Heat Flux Sensors Research Articles

Development and Performance Analysis of an Atomic Layer Thermopile Sensor for Composite Heat Flux Testing in an Explosive Environment

Traditional contact heat flux sensors suffer from a lack of dynamic performance, and existing non-contact optical heat measurement equipment fails to detect convective heat transfer effectively. This limitation precludes the effective testing of composite heat flux in explosive fields. This study introduces an ultra-responsive atomic layer thermopile (ALTP) heat flux sensor, developed and employed for the first time, to evaluate the transient heat flux associated with thermobaric explosions. Measurements reveal that the ALTP sensor’s temporal resolution surpasses that of the thermal resistance thin film heat flux sensor (TFHF), attaining a spectral response time of 10 μs under pulsed laser irradiation. Beyond these radiation-based tests, the present work also conducted novel simulation analyses of high-temperature jet impacts using COMSOL software. Static simulation discovered that fluid velocity significantly influences ALTP’s sensitivity, resulting in an error of 71%. Conversely, dynamic simulation demonstrated that an increase in fluid velocity reduces the ALTP’s time constant, whereas other factors such as fluid temperature exert minimal impact on its dynamic characteristics. This confirms that the simulation model compensates for the cost and accuracy deficiencies of convection heating tests. It also provides a new way to analyze the error of explosive heat flux measurement caused by sensitivity fluctuation and insufficient dynamic performance. In thermobaric explosive trials, the maximum heat fluxes recorded were 202 kW/m2 in semi-enclosed environments and 526 kW/m2 in open environments. A distinctive double-wave phenomenon was evident in the test curve. By a fast-response thermocouple, the study was able to differentiate between radiation and convective heat flux in the explosion field. The findings substantiate that the ALTP sensor amalgamates the benefits of optical thermal measurement tools with those of traditional contact heat flux sensors, thereby facilitating composite heat flux measurements in the challenging conditions of an explosive field.

Lyophilization cycle design for highly concentrated protein formulations supported by micro freeze-dryer and heat flux sensor

High-concentration protein formulations (HCPFs) represent a common strategy and freeze-drying can mitigate the stability challenges of HCPFs. In general, an in-depth characterization of the lyophilization process is essential to not impair the product quality by inappropriate process parameters. The aim of this study was to create a primary drying design space for lyophilized HCPFs by utilizing the heat flux sensor (HFS) integrated in a MicroFD with a minimum number of cycles and product vials. All the necessary data to obtain the design space were determined starting from only two lyophilization cycles, each holding 19 vials. The vial heat transfer coefficient (Kv) was determined by the HFS and compared to gravimetric values. The results indicate a consistant offset between the HFS and the gravimetry based values for annealed samples with higher protein content. This work highlights a possibility of integrating new technologies, the HFS and the MicroFD to generate a design space for lyophilization of HCPFs, which enables to implement a QbD approach at minimal material and time investment.

Numerical Simulation of Unsteady Turbulent Flow and Heat Transfer of Dynamic Thermal Flow Sensor

Improving energy efficiency in the building’s design is a priority area. To avoid unnecessary energy consumption, electronic control (intelligent) systems can be used to measure and monitor heat exchange between building walls and the surrounding environment, as (Calorimetric Sensor, Heat Flux Sensor ...). They are ideally suited for research in rationalizing and improving thermal efficiency. The aim of this study was a computational fluid dynamics investigation of unsteady turbulent flow and heat transfer of dynamic heat flux sensor for quantitative description of the heat transfer between the building's walls and the surrounding environment.Using CFD software, we numerically simulated the wind tunnel where the sensor was installed; we used six different air speeds (Vinlet=2m/s to 12m/s) in the inlet. To improve the standard features of the CFD code, the User-Defined Function (UDF) was written in the C language program and integrated into the solver of ANSYS Fluent, in order to determine the thermal flow file applied to the surface of the sensor. Heat transfer coefficient (h0) values are obtained according to each speed. The results obtained were compared to results in previous experimental and theoretical literature. There is a good compatibility of all results that allows dependence on numerical simulations in the future as a way of stewardship when studying energy rationalization.

Roll-to-Roll Printing of Anomalous Nernst Thermopile for Direct Sensing of Perpendicular Heat Flux.

