for helium inlet temperature increase and the other for helium inlet temperature decrease, were experimentally carried out to assess the applicability of the dynamic model. Comparisons of the numerical results with the experimental data show that the dynamic model is successful in predicting the experimental transient scenarios. Although difference was observed between the numerical results and experimental data, the comparisons suggest that the numerical solutions are sufficiently accurate and conservative and that the applicability of the dynamic model proposed for predicting the steady-state and transient performance of the straight-channel PCHE has been confirmed. Furthermore, both the numerical and experimental studies provide insights into the dynamic performance of the PCHE.

Probing HAMR Media Thermal Properties With Pulsed Recording

A new technique for characterizing the thermal properties of heat-assisted magnetic recording media (HAMR) using pulsed near-field heating recording with a static tester is reported. It has the advantage over traditional recording techniques of enabling studies of the 1-100 ns transient thermal configurations rather than only thermal steady states. The technique is applied to HAMR media with different heatsink thicknesses. While each media has a different steady-state temperature profile, the heatsinking differences are eliminated or enhanced by tuning the pulse duration for each media. The technique is used to extract thermal properties of the media.

Thermal-Hydraulic Analysis of the Low- <inline-formula> <tex-math notation="LaTeX">$T_{c}$</tex-math> </inline-formula> Superconductor (LTS) Winding Pack Design Concepts for the DEMO Toroidal Field (TF) Coil

Three design concepts, namely, WP#1, WP#2, and WP#3, for the low- $T_{c}$ superconductor DEMO toroidal field coil was proposed in 2014. This paper is focused on the thermal-hydraulic analysis of all the designs using simplified models, which includes: 1) hydraulic analysis—calculation of the mass flow rates in each conductor at operating conditions during the dwell time; 2) heat removal analysis—calculation of the steady-state mass flow rates and temperature profiles in each conductor as functions of the nuclear heat deposition rate; and 3) estimation of the maximum quench temperature and pressure in each conductor assuming the extreme scenario for the maximum pressure. The detailed analysis of the WP#1 design in burn and in quench conditions using the THEA code was also carried out. It took into account the expected electromagnetic and heat load maps along each conductor and different quench initiation scenarios leading to the maximum hot spot temperature or to the maximum pressure. Our analysis shows that the temperature margin in the WP#1 and WP#3 conductors is sufficiently large, but it is too small in some WP#2 conductors. The hot spot temperatures in some WP#1 cables calculated with THEA are too high. These results provide information for further improvements of the conductors' design.

Three-Dimensional Finite-Element Analysis of the Short-Time and Peak Withstand Current Tests in Substation Connectors

Power devices intended for high-voltage systems must be tested according to international standards, which includes the short-time withstand current test and peak withstand current test. However, these tests require very special facilities which consume huge amounts of electrical power. Therefore, mathematical tools to simulate such tests are highly appealing since they allow reproducing the electromagnetic and thermal behavior of the test object in a fast and economical manner. In this paper, a three-dimensional finite element method (3D-FEM) approach to simulate the transient thermal behavior of substation connectors is presented and validated against experimental data. To this end, a multiphysics 3D-FEM method is proposed, which considers both the connector and the reference power conductors. The transient and steady-state temperature profiles of both the conductors and connector provided by the 3D-FEM method prove its suitability and accuracy as compared to experimental data provided by short-circuit tests conducted in two high-current laboratories. The proposed simulation tool, which was proven to be accurate and realistic, may be particularly useful during the design and optimization phases of substation connectors since it allows anticipating the results of mandatory laboratory tests.