Conductive Heat Loss Research Articles

Physics-informed convolutional neural networks for temperature field prediction of heat source layout without labeled data

Recently, surrogate models based on deep learning have attracted much attention for engineering analysis and optimization. Since constructing data pairs in most engineering problems is time-consuming, data acquisition is becoming the predictive capability bottleneck of most deep surrogate models, which also exist in surrogate for thermal analysis and design. In contrast with data-driven learning, enforcing the physical laws in building surrogates has emerged as a promising alternative to reduce the dependence on annotated data. This paper develops a physics-informed convolutional neural network (CNN) for the thermal simulation surrogate without labeled data. Firstly, we leverage the finite difference method to integrate heat conduction equation and loss function construction, guiding surrogate model training to minimize the violation of physical laws. Since the solution is sensitive to boundary conditions, we properly impose hard constraints by padding in the Dirichlet and Neumann boundaries. The proposed network can learn a mapping from heat source layout to the steady-state temperature field without labeled data, which equals solving an entire family of partial difference equations (PDEs). Moreover, the neural network architecture is well-designed to improve the prediction accuracy of the problem at hand, and pixel-level online hard example mining is proposed to overcome the imbalance of optimization difficulty in the computation domain, which is beneficial to the network training of physics-informed learning. The experiments demonstrate that the proposed method can provide comparable predictions with numerical methods and data-driven deep learning models. We also conduct various ablation studies to investigate the effectiveness of the proposed network components and training methods in this paper. Furthermore, the developed methods can be applied to other design and optimization applications which need to solve parameterized PDEs.

Nature-inspired pyramid-shaped 3-dimensional structure for cost-effective heat-localized solar evaporation with high efficiency and salt localization

• A nature-inspired material for heat-localized solar evaporation is proposed. • The durian-based evaporator forms a hierarchical structure for solar absorption. • An extremely high solar absorption of over 99% is achieved. • A high evaporation rate of 1.66 k g m - 2 h - 1 under one sun illumination is achieved. • The unique structure could enable localized salt localization for long-term operation. Solar evaporation by heat localization has drawn great interest in recent years to ease the global problem of freshwater shortage. Although many evaporators have been proposed, there is still great potential to develop extremely cost-effective solar evaporators with both high evaporation efficiency and salt resistance. Here, we propose a heat-localized solar evaporator based on wasted durian shells. After carbonization and polypyrrole deposition, this durian shell-based evaporator achieved a 99% absorption in the whole solar spectrum, owing to its hierarchical solar absorption structure from macroscale to nanoscale. We further make the bottom surface of the evaporator to be curved to reduce the conductive heat loss, and the structure-optimized durian shell-based evaporator achieved a high evaporation rate of 1.66 k g m - 2 h - 1 and evaporation efficiency of 91% under the solar intensity of 1000 W m - 2 . In addition, the pyramid-shaped structures on the surface of durian shells could enable localized salt crystallization, which enables long-term operation of such evaporators in the saline environment. This work presents an attempt with significance in developing extremely cost-effective materials for highly efficient heat-localized solar evaporation.

Design and multi-objective optimization of a new annular constructal bifurcation Stirling regenerator using response surface methodology

The irreversible losses such as the flow loss and axial heat conduction loss in traditional porous regenerators have limited the specific power and thermal efficiency of Stirling engines to a great degree. Thereby, the objective of this paper is to design and optimize a novel annular constructal bifurcation regenerator for diminishing the flow and axial heat conduction losses in the regenerator based on constructal concept and response surface methodology. First, the bifurcation type structure units with an inclined angle to the flow direction and the layered approach were applied to construct the regenerator matrix. Thereafter, the numerical simulations were employed to investigate the gas flow and heat transfer characteristics of the constructal bifurcation regenerator. Based on the numerical data, the quadratic polynomial regression models between the geometric parameters and the regenerator performance were established using response surface methodology, and the specific effects of the geometric dimensions were analyzed via 2-D and 3-D response surface plots. Subsequently, a multi-objective optimization was conducted to minimize the flow resistance and maximize the heat transfer rate by genetic algorithm. A most eclectic solution with the global friction factor f = 3.478 and the number of heat transfer units NTU = 1.135 was selected from the optimal Pareto front. Finally, the overall performance of the constructal bifurcation regenerator was compared with that of the porous regenerator and the parallel geometry regenerator. The results indicate that a low flow resistance, low axial heat conduction, and high thermal performance are obtained by the constructal bifurcation regenerator. Therefore, it is reasonable to conclude that the annular constructal bifurcation regenerator achieves a high comprehensive performance, with the potential to improve the performance of Stirling engines. The findings of this paper may provide some new ideas and guidelines for the design and optimization of the regenerator structures.

