The heated infinite cylinder with sheath and two thermal surface resistance layers

Macher, W.; Kömle, Norbert I.; Bentley, Mark S.; Kargl, Günter

doi:10.1016/j.ijheatmasstransfer.2012.10.070

Cited by 11 publications

(9 citation statements)

References 19 publications

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“…3). hese results demonstrated that the less early-time data were included in the itting process, the closer was the DT(t) curve to the PILS solution since the early-time data were afected more by the disturbance from inite probe geometry and the thermal contact resistance (Macher et al, 2013).…”

Section: Staisical Analysismentioning

confidence: 95%

“…Early work showed that for cylindrical probes, the effects of thermal contact resistance and deviations from the line heat source became less significant at longer heating times or under the conditions of large soil κ (de Vries and Peck, 1958). Macher et al (2013) evaluated the analytical model for the heated infinite cylinder probe, and showed that thermal contact resistance drastically affected the early‐time part of the temperature increase. Experimental evidence also suggested that the early‐time data were affected significantly by thermal contact resistance between the probe and soil, while late‐time data [in the decay period of the Δ T ( t ) curve] were believed to be more closely related to soil characteristics (Shiozawa and Campbell, 1990; Bristow et al, 1994b).…”

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confidence: 99%

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Using Late Time Data Improves the Heat‐Pulse Method for Estimating Soil Thermal Properties with the Pulsed Infinite Line Source Theory

Wang

Ren

2013

Vadose Zone Journal

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Soil‐probe contact resistance and finite radius and heat capacity of the heat pulse (HP) probe produce significant errors in thermal property estimates. In this study, we demonstrated that estimating soil thermal properties from late‐time data of the temperature change‐by‐time (ΔT(t)) curve reduces these errors effectively. The weighted nonlinear curve fitting method was applied to estimate soil thermal properties following the pulsed infinite line source (PILS) theory using ΔT(t) data from the complete (PILS‐Complete), peak‐time (PILS‐Peak), and late‐time (PILS‐Late) ranges. Three experiments on specific heat of soil solids (cs), soil thermal properties, and soil water content (θHP) were conducted to examine the performance of these approaches. The results showed that the PILS‐Complete and PILS‐Peak methods overestimated cs by 16.6% and 13.0% respectively, and the error from the PILS‐Late method reduced to 3.2%. Soil thermal conductivity measurements from the PILS‐Late method agreed well with those from the identical‐cylindrical‐perfect‐conductors theory and with the estimates from the heat flux plate data. The PILS‐Late method also effectively reduced the overestimation of soil heat capacity and underestimation of soil thermal diffusivity. In comparing to the PILS‐Complete method, the PILS‐Late method reduced the root mean square error (RMSE) of θHP from 0.039 to 0.021 m3 m−3 on a sand soil, and from 0.032 to 0.018 m3 m−3 on a clay loam soil. Thus, using late‐time data improved the accuracy of HP method for measuring soil thermal properties.

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Section: Staisical Analysismentioning

confidence: 95%

mentioning

confidence: 99%

Using Late Time Data Improves the Heat‐Pulse Method for Estimating Soil Thermal Properties with the Pulsed Infinite Line Source Theory

Wang

Ren

2013

Vadose Zone Journal

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“…Either a much more complicated formalism is used, applying the theory of "short and thick" sensors, or the same simple theory is used with an additional calibration function valid over the desired range of conductivities. The first method has been described in much detail in a recent paper by Hütter and Kömle (2012), in Hütter (2011) and most recently in Macher et al (2013). The second method is the topic of the current paper.…”

Section: Introductionmentioning

confidence: 99%

Calibration of non-ideal thermal conductivity sensors

Kömle

Macher

Kargl

et al. 2013

Geosci. Instrum. Method. Data Syst.