The anomalous Nernst effect (ANE) converts heat flux perpendicular to the plane into electricity, in sharp contrast with the Seebeck effect (SE), enabling mass production, large area, and flexibility of their devices through ordinary thin-film fabrication techniques. Heat flux sensors, one of the most promising applications of ANE, are powerful devices for evaluating heat flow and could lead to energy savings through efficient thermal management. In reality, however, SE caused by the in-plane heat flux is always superimposed on the measurement signal, making it difficult to evaluate the perpendicular heat flux. Here we fabricate ANE-type heat flux sensors that selectively detect the perpendicular heat flux by adjusting the net Seebeck coefficient in their thermopile circuit with mass-producible Roll-to-Roll sputtering methods. The direct sensing of perpendicular heat flux using ANE-based flexible thermopiles, as well as their simple fabrication process, paves the way for the practical application of thin-film thermoelectric devices. This article is protected by copyright. All rights reserved.

Simple experimental method to determine the specific heat capacity of cylindrical Lithium-Ion-Battery cells

This study presents a new method for determining the specific heat capacity of cylindrical Lithium-Ion-Battery (LIB) cells. In comparison to other available methods, the developed procedure is simple, cost-efficient, non-destructive and reliable. The experimental setup only requires a standard LIB power characterization setup and one additional heat flux sensor (HFS). The HFS is wrapped around the studied sample and the sample is suspended in the middle of a climate chamber. The specific heat capacity can be determined by increasing the climate chamber temperature by ΔT=5K while continually measuring the temperature and heat flux. The method has been validated with an Al7075 cylindrical sample, showing deviations in the specific heat capacity compared to the results with a differential scanning calorimeter (DSC) of 0.35%. Further validation of the developed method has been achieved for a nickel manganese cobalt (NMC) cell, having a mean error of −0.37% compared to the mass-weighted-average method. Additionally, the method has been used to determine the specific heat capacity of a nickel cobalt aluminum (NCA) and lithium iron phosphate (LFP) LIB cell. While the dependency of the specific heat capacity on the State of Charge (SOC) seems to be neglectable (maximum deviation 2.29% in a LFP-cell), the temperature dependency (maximum 0.23%K−1 for NCA/NMC-cell) should be considered for the thermal modeling of LIBs.

Structural Design of Dual-Type Thin-Film Thermopiles and Their Heat Flow Sensitivity Performance.

Aiming at the shortcomings of the traditional engineering experience in designing thin-film heat flow meters, such as low precision and long iteration time, the finite element analysis model of thin-film heat flow meters is established based on finite element simulation methods, and a double-type thin-film heat flow sensor based on a copper/concentrate thermopile is made. The influence of the position of the thermal resistance layer, heat flux density and thickness of the thermal resistance layer on the temperature gradient of the hot and cold ends of the heat flow sensor were comprehensively analyzed by using a simulation method. When the applied heat flux density is 50 kW/m2 and the thermal resistance layer is located above and below the thermopile, respectively, the temperature difference between the hot junction and the cold junction is basically the same, but comparing the two, the thermal resistance layer located above is more suitable for rapid measurements of heat flux at high temperatures. In addition, the temperature difference between the hot and cold contacts of the thin-film heat flux sensor increases linearly with the thickness of the thermal resistance layer. Finally, we experimentally tested the response-recovery characteristics of the sensors, with a noise of 2.1 μV and a maximum voltage output of 15 μV in a room temperature environment, respectively, with a response time of about 2 s and a recovery time of about 3 s. Therefore, the device we designed has the characteristic of double-sided use, which can greatly expand the scope of use and service life of the device and promote the development of a new type of heat flow meter, which will provide a new method for the measurement of heat flow density in the complex environment on the surface of the aero-engine.