Theoretically predicting the flame-spread limit of carbon-fiber-reinforced plastic

This work studied the flame-spread limit of carbon-fiber-reinforced plastic (CFRP) sheets and attempted estimating it theoretically. First, to measure the limiting oxygen concentration (LOC), the CFRP sheets with different carbon fiber (CF) orientations were combusted under variable opposed-flow velocity (Vg) and oxygen concentration. The flammability decreased as the CF orientation angle (θ) was increased. Increasing θ facilitated conductive heat losses sideways through the CFs, resulting in the low flammability. The LOC decreased with increased Vg. A flame leaned toward the solid surface as Vg was increased, leading to the high heat transfer rate from the flame. The increased heat transfer rate accelerated the flame spread to decrease the LOC. The decrease in the LOC was similar to the trend in the radiative regime for polymers. Next, the LOC was estimated via an equation that describes the radiative extinction. The calculated flame-spread limit, however, did not quantitatively agree with the measured LOCs, because that equation was derived from the conventional flame spread model that does not consider the solid-phase heat transfer. Nevertheless, the solid-phase heat transfer was dominant in the flame spread over the CFRP sheets. Then, a novel equation on the radiative extinction was formulated according to the flame spread model of CFRP. Although the response of the flame spread rate and the LOC to Vg was well simulated, a good agreement between the computed and measured LOCs was still not obtained. This is probably because the observed extinction of the CFRP sheets would not be governed by the radiative extinction, though both the radiative and blow-off extinctions are dominant. Therefore, to obtain the correct flame-spread limit, it is necessary to develop and solve an equation that considers both extinctions with true properties of the CFRP sheets.

Investigation of the thermal conductivity of molten LiF-NaF-KF with experiments, theory, and equilibrium molecular dynamics

• Thermal conductivity of molten eutectic LiF-NaF-KF is measured from 834 to 1195 K with the variable gap technique. • Thermal conductivity of LiF-NaF-KF is predicted with a kinetic theory derived model and equilibrium molecular dynamics. • Temperature dependence of the thermal conductivity of LiF-NaF-KF is discussed from an experimental and theoretical viewpoint. • Inconsistencies between experimental data on thermal conductivity of molten LiF-NaF-KF reported in literature are discussed. • Mapping of the thermal conductivity of LiF-NaF-KF is proposed in the entire range of temperature from 750 K to 1300 K. Molten salts are being proposed for numerous advanced energy applications, including advanced nuclear reactors, concentrating solar power plants, thermal energy storage, and fusion reactors. Accurate knowledge of the thermophysical properties of molten salts directly impact the performance of these energy systems and are essential for design and safety analyses. Thermal conductivity data for fluoride molten salt and mixtures are especially lacking. In this work, experimental measurements of thermal conductivity using the steady-state variable gap technique were performed on eutectic LiF-NaF-KF from 834 to 1195 K. The experiment accounts for radiative, convective, and conductive heat losses. In addition, theoretical and molecular dynamics models are used, from 750 K up to 1300 K, to estimate the thermal conductivity for comparison with the experimental results. The results of experiments show a weak negative deviation of thermal conductivity with temperature, unlike previous experimental results in the literature. The measured thermal conductivity magnitudes agree with the theoretical and molecular dynamics predictions, aside from the data above 1100 K, where heat losses and radiative errors are the most significant, having a 16% maximum deviation from theory. These experimental results provide new thermal conductivity data for the LiF-NaF-KF system and further validation of the predictive models. The theoretical model was used to map the composition and temperature dependent thermal conductivity of LiF-NaF-KF and the mapping’s deviation from a linear additivity estimation of thermal conductivity. This mapping showed the highest deviations from linearity for KF-LiF rich mixtures and increasing deviation with temperature. Notably, the deviation from linearity near the LiF-NaF-KF eutectic composition was around 25%.

