Heating rate dT/dt measurements developed from in-situ thermocouples using a voltage-rate interface

Frankel, J. I.; Arimilli, Rao V.; Keyhani, M.; Jiang, Wu

doi:10.1016/j.icheatmasstransfer.2008.04.019

Cited by 15 publications

(18 citation statements)

References 7 publications

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“…It is well known that numerical differentiation of raw data is ill-posed [15][16][17], and this is especially noticeable as the sample size is increased for a fixed time span. Measurement of acceleration can be performed without differentiation and thus one postulates that sensors capable of measuring higher time derivatives [8] of temperature are thus conceivable and could impact aerospace heat transfer studies. …”

Section: Discussionmentioning

confidence: 99%

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Locating Sudden Changes in Heat Flux Using Higher Temporal Derivatives of Temperature

Frankel

Keyhani

Arimilli

et al. 2008

Journal of Spacecraft and Rockets

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= plate thickness, m C = heat capacity, kJ=kg C k = thermal conductivity, W=m C L = length of the plate, m N n = nth normalization integral, m n = dummy index in summation q 00= half-length of the plate, m y = dimensional space variable, m z = dimensional space variable, m = thermal diffusivity, m 2 =s x = x 1 =10, m y = w=4, m n = nth eigenvalue, m 1 x; y; t = dimensional temperature, C = density, kg=m 3 n x = nth eigenfunction associated with nth eigenvalue

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Section: Discussionmentioning

confidence: 99%

“…In particular, focus is directed to the spatial region near the jump discontinuity and the local behavior of the time derivatives of temperature. As noted by Frankel et al [1][2][3][4][5][6][7][8], various types of inverse problems can also benefit from the development of ratebased sensors.…”

Section: Locating Sudden Changes In Heat Fluxmentioning

confidence: 99%

Locating Sudden Changes in Heat Flux Using Higher Temporal Derivatives of Temperature

Frankel

Keyhani

Arimilli

et al. 2008

Journal of Spacecraft and Rockets

Self Cite

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“…Finally, the numerical methods used in this paper are intentionally chosen to be simple while the important feature is the proper filtering of the data or developing rate sensors. Additionally, Frankel et al [32] have developed a rate interface that is applicable to both temperature and heat flux for providing time derivative information. Frankel et al [32] have performed a series of thermocouple experiments for demonstrating this new technology (Table 2).…”

Section: Discussionmentioning

confidence: 99%

Regularization of inverse heat conduction by combination of rate sensor analysis and analytic continuation

Frankel

2006

J Eng Math

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This paper describes some recent observations associated with (1) clarifying and expanding upon the integral relationship between temperature and heat flux in a half-space; (2) offering an analyticcontinuation approach for estimating the surface temperature and heat flux in a one-dimensional geometry based on embedded measurements; and, (3) offering a novel digital filter that supports the use of analytic continuation based on a minimal number of embedded sensors. Key to future inverse analysis must be the proper understanding and generation of rate data associated with both the temperature and heat flux at the embedded location. For this paper, some results are presented that are theoretrically motivated but presently adapted to implement digital filtering. A pulsed surface heat flux is reconstructed by way of a single thermocouple sensor located at a well-defined embedded location in a half space. The proposed low-pass, Gaussian digital filter requires the specification of a cut-off frequency that is obtained by viewing the power spectra of the temperature signal as generated by the Discrete Fourier Transform (DFT). With this in hand, and through the use of an integral relationship between the local temperature and heat flux at the embedded location, the embedded heat flux can be accurately estimated. The time derivatives of the filtered temperature and heat flux are approximated by a simple finite-difference method to provide a sufficient number of terms required by the Taylor series for estimating (i.e., the projection) the surface temperature and heat flux. A numerical example demonstrates the accuracy of the proposed scheme. A series of appendices are offered that describe the mathematical details omitted in the body for ease of reading. These appendices contain important and subtle details germane to future studies.

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“…This additionally suggests that new rate-based (time rate of change) thermal sensors should be developed that are analogous to mechanical systems. Frankel et al [12] have designed, tested, and demonstrated a new sensor that accurately estimates up to two time derivatives of temperature. Finally, the so-called inverse heat conduction problem [13] could make use of this analysis whereby one-sided conditions will be obtained at the plane where the sensors are placed.…”

Section: Derivationmentioning

confidence: 99%

A new three-dimensional heat flux–temperature integral relationship for half-space transient diffusion

Frankel

Keyhani

Arimilli

2010

Journal of the Franklin Institute

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Heating rate dT/dt measurements developed from in-situ thermocouples using a voltage-rate interface

Cited by 15 publications

References 7 publications

Locating Sudden Changes in Heat Flux Using Higher Temporal Derivatives of Temperature

Locating Sudden Changes in Heat Flux Using Higher Temporal Derivatives of Temperature

Regularization of inverse heat conduction by combination of rate sensor analysis and analytic continuation

A new three-dimensional heat flux–temperature integral relationship for half-space transient diffusion

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