Steady-state Heat Research Articles

Simulation of heat conduction in complex domains of multi-material composites using a meshless method

Several engineering applications involve complex materials with significant and discontinuous variations in thermophysical properties. These include materials for thermal storage, biological tissues, etc. For such applications, numerical simulations must exercise care in not smearing the interfaces by interpolating variables across the interfaces of subdomains. In this paper, we describe a high accuracy meshless method that uses domain decomposition and cloud-based interpolation of scattered data to solve heat conduction in such situations. The method is applicable to both steady state and transient problems. However, we have considered here only steady state heat conduction in complex domains. The polyharmonic spline (PHS) function with appended polynomial of prescribed degree is used for discretization. Flux balance condition must be satisfied at the interface points and the clouds of interpolation points are restricted to be within respective domains. Compared with previously proposed meshless algorithms with domain decomposition, the cloud-based interpolations are numerically better conditioned, and achieve high accuracy through the appended polynomial. The accuracy of the algorithm is demonstrated in several two and three dimensional problems using manufactured solutions with sharp discontinuity in thermal conductivity. Subsequently, we demonstrate the applicability of the algorithm to solve heat conduction in complex domains with practical boundary conditions and internal heat generation. Systematic computations with varying conductivity ratios, interpoint spacing and polynomial degree are performed to investigate the accuracy of the algorithm.

Multimode Brownian oscillators: Exact solutions to heat transport.

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local equation of motion for the reduced density operator, from which we can easily extract not only the reduced system but also hybrid bath dynamical information. The resulting steady-state heat current is found to be numerically consistent with another discrete imaginary-frequency method followed by Meir-Wingreen's formula. It is anticipated that the development in this work would constitute an indispensable component of nonequilibrium statistical mechanics for open quantum systems.

A high geothermal setting in the Linyi geothermal field: Evidence from the lithospheric thermal structure

The lithospheric thermal structure has a profound indicative significance for the potential evaluation and exploration of geothermal resources. The Linyi geothermal field, located in the southern section of the Yishu fault in Shandong Province, boasts abundant geothermal resources. However, its origin is still unclear. This study analyzed the characteristics of terrestrial heat flow using the temperature logging of geothermal wells and measurements of thermal conductivity and heat production. Combined with the geophysical information of the Xiangshui (Jiangsu Province)-Mandula (Nei Mongol) geoscience transect and the lithology revealed by the geothermal wells, this study built a conceptual model of the lithospheric thermal structure using the one-dimensional steady-state heat conduction equation. Based on this model, the heat flow is 64.9 mW/m2, indicating a high geothermal setting in the study area. Furthermore, the ratio of crustal to mantle heat flow is < 1 (0.67), implying that surface heat flow originates predominantly from the mantle. The Yishu fault probably acts as a pathway for heat transfer from the mantle. The temperature of the Moho boundary in the study area was estimated to be 614.8 °C. The Curie depth was calculated to be 29.5 km (585 °C), which is consistent with the depth estimated using the aeromagnetic data. In sum, the Linyi geothermal field has a high geothermal setting, which contributes to the formation of geothermal resources.

Concept of integrating geothermal energy for enhancing the performance of solar stills

Solar stills have been coupled to several preheating systems to increase their productivity, but never before to a borehole exchanger. In this work, a coaxial type borehole exchanger has been integrated with a single basin solar still. Transient and steady-state heat transfer models are presented to assess the behaviour of the combined system for a four-month winter period corresponding to the Urmia Lake region in Iran. Because ground serves as a heat source during winters and a heat sink during summer, integration with a ground exchanger is seen to increase the solar still's productivity for the winter months, by about 126 % for the considered values of parameters. It is also seen that the steady model over calculates the total distillate collected, by about 7 % for ground exchanger integrated still and underestimates it by about 0.2 % for an independent still, respectively. It is observed that larger inner and smaller outer radius of the ground exchanger are desirable. Further, the water mass flow rate is seen to possess an optimal value at which the still's output gets maximized. This work is proposed to be a first step in analysing the usefulness of extracting geothermal energy via a borehole exchanger for desalination application via a solar still.

Some Green’s functions for steady-state heat conduction in anisotropic plane media and their application to thermoelastic boundary element analysis

In this paper, we present several Green’s functions of steady-state heat conduction in anisotropic plane media, including (1) an infinite plane, (2) a half-plane, (3) a bi-material plane, (4) an infinite plane with an elliptical hole or a straight crack, and (5) an infinite plane with an elliptical elastic inclusion. These solutions are obtained by using the link between anisotropic elasticity and heat conduction. We start with reducing the Stroh formalism for two-dimensional anisotropic elasticity to anti-plane deformation and then use the analogy between anti-plane deformation and heat conduction. These Green’s functions serve as fundamental solutions of boundary element method, and the derived temperature field and gradients on the boundary are used as input for thermoelastic analysis. The results of heat conduction and thermoelasticity are verified with analytical solutions or finite element solutions.

Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction

Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Development of pebble-based extruded carbon rods for extreme plasma heat flux environments

This work presents first experiments toward the development of continuously renewable (extrudable) pebble-based carbon rods for use as plasma-facing components in extreme steady-state plasma flux environments. The primary envisioned application of this work is a first wall that can survive long-term in future magnetic fusion power reactors while also improving recovery of the reactor fuel (tritium and deuterium atoms). Bench tests applying extreme steady-state front-surface heat loads of up to 50 MW/m2 are presented. Continuous pebble rod front-surface recession and intact pebble recovery are successfully demonstrated, at a rate of order 0.2 cm/s. Numerical simulations of the pebble rod front-surface recession are able to match observations reasonably well, indicating that the recession mechanism can be understood as occurring due to pebble thermal expansion and resulting shock and cracking of the inter-pebble binder. Tests of the pebble rod extrusion demonstrate that friction between the rods and the stainless steel extrusion channel is tolerably low (<50 N for the expected channel length) over a wide range of temperatures. Front-surface outgassing rates below 1000 Torr L/s/m2 are achieved, believed to be sufficiently low for use in magnetic fusion reactors. Initial parametric scans over pebble rod size and binder fraction to vary front-surface recession rates are presented.

Efficiency at optimal performance of Brownian heat engines under double tangent constraint

The efficiency of a steady-state thermochemical Brownian heat engine is considered, where the heat flux from the hot to the cold reservoir drives particles from the lower chemical potential of the hot reservoir to the higher chemical potential of the cold reservoir, converting heat into chemical or potential energy. This model system is used to investigate the optimal performance of a Brownian heat engine under a new constraint based on a double tangent construction between the occupation number distributions of the particles in the two heat reservoirs with temperatures and chemical potentials . This constraint allows an operation mode that forces the heat engine to attain Carnot efficiency at nonvanishing power output when approaching thermal equilibrium. For classical particles, the efficiency at maximum power under double tangent constraint results to with the asymptotic series expansion , which shows Carnot behavior for toward zero. This efficiency is significantly higher than the corresponding efficiency at unconstrained maximum power derived by Tu (2008 J. Phys. A Math. Theor. 41 312003) for the classical Feynman ratchet and by van den Broeck and Lindenberg (2012 Phys. Rev. E 86 041144) for classical particle transport, which has the expansion showing the Curzon–Ahlborn behavior for toward zero. The applicability of the double tangent constraint to other optimization criteria is demonstrated using the ecological criterion as an example. The method can also be applied to quantum distributions, for which, however, only a numerical solution is possible.

Low cost energy-efficient preheating of battery module integrated with air cooling based on a heat spreader plate

Integration of heating and cooling functions has aroused increasing interest for the automotive battery modules. The proposed cylindrical 18650 battery module is equipped with an external sleeved spreader plate (SHSP), which features low thermal resistance and a large exchange area as an efficient heat transfer medium. The transient temperature characteristics of the battery module were experimentally investigated in both cooling mode and heating mode, respectively. In cooling mode, the temperature characteristics of the battery module equipped with SHSP were examined. With an inlet velocity of 1 m/s and a discharge rate of 3 C, the temperature rise and temperature difference are only 12.9 °C and 2.83 °C at an ambient temperature of 25 °C, respectively. In heating mode, the heat-up characteristics of the battery module were experimentally examined at a subzero temperature of −20 °C under three different heating protocols: continuous heating, fast-rest-slow heating, and slow-rest-fast heating. Immune from potential effects on the battery internal degradation, the heating rate of the battery module in a continuous heating protocol could reach 6.98 °C/min with a heating efficiency of 69.8%, which outperforms the existing external heating modes.Additionally, the fast-rest-slow heating protocol has clear-cut advantages in terms of heating rate while maintaining a smaller temperature difference during the heating phase. Finally, a simplified thermal resistance network model for the cell is established based on the analysis of the one-dimensional steady state heat transfer. According to projections, the thermal resistance of the present heating model is 2.03 K/W, which is less than the hot air convection heating model by 5.24 K/W. The proposed method exhibits excellent performance and provides a low-cost, highly efficient design solution for the battery module under varying conditions.

