Transient Conduction Research Articles

Method for determining the thermal conductivity of in situ formation rock using drilling cuttings

In this paper, a method for determining the thermal conductivity of in situ formation rock, which combines experimental measurements, theoretical model predictions, and geophysical logging of formation porosity, is presented to predict the thermal conductivity of in situ formation rocks (this method effectively combines experimental measurements, theoretical model, and geological conditions, referred to as “ETG,” where E is for experimental measurements, T is for the theoretical model, and G is for geological conditions). 24 drilling cuttings samples from rocks down to a depth of 2000 m were selected for transient plane source thermal conductivity tests, and an effective thermal conductivity method was used to predict the thermal conductivity of rocks corresponding to each formation. The predicted thermal conductivity of mudstone was 2.31–3.27 W/(m K), and that of sandstone was 2.40–3.69 W/(m K). An independent-samples t test was carried out between the thermal conductivity results from the ETG prediction method and those from a diagenetic mineral-theory model. The results showed that there were no statistically significant differences between the two groups (P > 0.05) and that the fitting degree was high. The mean-square error in the solid thermal conductivities determined by the two methods was about 0.3, which indirectly demonstrates that the ETG method has high accuracy for predicting the thermal conductivity of in situ formation rock. Therefore, this method is likely to become popular in engineering practice.

Analytical Model Quantifying the Net Coolant Flow Rate to a Microstructured Copper Surface Validated With Two-Phase Particle Image Velocimetry Measurements

Abstract Using particle image velocimetry (PIV), the amount of fluid required to sustain nucleate boiling was quantified to a microstructured copper circular disk. Having prepared the disk with preferential nucleation sites, an analytical model of the net coolant flow rate requirements to a single site has been produced and validated against experimental data. The model assumes that there are three primary phenomena contributing to the coolant flow rate requirements at the boiling surface; radial growth of vapor throughout incipience to departure, bubble rise, and natural convection around the periphery. The total mass flow rate is the sum of these contributing portions. The model accurately predicts the quenching fluid flow rate at low and high heat fluxes with 4% and 30% error of the measured value, respectively. For the microstructured surface examined in this study, coolant flow rate requirements ranged from 0.1 to 0.16 kg/s for a range of heat fluxes from 5.5 to 11.0 W/cm2. Under subcooled conditions, the coolant flow rate requirements plummeted to a nearly negligible value due to domination of transient conduction as the primary heat transfer mechanism at the liquid/vapor/surface interface. PIV and the validated analytical model could be used as a test standard where the amount of coolant the surface needs in relation to its heat transfer coefficient or thermal resistance is a benchmark for the efficacy of a standard surface or boiling enhancement coating/surface structure.

Analysis of Transient Teat Conduction in a 2-D Rectangular Fin with Constant Heat Flux.(Dept.M)

The objective of this work is to investigate the 2-D heat conduction in a convectively cooled rectangular fin whose base is subjected to constant heat flux with different fin tip conditions. For this purpose an analytical steady-state solution is obtained based on the traditional approach [separation of variables), Solution of the transient case of this problem isobtained by applying a new developed dimensionless finite difference technique.

Single-phase heat transfer regimes in forced flow conditions under exponential heat inputs

We present an experimental and theoretical investigation of single-phase heat transfer under exponential power inputs. We conduct forced flow experiments with water, covering a broad range of mass fluxes (from 0 to 19,300 kg/m2/s), bulk temperatures (from 25 to 100 °C), pressures (from 0.1 to 1.2 MPa), exponential power escalation periods (from 2.5 to 200 ms), and considering two different heater and channel geometries. We use a high-speed infrared thermometry technique to measure the space- and time-dependent heat transfer coefficient between the heated surface and the coolant, building a database covering 73 different experimental conditions. We consider turbulence as a diffusive process and develop an analytic model that can predict 80% of our database within a ±10% error, and the entire database within a ±20% error. We discuss the presence of three heat transfer regimes, i.e., transient conduction, transient turbulent diffusion, and quasi-steady turbulent heat transfer, and derive analytically the two associated transition criteria. These transitions depend on the power escalation period, fluid properties, and are connected to the profile of the turbulent diffusion properties across the boundary layer.

