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On Power Variation in Self-Heated Thermal Sensors
Abstract
Commercially available instrumentation is becoming increasingly fast and precise. This opens up possibilities to perform measurements of thermal transport properties using contact transient methods (CTM) with repeatability often less than one percent. At the same time it is not unusual to neglect non-ideal conditions in the experiments with an influence of approximately the same order of magnitude.
In this paper attention is focused on the non-ideal power variation, which normally is present when working with this kind of methods. The specific arrangement of the CTMs considered in this paper is that a resistive component is used both as a heat source and temperature sensor.
When solving the thermal conductivity equation the assumption is normally that the power delivered to the sample surface is strictly constant. This is rarely the case and the following conditions working against this assumption can be mentioned: a) the heat capacity of the sensor arrangement is not zero; b) there are electrical leads present which influence the temperature of the heat source; c) the temperature coefficient of resistivity of the sensor introduces a power variation due to the temperature increase of the sensor; d) the presence of a layer or coating between the sensing material and the surface of the sample with different thermal properties than those of the sample material.
The following ways to somewhat reduce these problems will be discussed: a) minimize the variation in the output of power from the sensor; b) incorporate the power variation in the analytical solution when this is possible; c) estimate the variation experimentally and compensate for its presence via numerical solutions of the thermal conductvitiy equation.
... The TPS method simplifies the actual model to obtain many ideal models [6][7][8], but the difference between the actual structure and the ideal model leads to measurement error, which is affected by the shape of the probe and the thermophysical properties of the sample. In order to approach the actual model, many scholars studied the various factors simplified in the ideal model to improve the solution accuracy [9][10][11][12]. ...
The transient plane source (TPS) method heat transfer model was established. A body-fitted coordinate system is proposed to transform the unstructured grid structure to improve the speed of solving the heat transfer direct problem of the winding probe. A parallel Bayesian optimization algorithm based on a multi-objective hybrid strategy (MHS) is proposed based on an inverse problem. The efficiency of the thermophysical properties inversion was improved. The results show that the meshing method of 30° is the best. The transformation of body-fitted mesh is related to the orthogonality and density of the mesh. Compared with parameter inversion the computational fluid dynamics (CFD) software, the absolute values of the relative deviations of different materials are less than 0.03%. The calculation speeds of the body-fitted grid program are more than 36% and 91% higher than those of the CFD and self-developed unstructured mesh programs, respectively. The application of body-fitted coordinate system effectively improves the calculation speed of the TPS method. The MHS is more competitive than other algorithms in parallel mode, both in terms of accuracy and speed. The accuracy of the inversion is less affected by the number of initial samples, time range, and parallel points. The number of parallel points increased from 2 to 6, reducing the computation time by 66.6%. Adding parallel points effectively accelerates the convergence of algorithms.
... To initiate and record the transient increase in the electrical resistance of the probe an electrical bridge has been introduced [1,21]. With the initially balanced bridge, the possibility opens to follow the resistance increases of the probe by recording the imbalance of the bridge with a sensitive voltmeter (Fig. 3) [22]. ...
This experimental method was first proposed in 1991 and is presently being used for determining thermal conductivity, thermal diffusivity, thermal effusivity, and volumetric heat capacity of solids. Under special and well-controlled conditions, it is possible to measure thermal conductivity over approximately six orders of magnitude at temperatures ranging from 25 K up to 1500 K. A feature of this method is the possibility to obtain both the thermal conductivity and thermal diffusivity from one single transient recording and in that way to open up convenient measurements of thermal transport of certain anisotropic materials. A further advantage of using a transient method relates to the possibility to eliminate the influence of the contact resistances always present between the heating element, functioning also as the temperature recorder, and the surface of the substrate under investigation. This review will touch upon the limitations of the method with an estimation of the measuring uncertainty together with a discussion on the influence of the difference between the experimental arrangement and the assumption made in the development of the analytical theory used for analyzing the experimentally recorded data. The method has turned out to be useful not only in measurements of the thermal transport but also for special quality control situations. It is used in both academic institutions and in industrial laboratories and has so far generated some 5000 scientific papers in international journals.
... Bohač et al. [31] improved the accuracy of the method by calculating the optimal time period for measurement using coefficient sensitivity analysis and difference analysis. In this research work [32], thermal contact A and time correction t c parameters were included which helped to describe the necessary period for the heating of the sensor. All these efforts led to the publication of an international standard for the TPS method in 2008 [33]. ...
This paper reports an experimental investigation focused on nano-enhanced phase change materials (NEPCM). Two different types of phase change materials (RT28 HC and RT26) with relatively low thermal conductivity and reasonable volumetric specific heat capacity were utilized as the base for NEPCMs with four types of nanoparticles (CuO, ZnO, Ag, and graphene). The novel four-phase preparation procedure was thoroughly presented together with a description of the measurement technology which was used for the examination of NEPCM thermal constants. The experimental results revealed that in most cases the thermal constants of samples were improved, such as thermal conductivity and volumetric specific heat capacity in a range of about 4% to 21% and 5% to 33%, respectively. In some cases, significant degradation of certain thermal constants was detected, such as in the case of the Graphene/RT26 nanocomposite. The possible nanomaterial selection strategies also discussed taking into account the economic aspects and experimental results related to the thermal constants. The results revealed that the selection of nanomaterials should be carefully considered with respect to the specific application since it is possible to manipulate the thermo-physical properties of the NEPCM as a unique combination of nanomaterial and PCM.
... In the context of TPS probe design, and electrical circuit used, in [8] is discussed a detailed analytical procedure which may be employed to account for power losses due to imperfect electronics (creating a non-constant output of electrical heating power), as well as power losses due to heat consumed for self-heating of the TPS sensor in an experiment, as well as compensating for heat losses through connecting electrical wires to the TPS sensor. ...
The present work presents some results and considerations for testing the specific heat of large-size samples (dimensions up to 250 mm x 250 mm in-plane, and 75 mm in thickness).
Recent interest on testing thermal transport properties of anisotropic composite structures, including highly-anisotropic stacked structures such as Li-Ion batteries, or weave structures with graphite- or nanotube fillers, may involve individual layer thicknesses of significant size. To estimate the effective, or total, heat capacity of such a structure may be rather challenging with a test method such as DSC – since it is difficult to prepare a small-volume sample which would represent the averaged heat capacity of the total structure.
An experimental method on utilizing Hot Disk sensors have earlier been presented, whereby a high-conducting metal cell containing the sample, of thickness within 5 mm, and maximum diameter of around 20 mm. Two experiments are carried out: One in which a constant heating power is heating this cell – when empty – and the cell is located within an insulated environment (to minimize heat losses from the cell). Another corresponding experiment is performed in which identical experimental conditions (possibly with a higher heating power) – but applied to a cell with an internal sample. Heat losses (from the cell to the surrounding insulation) can be approximately accounted for, allowing the estimation of the heat capacity of the sample inside the cell – by comparing these two experiments.
Some example applications are demonstrated and discussed, from testing of anisotropic rock samples, to a full-size Li-Ion battery used for automobiles.
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