Fabrication of High-Temperature Polymer- Derived Ceramic Thin-Film Heat Flux Sensor by 3-D Printing and Laser Pyrolysis

Heat flux density is an important parameter for evaluating the high-temperature performance of turbine blades. Accurate heat flux density data play a significant role in the design and manufacture of turbine blades and their heat-dissipation performance. Current studies have shown that thin-film heat flux sensors (TFHFSs) are suitable for signal monitoring of complex turbine blade surfaces. However, TFHFSs have a multi-layer structure, which is difficult to achieve using traditional physical vapor deposition (PVD). In this paper, we propose an approach to fabricating high-temperature polymer-derived ceramic (PDC) TFHFSs using 3D printing and laser pyrolysis. Through direct ink writing (DIW), sensitive, antioxidant, and thermal resistance layers were written directly on an alumina substrate. The sensitive layer was rendered electrically conductive owing to laser-induced graphitization. Thus, the structure of multi-layer TFHFS can be quickly achieved using the proposed method. The results showed that the sensor can operate at 800 °C. Its sensitivity was 1.349 mV/(kW/m²). Thus, it is feasible to prepare thin-film heat flux sensors by 3D printing and laser pyrolysis, which provides a new in situ integrated manufacturing method for fabricating heat flux sensors suitable for working in harsh environments such as aviation.

Convergence criteria analysis for thermal conductance measurements of building walls: A case study

The significance of on-site measurements for the thermal characterization of building components is widely recognized. Walls thermal performance can be identified through the widely used Heat-Flow Meter (HFM) method, which has been frequently applied in literature. However, only a few scientific works have examined the convergence criteria suggested by the ISO 9869–1. Starting from this, the aim of this work is evaluating the convergence criteria in a case study using the progressive average method. Thermal conductance (C-value) measurements were carried out in a small-scale building, placed in the external area of a building school site near Rome (Italy). The building is internally equipped with an electric heating system. Heat-flux sensor and surface temperature probes were applied to assess the C-value of the envelope. The different switching-on of the heater characterized by different power levels and the reaching of regular thermal conditions after initial transients were considered to evaluate the acquired data and their influence on the results. The known walls stratigraphy allowed to compute and compare theoretical and experimental C-values. Based on the examined data, it is possible to assert that the convergence conditions are very strict, mainly due to the third criterion.

Full thermoelectric characterization of a single molecule

Molecules are predicted to be chemically tunable towards high thermoelectric efficiencies and they could outperform existing materials in the field of energy conversion. However, their capabilities at the more technologically relevant temperature of 300 K are yet to be demonstrated. A possible reason could be the lack of a comprehensive technique able to measure the thermal and (thermo)electrical properties, including the role of phonon conduction. Here, by combining the break junction technique with a suspended heat-flux sensor, we measured the total thermal and electrical conductance of a single molecule, at room temperature, together with its Seebeck coefficient. We used this method to extract the figure of merit zT of a tailor-made oligo(phenyleneethynylene)-9,10-anthracenyl molecule with dihydrobenzo[b]thiophene anchoring groups (DHBT-OPE3-An), bridged between gold electrodes. The result is in excellent agreement with predictions from density functional theory and molecular dynamics. This work represents the first measurement, within the same setup, of experimental zT of a single molecule at room temperature and opens new opportunities for the screening of several possible molecules in the light of future thermoelectric applications. The protocol is verified using SAc-OPE3, for which individual measurements for its transport properties exist in the literature.

Effect of thin-film sensors on local heat transfer in convective heat flux measurement

Thin-film heat flux sensors are usually attached to the interesting surface for the measurement of wall heat flux in the aerospace industry. However, the presence of the surface-mounted sensors may disturb the velocity and thermal boundary layer, alert the local wall heat flux, and induce erroneous measured results. This study numerically investigates the effect of the presence of thin-film heat flux sensors on the local flow and heat transfer. The effects of both Reynold number of the flow and the geometry of the sensor are investigated. The results show that the local convective heat transfer can be remarkably enhanced by the presence of the sensor. In particular, when the height of the thin-film heat flux sensor is within 2% of the flow boundary layer, the enhancement of the convection heat transfer caused by the heat flux sensor is independent with the inlet velocity of the flow. Finally, an empirical model for estimating the influence of the sensor on the heat transfer is established based on the numerical findings, which can provide a useful tool for practical design to evaluate and minimize the effect of the sensor on the local convective heat transfer.