Verification of ansys and matlab Heat Conduction Results Using an “Intrinsically” Verified Exact Analytical Solution

Abstract A two-dimensional (2D) transient thermal conduction problem is examined, and numerical solutions to the problem generated by ansys and matlab, employing the finite element (FE) method, are compared against an “intrinsically” verified analytical solution. Various grid densities and time-step combinations are used in the numerical solutions, including some as recommended by default in the ansys software, including coarse, medium, and fine spatial grids. The transient temperature solutions from the analytical and numerical schemes are compared at four specific locations on the body, and time-dependent error curves are generated for each point. Additionally, tabular values of each solution are presented for a more detailed comparison. Two different test cases are examined for the various numerical solutions using selected grid densities. The first case involves uniform constant heating on a portion of one surface for a long duration, up to a dimensionless time of 30. The second test case still involves uniform constant heating but for a dimensionless time of one, immediately followed by an insulated condition on that same surface for another duration of one dimensionless time unit. Although the errors at large times for both ansys and matlab are extremely small, the errors found within the short-duration test are more significant, in particular when the heating is suddenly set “on.” Surprisingly, very small errors occur when the heating is suddenly set “off.” The solution developed using the matlab differential equation solver is found to have errors an order of magnitude larger than those generated using ansys with a similar mesh size and same FE type (quadratic triangular). This occurs not only during the transient but also for steady-state problems. However, the matlab computational efficiency is superior. Also, when using ansys, at early times the numerical errors are very sensitive to the time-step chosen rather than the spatial discretization. Therefore, the time-steps have to be very small near a singularity.

Space-time asymptotic expansion method for transient thermal conduction in the periodic composite with temperature-dependent thermal properties

Space-time asymptotic expansion method (AEM) is a rigorous method for solving the multiscale transient thermal conduction problem in periodic composites. However, the AEM is still difficult to model the thermal behavior in composites when temperature-dependent material properties are taken into account. Besides, its complex and costly implementation also restricts the usage of AEM. A space–time AEM for multiscale transient thermal analysis is comprehensively studied in this study to address these issues properly. After the constitutive equation of temperature-dependent characteristic temperature tensor and effective thermal properties in the transient thermal conduction is deduced from the solid theoretical base, a new implementation approach comprised of both homogenization and localization is developed. It can directly model the characteristic temperature tensor within a representative volume element model under simple periodic boundary conditions and linear temperature loads, differing from conventional AEM, which requires complex location-related heat flux loads. Moreover, a new characteristic heat flux tensor is proposed to replace the characteristic temperature tensor in the localization of heat flux. All these contributions simplify the localization in the new implementation. The thermal behavior of A fiber-reinforced composite during the forming process is investigated using the space–time AEM and multiscale finite element method. The comparison results between space–time AEM and multiscale finite element method indicate that the space–time AEM is accurate and efficient as the differences of local temperature and heat flux are 0.0051 °C and 7.2 × 10-5 W/mm2, and the total nodes in space–time AEM is only about half of the multiscale finite element method.

Mechanical and Thermal Behavior of Fibrous Carbon Materials.

The ability of various commercial fibrous carbon materials to withstand stress and conduct heat has been evaluated through experimental and analytical studies. The combined effects of different micro/macro-structural characteristics were discussed and compared. Large differences in mechanical behavior were observed between the different groups or subgroups of fibrous materials, due to the different types of fibers and the mechanical and/or chemical bonds between them. The application of the Mooney–Rivlin model made it possible to determine the elastic modulus of soft felts, with a few exceptions, which were studied in-depth. The possible use of two different mechanical test methods allowed a comparison of the results in terms of elastic modulus obtained under different deformation regimes. The effective thermal conductivity of the same fibrous materials was also studied and found to be much lower than that of a single carbon fiber due to the high porosity, and varied with the bulk density and the fiber organization involving more or less thermal contact resistances. The thermal conductivity of most materials is highly anisotropic, with higher values in the direction of preferential fiber orientation. Finally, the combination of compression and transient thermal conductivity measurement techniques allowed the heat conduction properties of the commercial fibrous carbons to be investigated experimentally when compressed. It was observed that thermal conductivity is strongly affected under compression, especially perpendicular to the main fiber orientation.