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Abstract.A popular method for measuring the thermal conductivity of solid materials is the transient hot needle method. It allows the thermal conductivity of a solid or granular material to be evaluated simply by combining a temperature measurement with a well-defined electrical current flowing through a resistance wire enclosed in a long and thin needle. Standard laboratory sensors that are typically used in laboratory work consist of very thin steel needles with a large length-to-diameter ratio. This type of needle is convenient since it is mathematically easy to derive the thermal conductivity of a soft granular material from a simple temperature measurement. However, such a geometry often results in a mechanically weak sensor, which can bend or fail when inserted into a material that is harder than expected. For deploying such a sensor on a planetary surface, with often unknown soil properties, it is necessary to construct more rugged sensors. These requirements can lead to a design which differs substantially from the ideal geometry, and additional care must be taken in the calibration and data analysis.In this paper we present the performance of a prototype thermal conductivity sensor designed for planetary missions. The thermal conductivity of a suite of solid and granular materials was measured both by a standard needle sensor and by several customized sensors with non-ideal geometry. We thus obtained a calibration curve for the non-ideal sensors. The theory describing the temperature response of a sensor with such unfavorable length-to-diameter ratio is complicated and highly nonlinear. However, our measurements reveal that over a wide range of thermal conductivities there is an almost linear relationship between the result obtained by the standard sensor and the result derived from the customized, non-ideal sensors. This allows for the measurement of thermal conductivity values for harder soils, which are not easily accessible when using standard needle sensors.

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“…(17) that a plot of T against ln t has a linear asymptote of slope Q l / (4π k), and so the thermal conductivity of the sample material k can be determined immediately if Q l is known. Furthermore, in Macher et al (2013) another interesting case for the development of thermal conductivity sensors is studied, which will not be discussed here. They considered temperature evolution in and around a heated infinite cylinder with a tubular sheath, assuming non-negligible surface resistances between core and sheath of the cylinder and between the sheath and the surrounding medium.…”

Section: Heat Source With Thermal Surface Resistance and Non-ideal Sementioning

confidence: 99%

“…Either one can use a much more complicated formalism, applying the theory of non-ideal (short and thick) sensors, or one can use the simple theory of ideal sensors with an additional calibration function. While the first method has been described in Hütter (2011), Hütter andKämle (2012) and Macher et al (2013), the second method is described in this section. The testing and calibration of the LNP03 sensor were already conducted by Kämle et al (2013) and is now verified by measurements in partly different sample materials and an adapted measurement set-up.…”

Section: Calibration Of the Lnp Sensorsmentioning

confidence: 99%

Influence of probe geometry on measurement results of non-ideal thermal conductivity sensors

Tiefenbacher

Kömle

Macher

et al. 2016

Geosci. Instrum. Method. Data Syst.

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Abstract. The thermal properties of the surface and subsurface layers of planets and planetary objects yield important information that allows us to better understand the thermal evolution of the body itself and its interactions with the environment. Various planetary bodies of our Solar System are covered by so-called regolith, a granular and porous material. On such planetary bodies the dominant heat transfer mechanism is heat conduction via IR radiation and contact points between particles. In this case the energy balance is mainly controlled by the effective thermal conductivity of the top surface layers, which can be directly measured by thermal conductivity probes. A traditionally used method for measuring the thermal conductivity of solid materials is the needleprobe method. Such probes consist of thin steel needles with an embedded heating wire and temperature sensors. For the evaluation of the thermal conductivity of a specific material the temperature change with time is determined by heating a resistance wire with a well-defined electrical current flowing through it and simultaneously measuring the temperature increase inside the probe over a certain time. For thin needle probes with a large length-to-diameter ratio it is mathematically easy to derive the thermal conductivity, while this is not so straightforward for more rugged probes with a larger diameter and thus a smaller length-to-diameter ratio. Due to the geometry of the standard thin needle probes they are mechanically weak and subject to bending when driven into a soil. Therefore, using them for planetary missions can be problematic.In this paper the thermal conductivity values determined by measurements with two non-ideal, ruggedized thermal conductivity sensors, which only differ in length, are compared to each other. Since the theory describing the temperature response of non-ideal sensors is highly complicated, those sensors were calibrated with an ideal reference sensor in various solid and granular materials. The calibration procedure and the results are described in this work.

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The heated infinite cylinder with sheath and two thermal surface resistance layers

Cited by 11 publications

References 19 publications

Using Late Time Data Improves the Heat‐Pulse Method for Estimating Soil Thermal Properties with the Pulsed Infinite Line Source Theory

Using Late Time Data Improves the Heat‐Pulse Method for Estimating Soil Thermal Properties with the Pulsed Infinite Line Source Theory

Calibration of non-ideal thermal conductivity sensors

Influence of probe geometry on measurement results of non-ideal thermal conductivity sensors

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