Experimental study on wall heat transfer from diesel spray flame in two-dimensional combustion chamber operated with rapid compression and expansion machine (RCEM)

Heat transfer phenomenon in internal combustion diesel engine is one of problems to be solved. This study was conducted to investigate the relationship between diesel spray impingement, combustion processes, and heat loss using a rapid compression and expansion machine (RCEM). Furthermore, spray combustion and heat transfer processes were investigated using multiple injection strategies with a 6-holes injector. The amounts of diesel fuel used in the pilot, pre-injection, and main injection sprays were 3.964, 0.747, and 11.205 mg, respectively. Variations in common rail pressure conditions (30, 120, and 180 MPa) were applied to properly investigate spray evaporation, air–fuel mixture formation, and heat transfer in the combustion chamber. In addition, a local wall heat flux sensor was installed in the cylinder (head and liner) and piston cavity (upper lip, lip, and bottom) to measure the heat flux distribution, and a diffused backlight illumination method was used to visualize the spray and flame behavior in the combustion chamber and 2D piston cavity. The results showed that the impingement flame surrounding the cylinder head contributed to the highest magnitude and longest duration of the heat flux on the cylinder side owing to the spray flame velocity, impingement, and residence time. Meanwhile, the highest different temperature at cavity bottom induced more heat flux on the cavity side than that on the squish side. In addition, the higher injection pressure increased the spray momentum and spray tip penetration which led to a better air–fuel mixture, better evaporation rate, and less flame residence that contributed to reduce the accumulated heat loss in combustion chamber. Furthermore, a low common rail pressure was found to induce a greater difference in the accumulated heat flux ratio than a high common rail pressure which is owing to longer flame residence time in the combustion chamber. They were approximately 14% and 6% greater than that compared to the baseline common rail pressure which mean that a high common rail pressure contributes for the improving thermal efficiency in spray combustion.

Design, Preparation, and Performance Study of a Miniaturized High-Temperature Thick-Film Heat Flux Sensor

Solving heat transfer problems in high-temperature and temperature-changing environments is critical in a variety of applications, including modern turbines, aerospace, and nuclear power plants. However, most current thin-film-type heat flow sensors operate at approximately 1000 °C. Thus, we fabricated a kind of platinum–platinum/rhodium thick-film thermopile-type heat flux sensor which can work stably at 1200 °C based on an alumina ceramic substrate. The entire electrode layer was prepared by screen printing process. The surface morphology of the Pt electrode and the material in thermal resistance layer at different stages were investigated using scanning electron microscopy. The steady-state characteristics of the sensor were evaluated by using a high-temperature test platform. The experiments show that the peak voltage of the sensor is 1.4126 mV at the temperature of 1200 °C and the heat flow density of 283.3 kW/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Moreover, the repeatability of sensor at 1200 °C and high temperature holding for 4 h experiments were performed, verifying that the sensor has good consistency and durability. Therefore, we infer that the designed sensor can be applied for a long time under high temperature and large heat flow conditions, such as aerospace, mechanical metallurgy and energy construction fields.

Experimental Investigation of Heat Transfer in a Flat-wall Impinging Diesel Spray Flame under Diesel-like Conditions

The heat loss through the walls of Internal Combustion Engines (ICEs) needs to be minimized and improved since it has a detrimental impact on the overall thermal efficiency of the engine. This study focuses on investigating heat transfer in a flat-wall impinging diesel spray flame, simulating diesel conditions, to optimize engine parameters. The effects of factors such as various injection pressures, nozzle hole diameters, impingement distances, and oxygen concentrations are analysed in combined and individually. Experimental techniques, such as high-speed imaging, heat flux sensors, and thermocouples, are used to visualize spray flame, measure heat flux profiles and temperature distributions, respectively. Preliminary results and their implications on heat transfer and heat loss are discussed. Regarding the parametric studies investigating the effect on wall heat loss under conditions similar to those of a small diesel engine, it was observed that the transferred heat on the wall was significant in certain conditions. These results emphasize the effectiveness of manipulating the injection rate profile as a viable step to suppress the heat transfer through the wall.

Design and performance evaluation of a novel thin-film heat flux sensor

Thin-film heat flux sensor is suitable for the harsh environment in aerospace application. To further improve the accuracy of testing and to realize the measurement in two directions, this work proposes a new design of the thin-film heat flux sensor. Based on the numerical simulation method, this work investigates the influence of geometric parameters, physical property and working conditions on the sensor test error, and analyzes the testing performances under steady and transient states. Results indicate that the sensor test error is mainly related to the thermal resistance ratio of the sensor in the measurement system. The accuracy of the thin-film heat flux sensor increases with the increase of sensor size or local total thermal resistance. Besides, the newly designed sensor has satisfying steady and transient characteristics, including the small time constant, fast response, and good linear relationship between the measured temperature difference and the surface heat flux.

