Inferring convective and radiative heating loads from transient surface temperature measurements in the half-space

Frankel, J. I.; Arimilli, Rao V.

doi:10.1080/17415970600795378

Cited by 24 publications

(29 citation statements)

References 10 publications

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“…Diffusion naturally damps high frequency information. Thus, digital filtering should be advocated and implemented [17,[26][27][28] in order to remove the unnecessary highfrequency components in the signal that play havoc on numerical differentiation. Signal-to-noise issues should be considered when designing the digital filter.…”

Section: Fundamental Results From This Notementioning

confidence: 99%

“…Several novel manipulations are proposed in the formalism that extend to three-dimensional considerations. The one-dimensional formulation is presented in Refs 13,17,18,22. However, increasing the dimensionality to two-and threedimensional studies requires some inspired additional analytic manipulations and generalizations.…”

Section: Derivation Of Integral Relationship: Green's Function Methodmentioning

confidence: 99%

“…In one-dimensional analysis [13,14,17,18,22], the strategy involved Abel regularization owing to the structure of the integral relationship and the nature of the kernel (i.e., weak singularity, 1/ √ t − t 0 ). Regularization in such cases follow classical doctrine [9].…”

Section: Derivation Of Integral Relationship: Green's Function Methodmentioning

confidence: 99%

“…Equation (17) indicates that it is possible to obtain the heat flux in the x-direction, at fixed x = η, based on a line of temperature sensors dispersed in the y-direction. Visual inspection of Eq.…”

Section: Vol 59 (2008)mentioning

confidence: 99%

“…That is, the root-mean square error of the heat flux grows as the sample density increases. In the presence of white noise [17], this error grows as the square-root of the sample density, √ M , where M is the total number of data in the set. Numerical calculations for the heat flux are unstable to input perturbations in the temperature data and hence it is ill posed (with respect to temperature data).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

Frankel

Keyhani

Arimilli

et al. 2007

Z. angew. Math. Phys.

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This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries. The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition. A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship; (b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions; and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept.

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Section: Fundamental Results From This Notementioning

confidence: 99%

Section: Derivation Of Integral Relationship: Green's Function Methodmentioning

confidence: 99%

Section: Derivation Of Integral Relationship: Green's Function Methodmentioning

confidence: 99%

Section: Vol 59 (2008)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

Frankel

Keyhani

Arimilli

et al. 2007

Z. angew. Math. Phys.

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Theoretical development of a new surface heat flux calibration method for thin-film resistive temperature gauges and co-axial thermocouples

Frankel

Keyhani

2012

Shock Waves

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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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Inferring convective and radiative heating loads from transient surface temperature measurements in the half-space

Cited by 24 publications

References 10 publications

A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

Theoretical development of a new surface heat flux calibration method for thin-film resistive temperature gauges and co-axial thermocouples

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

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