Quantifying the Potential of the Xtract Heatsaver System to Enhance Thermoregulation and Prevent Hypothermia in Combat Casualties

Conductive or convective heat loss is a serious concern in combat casualties that are an enhanced risk of hypothermia due to shock and environmental exposures. Eleven subjects participated in repeated measures study designed to assess whether alternative hypothermia prevention systems can retain body temperatures better in a cold environment than the currently fielded solution. Results showed that when the subjects were using the new Xtract Heatsaver System there was significantly less change in the body’s core temperature and less thermal discomfort as compared with the currently field Hypothermia Prevention and Mitigation Kit.

Experimental study on burning behavior of n-heptane in ice cavities with different aspect ratios

In situ burning is a widely used method in oil spill cleanup. This paper aims to study the burning behavior of n-heptane in ice cavities with aspect ratios ranging from 1 to 10. The depth and opening area of ice cavities were 9 cm and about 100 cm2, respectively, for all cases before ignition. Results show that the dynamic variation process of burning zone is different in square cavities and cavities with aspect ratio larger than one. For square cavities, the flame accumulates in the middle area of the cavity after ignition. For cavities with aspect ratio larger than one, at the early stage, there are unevenly distributed clusters of pulsating flames; and afterwards, the flames at different positions are gradually connected as a whole. A ring-shaped flame is observed in all cases before the extinguishing, and through theoretical analysis, it is believed that this phenomenon may be caused by the surface tension driven flow inside the water layer. In each case, at the same height, invasion lengths, i.e., horizontal distance between the cavity edge before and after burning, along the short and long sides are basically the same (average relative standard deviation: 1.60 %). And the invasion lengths show a non-monotonic trend of increasing first and then decreasing slightly with height in all cases. In addition, at the same height, the opening area of cavity increases as aspect ratio increases. For cavities with the same initial fuel layer thickness and fuel volume, the variation of aspect ratio results in little change in the growth and decay rate of mass loss rate, with the maximum relative standard deviation of 8.84 %. Heat is lost via thermal radiative penetration, conduction of fuel layer to ice walls, and conduction of fuel layer to water. Based on calculation, it is found the sharp decrease of mass loss rate cannot only be attributed to conductive heat loss, thermal radiative penetration is also an important part, which even accounts for about one-third of the total heat loss.

Stable circular and double-cell lean hydrogen-air premixed flames in quasi two-dimensional channels

In this work, a computational study on nearly two-dimensional reacting fronts under canonical configurations is proposed. Specifically, a quasi-2D description of the conservation equations with a one-step irreversible Arrhenius chemical model is used to simulate ultra-lean hydrogen-air premixed flames that slowly propagate over streams of reactants that are confined between plates and are subject to conductive heat losses. Under these conditions, recent previous experiments identified two unprecedented stable flame configurations: two-headed and circular isolated flames. This study identified buoyancy and the relative importance of conductive heat losses as the two parameters controlling the formation of these isolated flames. The numerical evaluation of the different terms ascertains the physical mechanisms that drive the formation of two-headed or circular flames. Additionally, the systematic variation of the controlling parameters depicts the maps of stable solutions that determine the capability of the two flame configurations to emerge. In particular, the existence of a range of parametric values in which both flame configurations are stable proves, also, that initial conditions are crucial to determine which of the two configurations prevails.

Emulsion‐templated synthesis of 3D evaporators for efficient solar steam generation

AbstractInterfacial solar steam generation holds great promise in water desalination thanks to its high energy efficiency by heating only the top layer of water for evaporation. While three‐dimensional (3D) evaporators have been proven to increase the evaporation rate by harnessing the energy from the surroundings, further development is still required in terms of convenient fabrication with potential scalability. Herein, we propose to overcome this challenge by using a high internal phase emulsion (HIPE) to template the synthesis of 3D hierarchically porous evaporators. The HIPE‐templated synthesis combined with a molding process can efficiently fabricate the desired 3D shape without wasting any materials and generate a hierarchically porous internal structure for continuous water supply. Engineering the overall shape and internal pores produces a 3D evaporator that can suppress conduction heat loss and efficiently collect thermal energy from its surroundings, boosting the evaporation rate to 2.82 kg/(m2 h) under 1‐sun illumination, which is significantly higher than conventional 2D evaporators. HIPE‐templating synthesis is an easy but effective way to produce various porous polymers, promising for a wide range of applications where easy production, excellent shape control, and potential scalability are critical.