Enabling direct microcalorimetric measurement of metabolic activity and exothermic reactions onto microfluidic platforms via heat flux sensor integration

All biological processes use or produce heat. Traditional microcalorimeters have been utilized to study the metabolic heat output of living organisms and heat production of exothermic chemical processes. Current advances in microfabrication have made possible the miniaturization of commercial microcalorimeters, resulting in a few studies on the metabolic activity of cells at the microscale in microfluidic chips. Here we present a new, versatile, and robust microcalorimetric differential design based on the integration of heat flux sensors on top of microfluidic channels. We show the design, modeling, calibration, and experimental verification of this system by utilizing Escherichia coli growth and the exothermic base catalyzed hydrolysis of methyl paraben as use cases. The system consists of a Polydimethylsiloxane based flow-through microfluidic chip with two 46 µl chambers and two integrated heat flux sensors. The differential compensation of thermal power measurements allows for the measurement of bacterial growth with a limit of detection of 1707 W/m3, corresponding to 0.021OD (2 ∙ 107 bacteria). We also extracted the thermal power of a single Escherichia coli of between 1.3 and 4.5 pW, comparable to values measured by industrial microcalorimeters. Our system opens the possibility for expanding already existing microfluidic systems, such as drug testing lab-on-chip platforms, with measurements of metabolic changes of cell populations in form of heat output, without modifying the analyte and minimal interference with the microfluidic channel itself.

Correlation between heat transfer and flow in an internal combustion engine evaluated with a MEMS sensor

Understanding heat transfer is important for developing high-performance internal combustion engines, but heat transfer mechanisms have not yet been elucidated. The objective of this study is to clarify the correlation between flow and heat transfer in an engine. Local instantaneous heat flux and advection speed adjacent to a wall were measured using a resistance-type three-point heat flux sensor to achieve this purpose. Furthermore, local instantaneous Nusselt and Reynolds numbers were calculated based on the measured heat flux and the advection speed using two characteristic lengths: (1) bore diameter and (2) penetration depth. Consequently, it was found that the ensemble-averaged Nusselt numbers varied exponentially as a function of the ensemble-averaged Reynolds numbers in both models, and good correlation equations could be derived. The penetration-depth model reproduced the experimental values more precisely. On the other hand, the Reynolds number index of the bore-diameter model corresponds with the heat transfer on the rear wall of a cylinder installed in a flow. This suggests an analogy between the engine and rear wall of a cylinder. Additionally, the impacts of each heat transfer factor were evaluated. As a result, it was found that a dominant factor until the heat flux peak is the temperature difference between the gas and wall. However, its effect becomes small after the heat flux peak, and it was found that the density and advection speed mainly affect the heat flux decrease.

The Thermal Conductivity and Matric Potential (Moisture Tension) Relationships for Soils of Different Gypsum Content

The soil samples have been taken from a soil profile at the Research Station of College of Agriculture in the University of Tikrit at a longitude of 430 38- 23= in the east and at a latitude of 340 48- 40= in the north. The samples were taken from the surface horizon with a gypsum content of 62 g.kg-1 (G1) and also from the subsurface horizon of 443g.kg-1 (G7) gypsum content. Different gypsum content samples were prepared as G2, G3, G4, G5, and G6 that have Gypsum contents of 106, 153, 202, 245, and 337 g.kg-1 respectively. These samples were prepared by mixing the surface soil samples with the soil of gypsic horizon. The prepared soil samples were wetted by water spraying to two thirds the field capacity levels (0.25 kg.kg-1). Then they incubated for two months in order to make soils homogeneity in addition to moisture distribution in soil. The plastic rings of 10.4 cm diameter and 10 cm heights were drilled from the middle to fix the sensor of heat flux of thermometer plug. The size and height of the soil to be placed in the plastic ring was calculated based on the area A and height h of ring and then the mass of the soil (m) was calculated based on the value of the bulk density. The samples were oven dried at 70° degree until the weight of samples were fixed to obtain the completely dry soils. The amount of water to be added per sample was calculated based on the moisture characteristics curve and by the tensions specified in this study (0.1, 5, 15, 33 and 100) kPa. The moisture was converted to a depth of water and then soil samples were wetted in a light spraying manner with continuous flipping and the thermometer sensors were fixed up and down the heat flux sensor and then six readings per replication were recorded. The time from one reading to another was 60 seconds and their rate was extracted. Based on the results of the experiment, it can be concluded that by the fixation of moisture tension, the thermal conductivity values of the soil decreased with the increased soil content of gypsum, as the G3 treatment with gypsum content 15% gave the highest significant value while the least significant average value of thermal conductivity values at the G7 treatment with gypsum content was 43%. The increase in gypsum from 25% at G5 to 30% and 44% in G6 and G7 successive treatments did not significantly affect the values of the soil’s thermal conductivity averages. The overlap point of the relationship between soil gypsum content and thermal conductivity was found at G3 and G4 that have gypsum content of 15% and 25% respectively. The average of gypsum decreases the thermal conductivity values of the soil with increased moisture tension values, as the tension gave 0.1 kPa a significant increase in the values of the average thermal conductivity from the rest of the tensions and for all treatments while the least significant average of thermal conductivity values at tension was 100 kPa.