Infrared high-speed thermography of combustion chamber wall impinged by diesel spray flame

As a demonstration of a new method to examine the extremely unsteady and spatially varying wall heat transfer phenomena on diesel engine combustion chamber wall, high-speed imaging of infrared thermal radiation from the wall surface impinged by a diesel spray flame was attempted using a high-speed infrared camera. A 35 mm-diameter chromium-coated quartz window surface was impinged by a diesel spray flame with an impinging distance of 27 mm from the nozzle orifice in a constant volume combustion chamber. The infrared thermal radiation from the back surface of the 0.6 µm thick chromium layer was successfully visualized at 10 kHz frame rate and 128 × 128 pixel resolution through the quartz window. The infrared radiation exhibited coherent and streaky structure with radial stripes extending and waving from the stagnation point. The width of the radial stripes, spatial amplitude and the period of the waving movement were comparable to the ones for turbulent heat transfer on the engine cylinder wall previously measured with a heat flux sensor, suggesting that they are resulting from the turbulent structure in the wall-impinging diesel flame. The radiation intensity was calibrated to temperature and converted to heat flux via 3-D numerical analysis of transient thermal conduction in the quartz window. The peak-to-peak variation amplitudes of temperature and heat flux among the radial stripes during the diesel spray flame impingement were about 20 K and 2.3 MW/m2, corresponding to 13% of 150 K maximum temperature swing amplitude and 18 MW/m2 maximum heat flux, respectively.

Understanding the sodium cation conductivity of human epileptic brain tissue.

Transient and frequency-dependent conductivity measurements on excised brain-tissue lesions from epilepsy patients indicate that sodium cations are the predominant charge carriers. The transient conductivity ultimately vanishes as ions encounter blockages. The initial and final values of the transient conductivity correspond to the high-frequency and low-frequency limits of the frequency-dependent conductivity, respectively. Carrier dynamics determines the conductivity between these limits. Typically, the conductivity rises monotonically with increasing frequency. By contrast, when pathology examinations found exceptionally disorganized excised tissue, the conductivity falls with increasing frequency as it approaches its high-frequency limit. To analyze these measurements, excised tissues are modeled as mixtures of “normal” tissue within which sodium cations can diffuse and “abnormal” tissue within which sodium cations are trapped. The decrease in the conductivity with increasing frequency indicates the predominance of trapping. The high-frequency conductivity decreases as the rate with which carriers are liberated from traps decreases. A relatively low conductivity results when most sodium cations remain trapped in “abnormal” brain tissue, while few move within “normal” brain tissue. Thus, the high densities of sodium nuclei observed by 23Na-MRI in epilepsy patients’ lesions are consistent with the low densities of diffusing sodium cations inferred from conductivity measurements of excised lesions.

Modelling and Simulation of Thermo-Physical Property of Composite Material

Thermo-physical property measurement is a significant methodology as these properties are the input for designing thermal systems. Properties of materials like thermal conductivity, thermal diffusivity and specific heat capacity has to be estimated in prior to estimate the thermal performance of any material. In the present work, numerical simulations were performed to estimate the thermo-physical properties of a polymer based composite material using porous medium modelling. The weight fraction of the composites and fibres are incorporated into the simulations through porosity. The transient heat diffusion equation are solved using ANSYS Fluent for a polymer based composite material using semi-infinite transient conduction approach. The thermal conductivity and thermal diffusivity are estimated simultaneously for various volume fractions of polyester and banana fibre. The temporal temperature distribution data predicted from ANSYS Fluent is curve fitted using MATLAB and the obtained values of thermal conductivity and thermal diffusivity are compared with the previously reported experimental results and are found to be within a deviation of 7 % for all cases.