3D Hydrogel Evaporator with Vertical Radiant Vessels Breaking the Trade-Off between Thermal Localization and Salt Resistance for Solar Desalination of High-Salinity.

Delivering sufficient water to the evaporation surface/interface is one of the most widely adopted strategies to overcome salt accumulation in solar-driven interfacial desalination. However, water transport and heat conduction loss are positively correlated, resulting in the trade-off between thermal localization and salt resistance. Herein, a 3D hydrogel evaporator with vertical radiant vessels is prepared to surmount the long-standing trade-off, thereby achieving high-rate and stable solar desalination of high-salinity. Experiments and numerical simulations reveal that the unique hierarchical structure, which consists of a large vertical vessel channel, radiant vessels, and porous vessel walls, facilitates strong self-salt-discharge and low longitudinal thermal conductivity. With the structure employed, a groundbreaking comprehensive performance, under one sun illumination, of evaporation rate as high as 3.53kgm-2 h-1 , salinity of 20wt%, and a continuous 8h evaporation is achieved, which thought to be the best reported result from a salt-free system. This work showcases the preparation method of a novel hierarchical microstructure, and also provides pivotal insights into the design of next-generation solar evaporators of high-efficiency and salt tolerance.

Alkali treatment combined with surface carbonized wood for high-efficiency solar interfacial evaporation

With the shortage of fresh water, one of the most promising strategies to solve this problem is solar interfacial evaporation. Due to the porous structure, low heat conduction, high hydrophilicity and renewability, we develop a wood-based solar generator by a facile method of alkali treatment and surface carbonization (ASC-wood). Surface carbonization could endow wood generators with a high sunlight absorbency and alkali treatment could improve the water delivery capacity. For further reduce heat conduction loss, an insulation-layer system was proposed in this work. Benefiting from these advantages, the ASC-wood generator can reach an evaporation rate of 1.21 kg m−2 h−1 and an evaporation efficiency of 81.3% under 1 sun irradiation. In addition, the ASC-wood generator shows an outstanding cycling performance and structural stability, which is favorable for outdoor applications. This work provides a simple method to manufacture a scalable, cost-effective, high-efficiency and high-strength solar steam generator. Also, the effect of water temperature on solar evaporation performance was studied, and results show that the pure evaporation efficiency will first increase and then decrease with the increase of water temperature from 20 ℃ to 40 ℃, indicating a way for improving the evaporation efficiency by matching the sensible heat as well as the latent heat.

Different Ice-shell Geometries on Europa and Enceladus due to Their Different Sizes: Impacts of Ocean Heat Transport

On icy worlds, the ice shell and subsurface ocean form a coupled system—heat and salinity flux from the ice shell induced by the ice-thickness gradient drives circulation in the ocean, and in turn, the heat transport by ocean circulation shapes the ice shell. Therefore, understanding the dependence of the efficiency of ocean heat transport (OHT) on orbital parameters may allow us to predict the ice-shell geometry before direct observation is possible, providing useful information for mission design. Inspired by previous works on baroclinic eddies, I first derive scaling laws for the OHT on icy moons, driven by ice topography, and then verify them against high-resolution 3D numerical simulations. Using the scaling laws, I am then able to make predictions for the equilibrium ice-thickness variation knowing that the ice shell should be close to heat balance. The ice shell on small icy moons (e.g., Enceladus) may develop strong thickness variations between the equator and pole driven by the polar-amplified tidal dissipation in the ice; in contrast, the ice shell on large icy moons (e.g., Europa, Ganymede, Callisto, etc.) tends to be flat due to the smoothing effects of the efficient OHT. These predictions are manifested by the different ice-evolution pathways simulated for Enceladus and Europa, considering the ice freezing/melting induced by ice dissipation, conductive heat loss, and OHT as well as the mass redistribution by ice flow.

