What question did this study set out to answer?

To derive an exact analytical solution for inverse unsteady heat conduction problems where unknown surface conditions must be determined from internal boundary measurements.

August 1, 1964Journal of Heat Transfer

An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications

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Authors

OBO. R. BurggrafThe Ohio State University

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Implication

Theoretical study demonstrates an exact series solution for inverse unsteady heat conduction across various geometries, highlighting simple and accurate truncated approximations for thermal analysis.

Key Points

To derive an exact analytical solution for inverse unsteady heat conduction problems where unknown surface conditions must be determined from internal boundary measurements.
Formulated an exact series solution by specifying boundary conditions at a single internal location, utilizing the lumped capacitance approximation as the leading term.
Derived specific series forms for standard geometric configurations, including solid slabs, cylinders, spheres, and transpiration-cooled slabs.
Extended the series to direct problems with two-point boundary conditions and evaluated truncated one-term and two-term approximations against exact benchmarks.
Obtained a rapidly convergent series that yields exact solutions for inverse boundary condition determinations across slabs, cylinders, and spheres.
Demonstrated that truncated one-term and two-term approximations provide simple, highly accurate representations that agree closely with exact solutions.

Cite This Study

O. R. Burggraf (1964) studied this question.

synapsesocial.com/papers/6a916ce02d14ef2b6ea1628e https://doi.org/10.1115/1.3688700

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Implication

Theoretical study demonstrates an exact series solution for inverse unsteady heat conduction across various geometries, highlighting simple and accurate truncated approximations for thermal analysis.

An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications

Discussion

Member takes

Implication

Key Points

Cite This Study

An Exact Solution of the Inverse Problem in Heat Conduction Theory and Applications

Discussion

Member takes

Implication

Key Points

Cite This Study

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