Characteristics of geothermal field and evaluation of geothermal resource potential in the Yingjiang Basin

Geothermal resource, a green and sustainable energy resource, plays an important role in achieving ‘emission peak’ and ‘carbon neutrality’ targets. The Yingjiang Basin is located in the eastern branch of the Mediterranean-Himalayan high-temperature geothermal belt and exhibits considerable potential for geothermal resources. However, current investigations into the distribution of deep geothermal resources in this region are somewhat limited. In this paper, the transient plane source (TPS) method is used to measure the thermal conductivity parameters of 31 rock samples within the study area. Additionally, the one-dimensional steady-state heat conduction equation is employed to calculate the deep geothermal field, considering the constraints of rock thermal properties and terrestrial heat flow in the study area. Furthermore, the “stripping method” is used to determine the contribution rate of sedimentary layer to terrestrial heat flow, while the volume method is applied to estimate the geothermal resources at burial depths of 3000–5000 m. The results show that (1) The heat generation rate of granite is the highest with an average value of 4.52 μW/m3, followed by gneiss with an average value in the range of 2.0–3.5 W/(m·K), mudstone and sandstone being the lowest with an average value between 1.0 and 2.0 W/(m·K). (2) The main contributor of terrestrial heat flow in the study area is mantle heat flow, and the contribution of sedimentary layers to terrestrial heat flow only accounts for about 2%. (3) The geothermal resources in Yingjiang Basin within the depth range of 3000–5000 m is 93.6 × 1015 kJ, or 3.2 × 109 tonnes standard coal equivalent (SCE).

Energy and exergy analysis of phase change material based thermoelectric generator with pulsed heat sources

Previous studies focus on the generation capacity of phase change material based thermoelectric generator (PCM-TEG) under a steady-state heat source or single pulsed heat source, which cannot fully reflect the dynamic characteristics of TEG under a diversified actual heat source. Meanwhile, the actual heat sources have unstable characteristics of intermittence and fluctuation, resulting in troubles for TEG to maintain effective thermal management and stable generation. In this work, a three-dimensional transient numerical model of PCM-TEG is proposed to characterize its energy harvesting process under multiple pulsed heat sources, including square, triangular, linear and sinusoidal patterns. The effect principle of heat fluxes and heat source periods on PCM-TEG is sensitively performed, aiming to detect the evolution laws of the temperature field and electric field. The energy and exergy analysis of PCM-TEG is determined to indicate its transmission and conversion process. A comparison analysis of PCM-TEG and TEG is carried out to appreciate the thermal management of PCM from temperature difference and failure-free cycle times. The power generation coupling mechanism of PCM-TEG is further developed concerning the phase transition process and power generation process. The results demonstrate that the temperature difference and output power of PCM-TEG change periodically with the pulsed heat sources. The electrical energy and exergy efficiencies of PCM-TEG under square pulsed heat source are 0.10% and 0.45%, higher than other heat sources. Simultaneously, the maximum output power and the electrical energy efficiency of PCM-TEG can be improved by 173.29% and 80% respectively with the enhanced heat flux. Furthermore, although the transient power generation capacity of TEG is weakened by integrating PCM on the hot side, it can alleviate the thermal fatigue of thermoelectric device and meet its thermal management requirements. This paper is informative to understand the dynamics characteristics and power generation coupling mechanism of PCM-TEG for energy harvesting.

Uncertainty quantification by probabilistic analysis of circular fins

Abstract The temperature distribution and thermal Stresses induced by a temperature difference for steady state heat transfer in silicon carbide (SiC) ceramic tube heat exchanger with circular fins was computationally simulated by a finite element method and probabilistically evaluated in view of the several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for the hoop stresses due to the structural and thermodynamic random variables. These results are used to identify the most critical design variables in order to optimize the design and make it cost effective. The probabilistic analysis leads to the selection of the appropriate measurements to be used in structural and heat transfer analysis and to the identification of both the most critical measurements and parameters.

An experimental study to show the effect of forced vertical vibrations on the thermal heat transfer coefficient of a flat plate