A Numerical Study on the Energization of the Field Coils of a Full-Size Wind Turbine with Different Types of Flux Pumps

High temperature superconductivity is emerging as a solution for lightweight, cost-effective and high-power wind generators. Current injection and maintainment/sustainment in the field winding are obtained by metal current leads which, due to persistent heat conduction and joule loss, are responsible for a large part of the total cryogenic heat load. Slip rings, which further reduce the overall performance and reliability of the system, are also required. In this paper we assess the viability of the HTS dynamo and the rectifier flux pumps for energizing the field coils of the EcoSwing 3.6 MW HTS wind generator. Both a “warm” solution, with the rectifier at room temperature, and a “cold” solution, in which the latter is integrated into the cryostat, are investigated with regard to the rectifier flux pump. A comparison with the actual, state-of-the-art, system of the EcoSwing machine is carried out in terms of the total required cooling power and the ability to charge the HTS field winding up to the rated current. It is found that the dynamo flux pump, beside avoiding the need of slip rings, allows the reduction in the required cooling by about 74% with respect to the conventional current-leads-based solution.

A Warm Approach to Reduce Hypothermia in Preterm Neonates in a Resource-Limited Setting

Hypothermia at birth can lead to significant morbidity and mortality in neonates. Due to greater evaporative, convective, conductive, and radiation heat losses and diminished physiological response to cold stress, preterm newborns are at higher risk for hypothermia. This poster presentation supports the mission of Association of Women’s Health, Obstetric and Neonatal Nurses by providing education on how ambient temperature affects preterm neonates at or less than 36-weeks’ gestation.

Conductive heat loss of sows in a ventilated environment identified by steady CFD-CHT modelling considering thermophysiological effects

Quantifying the conductive heat loss of sows is important in establishing the heat balance equation of sows to evaluate the heat stress because sows spend a significant amount of time lying on the floor. However, previous studies did not offer explicate relationships between the floor heat transfer coefficient (FHTC) and the potential influential factors, making it difficult to estimate the conductive heat loss from sows in commercial productions. This study employed steady-state CFD-CHT simulations to investigate the conductive heat transfer from sows to three typical types of floor system in sow houses, considering the sizes of sows, contact ratios, air distribution strategies, and ambient temperatures. A co-simulation approach was proposed in order to involve the thermoregulation effect of sows under different ambient thermal conditions. The results indicated that the FHTC increased with the air movements and contact ratios, and decreased with the sizes of sows. The proportion of the conductive heat loss decreased with increased ambient temperature and contact ratio. The energy partition suggested that the conductive heat loss accounted for 6–19% of the total heat loss from sows at 20 °C ambient temperature and reduced to 5%-11% at 30 °C ambient temperature. The established relationships between the FHTC and convective heat transfer coefficient, and between the FHTC and interface temperature enabled the calculation of conductive heat loss from sows under various circumstances.

Synchronously managed water and heat transportation for highly efficient interfacial solar desalination

Interfacial photothermal water evaporation technology has shown great potentials in the fields of water resource exploitation and solar energy utilization. The trade-off between rapid evaporation and salt accumulation has been continuously explored in recent years. Herein, a two-stage evaporator (TSE) that synchronously manages the water and heat transportation is introduced. The TSE is designed to improve the evaporation rate by harvesting the dissipated heat including the radiative and convective heat losses on the surface of the solar absorber together with the conductive heat loss to the insulator. The surface temperature of the upper solar absorber is lower than that of a conventional single-stage evaporator (SSE) with a thermal insulator because energy from the upper evaporation surface is partially transferred to the secondary evaporation surface. Importantly, the typical TSE configuration improves the evaporation rate of the traditional SSE from 1.39 to 1.57 kg m−2 h−1, which excludes the contribution of the ambient energy-assisted heating to evaporation. Importantly, by introducing a unilateral water supply channel, the TSE maintains a high evaporation flux of 1.48 kg m−2 h−1 in saline water with a concentration of up to 20% (w/w). The synchronous scheme of water and heat management provides an effective way to overcome the contradiction between rapid evaporation and salt accumulation.

All-Day Freshwater Harvesting by Selective Solar Absorption and Radiative Cooling.