Analysis of the transient Joule heating effect in a conductive-bridge random-access memory (CBRAM) using a single-phase-lag (SPL) model

The main objective of this work is to study the transient Joule heating effect in a conductive-bridge random-access memory (CBRAM) using the single-phase-lag heat conduction model to describe the effects of the metallic conductive filament (CF) radius and the reset voltage on the thermal and electric field. The results reveal that the CF geometry plays an important role in the transient Joule heating. The heat wave of fast transient conduction is stronger in the narrow region of the CF during the reset process for a high applied voltage and a small top radius of the CF. It is demonstrated that the presented model can predict the nanoscale heat transfer in the transient state and during the reset process in the CBRAM. Finally, numerical computations are carried out using the finite-element method to solve the nonlinear heat conduction equations.

Epidemiological, demographic, laboratory, clinical management, and outcome data of symptomatic bradyarrhythmia in COVID-19 patients

BackgroundCardiovascular manifestations are an important cause of mortality and morbidity in COVID-19 infections. Conduction system abnormality in the form of symptomatic bradyarrhythmia is underreported in the literature. AimTo evaluate epidemiological, demographic, laboratory, clinical management, and outcome data of symptomatic bradyarrhythmia in COVID-19 patients. MethodsThis was a retrospective, observational study including all the adult patients (>18 years) who were diagnosed with COVID-19 infection and had complete heart block (CHB) or symptomatic high-grade Atrio-Ventricular (AV) block requiring a temporary pacemaker insertion (TPI). Epidemiological, demographic, laboratory, clinical management, and outcome data were extracted from all the enrolled patients and studied for the primary clinical composite endpoint of all-cause death. ResultsThe study population included 15 patients, including 14 patients with CHB and 1 patient with 2:1 AV block. Syncope was the most common presentation. The clinical endpoint in the form of death was seen in 5 patients (33.3%), 3 patients reverted to sinus rhythm, and 7 patients required permanent pacemaker implantation. The markers of inflammation were raised in all patients; however trend toward more inflammation was seen in patients reaching the primary clinical endpoint. 3 out of 7 patients with narrow QRS rhythm reverted to normal sinus rhythm, while all 8 patients with broad complex QRS either died or required a permanent pacemaker insertion. ConclusionSymptomatic bradyarrhythmia is associated with a high inflammatory state, and high mortality in COVID-19 infection and a transient conduction block in patients with narrow QRS rhythm may suggest local subclinical myocardial inflammation.

Experimental study of critical heat flux in pool boiling using visible-ray optics

Liquid, vapor and their dynamics on boiling surfaces were directly observed by a simple visible-ray optics with a sub-millisecond time scale. The observation results revealed that the critical heat flux (CHF) was triggered by a localized dry region. The fast and dense nucleation of vapor bubbles, and liquid supplied to the dry regions by bubbles, afford the boiling process with extremely high heat transport capability. However, the intensive nucleation of the bubbles in a narrow region, and their coalescence, generated a large, irregularly shaped dry region at high heat flux that functioned to impede heat transfer between the boiling surface and fluid. Sequential images showing the phase distribution revealed that the gravity-driven liquid flow was obstructed by the excessive evaporation occurring around the local dry region that triggered the CHF condition. We propose a CHF triggering mechanism based on gravity and vapor recoil force balance. Under the conditions of saturated water boiling under 1 atm of pressure, these forces balance were balanced when the temperature of the dry region was approximately 130°C. The temperature limit corresponding to the non-wetting of a local dry spot was found to be in agreement with previous studies and our simulation results for transient thermal conduction on a boiling surface.