The objective of this study is to conduct an experiment that considers the influence of vertical oscillations on the heat transfer coefficient of free convection in an aluminum flat plate component measuring 3 × 100 × 300 mm. The plate is subject to a steady-state heat transfer; whereby it experiences a sustained heat flux ranging from (250–1500) W/m2. The orientation of the flat plate can be either horizontal or inclined at particular angles, specifically at 0°, 30°, 45°, 60°, and 90°. The experimental tests conducted were characterized by an expanded frequency spectrum ranging from 2 to 16 Hz, a variable amplitude range spanning from 1.63 to 7.16 mm, and a range of Rayleigh number values upon activation of the system, with minimum and maximum thresholds of 138.991 and 487.275, respectively. The impact of vibration frequency upon both the amplitude and velocity of vibrations for a heat flow of 250 W/m2, situated at an angle of θ = 0°, was examined. The impact of the Reynolds number upon the total vibrational heat transfer coefficient, as well as the total Nusselt number, was investigated with and without the presence of angle vibration θ = 0°, across diverse degrees of heat flux. This study investigates the impact of the Rayleigh number on the overall Nusselt number under varying conditions of thermal flux, with and without the application of vibration at angles of θ = 30°, 45°, 60°, and 90°. The findings of this analysis demonstrate that there exists a discernible correlation between the incremental amplitude of vibration and the coefficient of heat transfer, manifesting as a negative slope within the range of 0° to 60°. Such correlation reaches its optimal magnitude of 13.2894% under the condition of flat vibration mode, whereas the coefficient of heat transfer declines progressively as vertical vibration is augmented, culminating in a maximum decline of 7.6475%. The present study reports a decrease in the overall vibrational heat transfer coefficient with increasing vibrational Reynolds number. The total Nusselt number was found to increase with or without vibration as the Rayleigh number increased.

Modeling the Effects of Horizontal Transverse Vibrations on the Thermal Behavior and the Ampacity of Rectangular Bus Bars

The purpose of this research is to correctly model steady-state heat transfer in and around rectangular bus bars installed horizontally in an indoor environment and to estimate the corresponding ampacities, considering the effects of horizontal transverse vibrations caused by electromagnetic forces. This thermo-electro-magneto-mechanical problem is solved analytically using correlations determined experimentally by other researchers, while the accuracy of the obtained results is verified numerically using the finite element method (FEM). The novelties of the developed model are as follows. First, modeling the effects of horizontal transverse vibrations on free convection from the top and bottom surfaces of rectangular bus bars via forced convection for different characteristic lengths. Second, modeling the effects of vibration amplitudes and vibration frequencies on the bus bar ampacity. Third, introducing the existing vibration classes (A, B, and C) into the analytical and FEM-based thermal analyses. The results show that with an increase either in the vibration amplitude or the vibration frequency, there is a greater convection-based dissipation of heat from the bus bars and an increase in their ampacity. Finally, for the standard vibration classes, it is found that the effect of horizontal transverse vibrations on the ampacity can be up to 41.99% for Class C.

Resistive Switching: Physics, Devices and Applications

Resistive Switching: Physics, Devices and Applications

Steady-state and power transient critical heat flux experiments of FeCrAl and Zircaloy claddings under saturated pool boiling

FeCrAl and Zircaloy cladding tubes are vertically placed in the saturated pool boiling chamber to perform steady-state and power-transient critical heat flux (CHF) experiments. Three FeCrAl-variants, including FeCrAl-C26M, FeCrAl-B126Y, and FeCrAl-B136Y, are tested to compare their pool boiling thermal performances with traditional Zircaloy claddings including Zirlo, Zr705, and Zircaloy-4. In the steady-state pool boiling experiments, it was confirmed that FeCrAl alloys have higher pool boiling CHF values than Zircaloys. Among these tested materials, FeCrAl-C26M has the highest pool boiling CHF, but the FeCrAl-C26M nucleate boiling heat transfer coefficient is less than that of FeCrAl-B136Y. It reconfirms that CHF is enhanced on the post-CHF oxidized samples. However, as the cycling number of post-CHF oxidization increases, the CHF enhancement becomes less appreciable due to the limited physics contributions of the oxide layer. It is noteworthy that the finalized CHF enhancement can vary a lot between different cladding materials. For example, in three Zircaloy variants, their saturated pool boiling CHF results converge to 980 kW/m2 on the post-CHF oxidized samples. In three FeCrAl variants, their pool boiling CHF results are finalized to 1400 kW/m2. This CHF enhancement difference could be possibly attributed to the chemical constituents of oxide layers presented on cladding surfaces. The Fuchs-reactivity initiated accident transients are simulated by direct current programmable power supply to characterize thermal responses of different claddings to various pulse-width power transients. It is found that the heat transfer coefficients show monotonically increasing parametric trend with respect to faster power-transient rates, i.e., shorter pulse widths. Different from the steady-state pool boiling, the transition boiling regime is phenomenologically reflected in the power-transient pool boiling curve. This potentially implies that power-transient CHF featured by surface temperature overshoot may indicate transient thermal-safety margins not so accurately as the power-transient maximum heat flux. The difference gap of power-transient maximum heat flux between various cladding materials can be gradually closed by the progressive increasing of power transient rates.