Solar interfacial evaporation for freshwater harvesting has received attention recently due to its high evaporation rate and environmental friendliness. Traditional interfacial evaporation mostly uses black porous polymers to absorb solar radiation and transport water which involve high thermal radiation loss to the environment and heat conduction loss to the bulk water. In addition, the freshwater collection ratio is usually lower than the solar evaporation ratio due to the high temperature of the condensation surface under solar irradiation, and no freshwater can be harvested at night due to the absence of sunlight. Here, we design an all-day freshwater-harvesting device using a solar-selective absorber (SSA) and sky radiative cooling. The prepared SSA with a high solar absorptance of 0.92 and a mid-infrared thermal emittance of 0.11 provides a great solar-thermal conversion performance (87.1% vs 51.4% for the black porous polymer at 25 °C) by minimizing the thermal radiation loss, and a hollow structure is also used to reduce the conductive heat loss, resulting in a high solar evaporation rate (1.23 vs 0.79 kg m-2 h-1 for the black porous polymer). In addition, a transparent radiative cooling polymer after plasma treatment is used for freshwater collection by enhancing the solar transmittance (0.92) and mid-infrared thermal emittance (0.91 at 25 °C). A theoretical freshwater collection rate of 0.044 kg m-2 h-1 is achieved at night-time. Outdoor results show that the all-day water harvesting is 0.87 kg m-2. This strategy to achieve all-day water collection by coupling with the SSA and transparent radiative cooling has potential application in the field of desalination and freshwater harvesting in tropical desert areas.

A Comprehensive Study on Flame Length under Oxygen Enhanced Laminar Non-premixed Combustion

ABSTRACT The study of stoichiometric flame lengths of laminar jet or co-flow diffusion flames has been a major topic of research in last few decades, mostly focusing on flames of either undiluted or slightly diluted fuel reacting with air. However, the flame characteristics under extremely diluted fuel conditions are not well studied. Hence, a set of experiments and numerical simulations have been performed in the present work to study the flame lengths for a wide range of fuel and oxidizer dilutions using two different jet diameter burners (4 and 9 mm with identical volume flow rates). Both experimental and numerical results confirm that the 4 mm burner flame length is consistently higher than the 9 mm burner counterpart. This difference is attributed to the higher temperature of the 9 mm burner flame, which in turn is due to its lower conductive heat loss to the ambient. Several analytical models, available in the literature to predict the flame lengths, such as Roper, Li-Gordon-Williams (LGW), and Wang-Sunderland-Axelbaum (WSA), have also been analyzed and compared with the experimental data. A new analytical model is also proposed in this study by modifying the species diffusivity and flame temperature in WSA model. This revised model predicts the flame lengths better than the other analytical models, especially when the fuel stream is diluted.

Harvesting conductive heat loss of interfacial solar evaporator for thermoelectric power generation

• The conductive heat loss of an interfacial photothermal evaporator is harvested. • The evaporation rate is up to 4.51 kg m -2 h −1 with excellent salt-resistance. • The device obtains a considerable power density of 1.2 W m −2 at 4 suns. • The output current becomes stable within 2 min if the light intensity is changed. The solar-driven interfacial water evaporation technique enables to sustainably produce potable water from sewage, wastewater, and seawater. Limited by the advanced functional materials and structures, however, the contradiction between high evaporation rate and low heat loss needs to be further optimized in terms of improving energy efficiency. Herein, a two-dimensional solar absorber in which the vertical substrate pumps water to the top surface for sustainable evaporation and reducing heat conduction channels between the evaporation surface and the bulk water is introduced. In addition, the surplus heat of the solar absorber is directly and quickly conducted to a thermoelectric device for electricity generation. This configuration endows the hybrid device with a power density of 1.2 W m −2 at an external resistance of 4 Ω together with an evaporation rate of 4.51 kg m −2 h −1 at 4 suns illumination. Importantly, both the fast response of the hybrid device to the optical concentration and the repeatability of the output current are well supported. Such a hybrid device provides an opportunity to construct an on-site and/or off-network water treatment system with low energy consumption and trade investment.

A Nanoscale Hot-Wire Flow Sensor Based on CMOS-MEMS Technology

In this paper, we proposed an ultrafast and nanoscale hot-wire flow (NHF) sensor implemented in a 0.18 µm complementary metal-oxide-semiconductor microelectromechanical system (CMOS-MEMS) technology. The nanoscale wire was released and reduced in thickness and width by an in-house developed post-CMOS fabrication process, hence the heat conduction loss is greatly suppressed, while the response time of the NHF sensor is significantly improved. Benefiting from the nano size of the hot-wire (a width of 622 nm), the NHF sensor exhibits an ultrafast response time of 30 µs (@ airflow velocity of 0 m/s), a wide flow range of 0–30 m/s, and a cut-off frequency of 21 kHz under the constant temperature (CT) mode. In addition, an equivalent circuit model (ECM) was established in PSPICE to predict the NHF sensor performance, and the theoretical simulation results were in good agreement with the experiment results.