Numerical study of the influence of thermal radiation on measuring semi-transparent thermal insulation material with hot wire method

Semi-transparent thermal insulation material has very low extinction coefficient and will transmit infrared spectrum within some wavelength range. When measuring the thermal conductivity (TC) of such kinds of material with transient methods, both heat conduction and thermal radiation occur within material. Transient hot wire (HW) method is a widely used method for thermal insulation measurement. It is developed with the assumption that heat only transfers via conduction. Since thermal radiation within low density thermal insulation material is a pronounced heat transfer mode at high temperature, the TC of radiation participating medium measured by HW method might be incorrect. To reveal the inconsistency between test theory and practical heat transfer process when measuring semi-transparent thermal insulation material with HW method, the transient conduction and radiation coupled heat transfer process is simulated numerically. The uncertainty caused by thermal radiation is investigated for material with different extinction coefficient at various temperature. The deviation increases with the increment of temperature and decreases with increment of extinction coefficient compared to results obtained from the one dimensional (1D) steady state method. The numerical analysis indicates that the TC of thermal insulation material with low extinction ability measured by HW method is overestimated at high temperature.

Mechanism of the Initial States of a Bubble Formation and Departure from a Heated Surface in a Subcooled Flow

Growth of a nonisothermal bubble on a heated horizontal surface in a subcooled flow is studied to determine the significance of different heat transfer mechanisms on the bubble growth. The heat transfer mechanisms that are considered are (1) microlayer evaporation, (2) transient thermal boundary layer conduction, and (3) bubble surface evaporation and condensation. The results indicate that a different heat transfer mechanism dominates the bubble growth at different stages of the bubble growth. And, the temperature gradient inside the bubble decreases after bubble liftoff in high Reynolds numbers. The results also show an oscillatory heat flux during the initial stages of the bubble growth.

Usage of the finite difference method for solving one-dimensional heat equations*

In this paper the one-dimensional heat equations with the heat generation arising in the associated fractal transient conduction is investigated. Analytical solutions are obtained by using the finite difference method (FDM). The method, in general, is easy to implement and it yields good results. In addition, the uniqueness and stability results are also discussed. Some illustrative examples are included to demonstrate the validity and applicability of the technique.

Four‐phase interleaved TCM DC‐DC buck converter with matrix inductor in battery charging application

In this paper, a 1-kW DC-DC buck converter with a four-phase interleaved matrix inductor is proposed for battery charging applications. It is well-known that the DC bias on the inductor will cause high core loss as it changes the B–H characteristic. Typically, the transient conduction mode employed in high voltage applications for zero-voltage-switching of devices would cause higher inductor current ripple. The conventional approach to reduce the effect of DC bias and inductor current ripple is employing multi-phases. However, the cost and size of the converter will increase significantly. This paper proposes the matrix inductor which has a small volume and reduces the effect of the DC bias by flux sharing and flux cancellation at the same time, results in low inductor core loss. With the interleaved operations the output current ripple can be lower which is suitable for battery charging application. Besides, the comparison of the synchronous and interleaved operation is presented. A 1-kW prototype is built and the experimental results show that the peak efficiency is 99.1% and 99.2% for synchronous and interleaved control, respectively. Additionally, the output current ripple of the interleaved operation is reduced by 85% in comparison with the synchronous operation.

Coupling the BEM and analytical solutions for the numerical simulation of transient heat conduction in a heterogeneous solid medium

This paper simulates the three-dimensional transient heat diffusion conduction in a solid medium containing multi-layered cylindrical circular heterogeneities using a coupling formulation between the boundary element method (BEM) and analytical solutions. The analytical solutions are incorporated as Green's functions, thereby making the discretization of the interfaces of the multi-layered system unnecessary; this improves the efficiency of the algorithm. The coupling is enforced by imposing the continuity of temperature and heat fluxes at virtual interfaces created around each heterogeneity.The solution is first computed in the frequency domain, for a wide range of frequencies and axial wavenumbers, using complex frequencies to avoid aliasing phenomenon. Time series can then be obtained by means of a (fast) inverse Fourier transform.The accuracy, efficiency, and stability of the proposed algorithms are confirmed by comparing the results against reference solutions. The transient analysis of heat diffusion in a solid medium in the presence of multi-layered inclusions is used to illustrate the potential of the proposed coupling formulation.