Comparison of vial heat transfer coefficients during the primary and secondary drying stages of freeze-drying

This study uses a heat flux sensor and temperature probes to directly measure vial heat transfer coefficients (Kv) during primary and secondary drying stages of lyophilization. It is observed that Kv is 40–80% smaller during secondary drying than primary drying, and this value exhibits a weaker dependence on chamber pressure than in primary drying. These observations arise because water vapor in the chamber significantly decreases between primary and secondary drying, which alters the gas conductivity between the shelf and vial. This study tabulates Kv values for secondary drying for different vials and different chamber pressures, and demarcates the contributions from gas conduction. Lastly, the study performs an energy budget analysis on two different vials (10R glass vial and 10 mL plastic vial) to determine the major factors that contribute to vial energy consumption. During primary drying, the majority of energy supplied goes towards sublimation, while for secondary drying, the majority of energy goes towards heating the vial wall rather than desorbing bound water. We discuss the consequences of this behavior for heat transfer modeling. During secondary drying, the heat of desorption can be neglected in thermal modeling for some materials (e.g., glass) but not others (e.g., plastic vials).

Assessing the Performance of Building Mechanical Systems in an Office Building

The purpose of this research is to evaluate the performance of building mechanical systems in an office. The mechanical systems include eleven variable air volume (VAV) units that provide outdoor air to the office spaces and induction units that provide heating and cooling to the office spaces. This study presents the data collection, sensor installation, and analyses of the ventilation, heating, and cooling provided to the spaces. Differential pressure transducers, temperature sensors, and heat flux sensors were installed on-site to monitor these systems at every one-minute and five-minute interval. The process of analyzing datasets from these sensors is automated and used to calculate ventilation, heating, and cooling under current building automation sequences of operation. The results of this study will aid our understanding of the impacts of different building mechanical systems, occupancy patters, time of the day on the ventilation, heating, and cooling use for the selected building.

Temperature dependent performance of Schmidt-Boelter heat flux sensors.

The total heat flux sensors for NASA's Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) sensor suite on the Mars 2020 vehicle and the Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) technology demonstration mission are passively cooled Schmidt-Boelter gauges. The output of these sensors has been experimentally demonstrated to be dependent on the temperature of the sensing element. The experimental results are shown to align with a model that assumes temperature-dependent material properties, specifically the Seebeck coefficient. The MEDLI2 and LOFTID flight total heat flux sensors did not undergo a full thermal calibration prior to being installed on the flight vehicles since the temperature dependence was unknown ahead of time. Additionally, the material properties are not known due to the designs being proprietary. For these reasons, an approximate correction factor was derived. The applicability and associated uncertainty of this temperature-dependent correction factor are presented. The error that would be introduced into the measurement if temperature effects were not accounted for would be as high as 9.5% and 16% for the MEDLI2 and LOFTID total heat flux sensors, respectively. As a best practice for future flight missions and ground-based applications that employ similar passively cooled heat flux sensors, it is recommended to individually calibrate each sensor across all applicable use temperatures to account for sensor-to-sensor variations and minimize measurement uncertainty.