Performance Comparison of Helium and sCO2 as Coolants for Modular Finger-Type Divertors

Several studies at the Georgia Institute of Technology have evaluated the thermal and fluids performance of the helium-cooled modular divertor with multiple jets (HEMJ) over the past decade. This finger-type divertor was studied both experimentally at nearly prototypical conditions and numerically at fully prototypical operating conditions using experimentally validated simulations. Recently, supercritical carbon dioxide (sCO2) has been studied as the primary coolant in power cycles and other applications in various systems, in part because CO2 achieves the high densities typical of supercritical fluids at relatively low temperatures and pressures, with a critical point of (7.38 MPa, 31°C). This density makes it possible to realize very compact and efficient sCO2 power cycles. The feasibility of sCO2 as a coolant for plasma-facing components, specifically the divertor, was therefore evaluated as part of the Fusion Energy System Studies design study activities. This work compares the thermal-fluid performance of helium and sCO2 in the HEMJ divertor geometry using numerical simulations at prototypical conditions: inlet temperatures Ti = 600°C to 700°C, pressures p ≈ 10 MPa, and steady-state incident heat fluxes on the tile q″ < 17 MW/m2. The performance is quantified here as the maximum heat flux that can be accommodated by the plasma-facing tile, the pumping power fraction, defined as the ratio of the coolant pumping power to the incident thermal power, and the operating stress limits based on ASME pressure vessel criteria. As expected, helium requires lower mass flow rates and pumping power fractions within imposed maximum temperature limits for the HEMJ pressure boundary. However, it also appears that neither helium nor sCO2 can remove 10 MW/m2 of incident heat flux while meeting ASME pressure vessel criteria. Finally, the numerical modeling reveals that sCO2 may remove slightly higher incident heat fluxes than helium due to the imposed stress limits due to the sCO2 coolant resulting in smaller local temperature gradients, albeit at a considerably higher pumping power fraction.

Long-pulse H-mode operation with stored-energy monitoring for detachment feedback control with a new lower tungsten divertor in EAST

One of the key challenges for future fusion research is to mitigate the high steady-state heat load on the divertor target plates, and divertor detachment offers a promising solution. The Experimental Advanced Superconducting Tokamak (EAST) has developed several feedback control methods for divertor detachment. However, when an off-normal event momentarily disturbs the main plasma, impurity seeding may still be conducted by these methods for detachment, which probably drives the main plasma further away from its stable equilibrium or even causes the disruption. These off-normal events include excessive impurity seeding, loss of heating and dust droplets, which are not rare in current tokamak experiments, especially in long-pulse operation. To compensate for the drawbacks of these methods, we propose and develop a module of stored-energy monitoring to ensure stable plasmas in long-pulse operation. The stored energy usually decreases when the main plasma is away from its stable equilibrium, which is suitable for monitoring the state of the main plasma. Once the stored energy falls below a certain threshold, the module actively switches off the impurity seeding system. Without impurity seeding, the main plasma can recover with the increase in the stored energy. Only when the stored energy exceeds another threshold does the module switch on the impurity seeding to continue the detachment operation. The module function has been verified during the EAST radiative divertor experiments in the newly-upgraded lower tungsten divertor. A typical ∼20 s discharge in grassy-ELM H-mode regime with ∼5 MW source heating power is demonstrated with divertor partial detachment and good energy confinement by active impurity seeding (50% neon, 50% D2). The energy confinement factor is maintained at a high level, i.e. The electron temperature in the core region only has a slight change after the impurity seeding, while the electron density has a ∼10% increase. Furthermore, the ion temperature near the axis also has a remarkable increase. These achievements provide an important demonstration of the actively controlled radiative divertor mitigating the heat loads with good core confinement, which is an essential step toward steady-state operation of fusion reactors.

EXPERIMENTAL AND THEORETICAL STUDY OF TWO-PHASE HEAT PIPE

In this study, thermal characteristics of a two-phase closed heat pipe were investigated experimentally and theoretically. A two-phase closed heat pipe (copper container, Fluorocarbon FC-72 (C6F14) working fluid) was fabricated to examine its performance under the effect of input heat flux range of 250–1253 W/m2 , 70% fill charge ratio and various tilt angles. The temperature distribution along the heat pipe, input heat to evaporator section, and output heat from condenser were monitored. A comprehensive mathematical model was developed to investigate the steadystate heat transfer performance of a two-phase closed heat pipe. A steady state analytical model, is presented to determine important parameters on the design of two-phase closed heat pipe, including temperature levels and heat transfer coefficients for condenser and evaporator. The experimental and simulation results of this work are found in good agreement. The experimental boiling heat transfer coefficients were compared with existing previously reported correlations.