Composite Laminate Delamination Detection Using Transient Thermal Conduction Profiles and Machine Learning Based Data Analysis.

Delaminations within aerospace composites are of particular concern, presenting within composite laminate structures without visible surface indications. Transmission based thermography techniques using contact temperature sensors and surface mounted heat sources are able to detect reductions in thermal conductivity and in turn impact damage and large disbonds can be detected. However delaminations between Carbon Fibre Reinforced Polymer (CFRP) plies are not immediately discoverable using the technique. The use of transient thermal conduction profiles induced from zonal heating of a CFRP laminate to ascertain inter-laminate differences has been demonstrated and the paper builds on this method further by investigating the impact of inter laminate inclusions, in the form of delaminations, to the transient thermal conduction profile of multi-ply bi-axial CFRP laminates. Results demonstrate that as the distance between centre of the heat source and delamination increase, whilst maintaining the delamination within the heated area, the resultant transient thermal conduction profile is measurably different to that of a homogeneous region at the same distance. The method utilises a supervised Support Vector Classification (SVC) algorithm to detect delaminations using temperature data from either the edge of the defect or the centre during a 140 s ramped heating period to 80 C. An F1 score in the classification of delaminations or no delamination at an overall accuracy of over 99% in both training and with test data separate from the training process has been achieved using data points effected by transient thermal conduction due to structural dissipation at 56.25 mm.

Kv11 (ether-à-go-go-related gene) voltage-dependent K+ channels promote resonance and oscillation of subthreshold membrane potentials.

Key points Some ion channels are known to behave as inductors and make up the parallel resonant circuit in the plasma membrane of neurons, which enables neurons to respond to current inputs with a specific frequency (so‐called ‘resonant properties’).Here, we report that heterologous expression of mouse Kv11 voltage‐dependent K+ channels generate resonance and oscillation at depolarized membrane potentials in HEK293 cells; expressions of individual Kv11 subtypes generate resonance and oscillation with different frequency properties.Kv11.3‐expressing HEK293 cells exhibited transient conductance changes that opposed the current changes induced by voltage steps; this probably enables Kv11 channels to behave like an inductor.The resonance and oscillation of inferior olivary neurons were impaired at the resting membrane potential in Kv11.3 knockout mice.This study helps to elucidate basic ion channel properties that are crucial for the frequency responses of neurons. The plasma membranes of some neurons preferentially respond to current inputs with a specific frequency, and output as large voltage changes. This property is called resonance, and is thought to be mediated by ion channels that show inductor‐like behaviour. However, details of the candidate ion channels remain unclear. In this study, we mainly focused on the functional roles of Kv11 potassium (K+) channels, encoded by ether‐á‐go‐go‐related genes, in resonance in mouse inferior olivary (IO) neurons. We transfected HEK293 cells with long or short splice variants of Kv11.1 (Merg1a and Merg1b) or Kv11.3, and examined membrane properties using whole‐cell recording. Transfection with Kv11 channels reproduced resonance at membrane potentials depolarized from the resting state. Frequency ranges of Kv11.3‐, Kv11.1(Merg1b)‐ and Kv11.1(Merg1a)‐expressing cells were 2–6 Hz, 2–4 Hz, and 0.6–0.8 Hz, respectively. Responses of Kv11.3 currents to step voltage changes were essentially similar to those of inductor currents in the resistor–inductor–capacitor circuit. Furthermore, Kv11 transfections generated membrane potential oscillations. We also confirmed the contribution of HCN1 channels as a major mediator of resonance at more hyperpolarized potentials by transfection into HEK293 cells. The Kv11 current kinetics and properties of Kv11‐dependent resonance suggested that Kv11.3 mediated resonance in IO neurons. This finding was confirmed by the impairment of resonance and oscillation at –30 to –60 mV in Kcnh7 (Kv11.3) knockout mice. These results suggest that Kv11 channels have important roles in inducing frequency‐dependent responses in a subtype‐dependent manner from resting to depolarized membrane potentials.